Novel Paradigms in Many-Body Physics from Open Quantum Systems

Recent experimental progress has made it possible to realize strongly interacting photons in Rydberg-polariton systems, while theoretical studies suggest that it is possible to tune interactions in these systems with Feshbach like resonances. These developments open up the possibility of exploring the many body physics of bosons close to the unitary limit in an out-of-equilibrium setting, as Rydberg-polariton systems are inherently lossy and driven. We employ Keldysh field theoretical techniques in order to investigate different possible Bose-Einstein condensed (BEC) phases in this type of systems. Our results indicate a possibility of observing an out-of-equilibrium discrete symmetry breaking phase transition between different BEC phases of the system.

We study here a dissipative quantum Ising chain in transverse field, where the field is varied linearly in time from a high value to zero at a certain speed $v$. This is a simple realization of the so-called quantum annealing, the protocol employed in adiabatic quantum computers such as the one built by the D-Wave company. Dissipation in our model is provided by interaction with a thermal bosonic bath with Ohmic spectrum, and the system dynamics is studied via a perturbative Bloch-Redfield master equation. We analyze the conditions under which one can find an optimal annealing velocity $v_{opt}$, which optimizes the annealing performance in presence of dissipation. We remarkably find that no optimal working point can be found in the range of temperatures relevant for current adiabatic quantum computers.

Neutral Atoms, which can have both bosonic and fermionic character, are well known for their extraordinary coherence properties which makes them ideal candidates for quantum information and simulation applications. Their interactions, however, are generally local which limits some of their applications, e.g., the simulation of long-range interacting models. Recent experimental avenues have provided several platforms where atom-like systems interact with structured (and low dimensional) photonic baths.The motivation is to exploit the characteristic of the structured baths to generate strong and longer range interactions. Here, we explore an anisotropic 2D bath with square geometry, that interpolates from 1D to 2D and gives rise to several non-trivial phenomena such as non-perturbative dynamics, perfect super/subradiance and tuneable spin interactions.

In a closely packed ensemble of quantum emitters, cooperative effects are typically suppressed due to the dephasing induced by the dipole-dipole interactions. Here, we show that by adding sufficiently strong collective dephasing cooperative effects can be restored. In particular, we show that the dipole force on a closely packed ensemble of strongly driven two-level quantum emitters, which collectively dephase, is enhanced in comparison to the dipole force on an independent non-interacting ensemble. Our results are relevant to solid state systems with embedded quantum emitters such as colour centers in diamond and superconducting qubits in microwave cavities and waveguides.

We present a novel method for computing the full spectrum and eigenmodes of a Liouvillian that is given by an integrable Hamiltonian and purely loss (or alternatively, gain) terms (modeled by Lindblad operators). The method is based on an extension of the standard Bethe ansatz and is quite versatile. We show how to use this method to compute the spectra of various open quantum models (e.g., an open lossy XXZ spin chain). In particular, we also discuss exotic many-body eigenmodes with purely oscillatory dynamics. These unconventional eigenmodes exist in open quantum systems fulfilling algebraic conditions that are particularly easy to verify for integrable Hamiltonians, and their presence shows that these open quantum systems never relax.

In this work we study the phenomenology that arises as photons leak in a ultracold system inside a high-Q cavity. The atoms are subject to confinement via an optical lattice (classical), while due to cavity back action there is a long-range light-induced interaction (quantum optical lattice). We study the competition between self-ordered many-body quantum phases due to the cavity back-action and the dynamics introduced by photon leakage.

By analyzing a paradigmatic example of the theory of dissipative systems—the classical and quantum dissipative standard map—we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kinds of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.

The Born-Markov approximation is widely used to study dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to non-interacting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has non-analyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power law tails. The Green's functions show a short time ``quasi'' Markovian exponential decay before crossing over to a power law tail governed by the non-analyticity of the spectral function. We study a system of bosons (fermions) hopping on a one dimensional lattice, where each site is coupled linearly to an independent bath of non-interacting bosons (fermions). We obtain exact expressions for the Green's functions of this system which show power law decay ~ |t-t'|^{-3/2}. We use these to calculate density and current profile, as well as unequal time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long time power law tails |t-t'|^{-3} characteristic of non-Markovian dynamics. We show that the power law decays survive in presence of inter-particle interaction in the system, but the cross-over time scale is shifted to larger values with increasing interaction strength.

Thermoelectricity describes the phenomenon by which a temperature gradient drives transport of energy and particles and vice versa. It is of great technological importance for cooling materials (Peltier effect) or power generation (Seebeck effect), but it is also a fundamental probe of the physics of the medium in which the energy and particle currents are created. Experimentally, thermoelectric effects have already been studied with ultracold fermionic lithium atoms using a two-dimensional constriction for weak interactions [1]. These effects are affected by the properties of both the constriction and the reservoirs, which we here control in our mesoscopic transport setup to explore new conduction regimes. First, we reduce the dimensionality of the constriction: two temperature imbalanced reservoirs are connected via a one to few mode channel, which is similar to the condensed matter quantum point contacts. Second, we can change the reservoirs' properties by varing the interaction strength to reach the unitary regime. The evolution of particle and energy currents to a temperature gradient are strongly modified compared to the weakly interacting case, where a transient particle imbalance builds up before relaxing. In the strongly interacting regime, this imbalance persists within experimentally reachable durations, reminiscent of the fountain effect. Our next goals consist in shaping some devices probed by two-terminal conductance measurements [2, 3]. In particular, we want to study the influence of a dissipative beam on the coherence of the transport. [1] J. - P. Brantut, C. Grenier, J. Meineke, D. Stadler, S. Krinner, C. Kollath, T. Esslinger, and A. Georges: A Thermoelectric Heat Engine with Ultracold Atoms Science 342, 713-715 (2013). [2] S. Häusler, S. Nakajima, M. Lebrat, D. Husmann, S. Krinner, T. Esslinger, and J. - P. Brantut: Scanning Gate Microscope for Cold Atomic Gases Physical Review Letters 119, 030403 (2017). [3] M. Lebrat, P. Grišins, D. Husmann, S. Häusler, L. Corman, T. Giamarchi, J.-P. Brantut, T. Esslinger Assembling a mesoscopic lattice in a quantum wire for ultracold fermions arXiv:1708.01250

We report on the observation of strong opto-magnetical effects on the self-organization of a degenerate atomic system coupled to a single-mode high-finesse optical cavity and subjected to an off-resonant pump field, propagating transversely to the cavity axis. The opto-magnetical effects arise from the presence of multiple atomic transitions which gives rise to non-zero vectorial polarizability and hence spin dependent atom-cavity (vectorial) coupling. The relative strength of the vectorial coupling with respect to the scalar coupling can be tuned by changing the polarization of the pump field. We observe spin dependent threshold of the self-organization process and spin dependent phase of the scattered light in the organized phase as a function of the pump field polarization. The observed behaviour can be understood in the context of a modified Dicke model. By starting with a mixture of two spin states, we identify two different regimes. In the regime of strong scalar coupling, the self-organization process generates density modulations in the atomic system. By increasing the ratio of vectorial over scalar component beyond a critical point, we observe the appearance of a new self-organization pattern consisting of magnetization modulations, a spin texture. We locate the transition point by analysing the phase of the light emitted by the atoms in the organized phase. Our findings pave the way to the exploitation of opto-magnetic effects for quantum simulation of long-range magnetic interactions.

Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain. We report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms.

We consider a $XXZ$ spin-1/2 chain whose first and last spin are dissipatively oriented into chosen directions. Via perturbation theory we show that the effective dynamics leading to a NESS in the limit of strong dissipation is governed by a stochastic process. This enabled us to predict the rank of the NESS in Zeno-limit for small systems and arbitrary boundary spin polarization. In particular for parallel boundary spins a NESS of rank 2 composed of two spin-helix states of opposite winding could be proven for spin-chains of length N, with N-1 being prime and certain anisotropy.

It is known that quantum gases in single-mode optical cavities and along optical fibres can undergo a transition to a self-organised state. We study the phase diagram and collective excitations of a degenerate Fermi gas coupled to the propagating modes of a multimode optical waveguide. The interplay between superradiant and umklapp scattering gives rise to a rich phase diagram and to peculiar collective excitations.

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.

We consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density matrix renormalization group method, we obtain a rich steady state diagram of self-organized steady states. Transitions between superfluid to Mott-insulating states occur, on top of which we can have Meissner, vortex liquid, and vortex lattice phases.

We develop a method for solving the real-time evolution of Markovian quantum systems based on the 2-particle irreducible (2PI) effective action. In general, wave-function based methods are restricted to small systems owing to the exponential growth of the Hilbert space with the system size. Similarly, the density matrix renormalization group (DMRG) is restricted to short times owing to the exponential growth of entanglement with time. In contrast, the computational cost for solving the 2PI equations of motion scales only polynomially with both space and time. This allows for ab initio simulations that connect the early-time dynamics of large Markovian quantum systems with its late-time asymptotics. As a specific example, we study the cooling of a system of initially free bosons into a Bose-Einstein condensate via engineered dissipation.

Spontaneous emission constitutes a fundamental limit in nearly all platforms interfacing quantum light and matter. In typical theoretical treatments, spontaneous emission events are assumed to occur independently, and at a rate given by a single isolated atom. However, this assumption can be dramatically violated in atomic arrays. Here, strong destructive interference in wave emission can lead to the phenomenon of subradiance, wherein collective atomic excitations are unable to decay away. Here, we provide the first comprehensive look at the exotic properties of subradiant dynamics in the many-excitation limit, considering a model of a chain of regularly spaced two-level atoms, which interact through a one-dimensional waveguide. Starting from an initially highly excited state, we find that at long times the total population and the density-density correlation exhibit a power-law decay, associated in part with the closing of a Liouvillian gap in the thermodynamic limit. At long times, we also find the emergence of "fermionic" density-density correlations, reflecting the fact that subradiant excitations exhibit a Pauli exclusion property in space. These results should inspire a more detailed look into the properties of many-body subradiance in systems ranging from waveguide QED to free-space atomic ensembles.

We demonstrate that the open quantum Rabi model (QRM) exhibits a second-order dissipative phase transition (DPT), which belongs to the same universality class of the open Dicke model, and propose a method to observe this transition with trapped ions [1]. This work extends the recent findings that paradigmatic models of quantum optics describing a single oscillator coupled to a single qubit, such as QRM and Jaynes-Cummings model, undergo a quantum phase transition away from the thermodynamic limit to the open quantum system setting [2,3]. We find that the interplay between the ultrastrong qubit-oscillator coupling and the oscillator damping brings the system into a steady-state with a diverging number of excitations, in which a DPT is allowed to occur even with a finite number of system components. The universality class of the open QRM, modified from the closed QRM by a Markovian bath, is identified by finding critical exponents and scaling functions using the Keldysh functional integral approach. We propose to realize the open QRM with two trapped ions where the coherent coupling and the rate of dissipation can be individually controlled and adjusted over a wide range. Thanks to this controllability, our work opens a possibility to investigate potentially rich dynamics associated with a dissipative phase transition. Ref: [1] M.-J. Hwang, P. Rabl, and M. B. Plenio, arXiv:1708.08175 [2] M.-J. Hwang and M. B. Plenio, Physical Review Letters 117, 123602 (2016) [3] M.-J. Hwang, R. Puebla, and M. B. Plenio, Physical Review Letters 115, 180404 (2015)

We study the non-equilibrium dynamics of ultracold Bose gases in optical lattices using a scanning electron microscope. In a first experiment we characterize the emerging steady-states of a driven-dissipative Josephson junction array, realized with a BEC in a one-dimensional optical lattice. By locally applying dissipation using the electron beam at an initially full site, the superfluid response of the respective site breaks down. This can be seen as an extension of the paradigm of Coherent Perfect Absorption (CPA). In its original occurrence CPA refers to the complete extinction of bidirectional incoming radiation by spatially localized absorber embedded in a wave-guiding medium. Furthermore, we make use of the Talbot effect to study phase coherence in an optical lattice at a finite range. The interferometer which relies on the fast blanking of the lattice potential is applied to study the spread of phase coherence after a quench of the lattice depth. Our current work is focus on the generation and stabilization of dark solitons in 3D. To imprint the phase step of π onto a BEC we use a Digital Micromirror Device to create a sharp edge in the beam profile of a 532nm laser. We will then make use of the electron beam as a source of local dissipation to stabilize the dark soliton.

In the contribution I address two particular problems of non-equilibrium dynamics of an open many-body system. The first problem is evaporation dynamics of weakly interacting fermions [1,2]. The second problem is equilibration dynamics between two bosonic reservoirs with different chemical potentials [3,4]. [1] A.R.Kolovsky and D.L.Shepelyansky, Dynamical thermalization in isolated quantum dots and black holes, Europhys. Lett. 117 (2017), 10003. [2] D.L.Shepelyansky and A.R.Kolovsky, Evaporation dynamics of weakly interacting fermions (in progress). [3] A.R.Kolovsky, Microscopic models of source and sink for atomtronics, Phys. Rev. A 96 (2017), 011601(R). [4] D.N.Maksimov and A.R.Kolovsky, Coherent properties of carriers in a 1D chain connecting two bosonic reservoirs (in progress).

We present a Keldysh theory for excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. We show that the product boson approximation for the nonlinear phonon bath can be reproduced by a resummation of a systematic perturbation theory. We give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density-wave mode. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density-wave modes.

In classical non-equilibrium systems directed percolation (DP) is one of the fundamental universality classes featuring an absorbing state inherently breaking detailed balance. We analyze a DP-like model of quantum mechanical origin in an eventually classical description (MSRJD), which due to the coherent quantum processes drastically changes the physics in contrast to DP, but similarly features an absorbing state and can be described by a Langevin equation with multiplicative noise. One of the main differences is the possibility of a meta-stable minimum in the potential landscape and thereby the possibility of a first order phase transition. Especially in one dimension the question is whether a first-order phase transition is possible, given the massive influence of spatial fluctuations and how the phase transition takes place on a mesoscopic level. We find evidence that the transition is actually of second order, but nevertheless the physical phenomenology is more the one of a first order transition: Parts of the system in the meta-stable state can nucleate into the stable state by forming droplets of some critical width, which are features of a first order transition. The effective degrees of freedom at the mesoscopic level are exactly these droplets, emerging as soliton solutions of the equations of motion, nucleating from the meta-stable phase into the absorbing phase. However these effective degrees of freedom strongly influence the long-wavelength physics and turn the transition into a second order one. The dynamics at an early stage is dominated by these nucleations, which we describe by a non-equilibrium model for nucleation rates. At larger time-scales the growth of the droplets dominates the dynamics and determines the kind of phase transition.

We study the electromagnetically induced transparency (EIT) window of strongly interacting polaritons in a photonic crystal waveguide. The system exhibits a nonequilibrium phase transition and an associated bistable, nonthermal occupation in the EIT window. Our investigation uses a self-consistent (SC) systematic expansion in Feynman diagrams that yields quantitatively valid predictions. The tunability of interactions in the present system allows the bistability to occur even at low polariton densities.

We introduce a frequency-dependent incoherent pump scheme with a square-shaped spectrum in order to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a nonequilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or noninteger densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic nonequilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero-temperature many-body physics is highlighted.

When a degree of freedom is approximately protected by a conservation law even weak perturbations can cause strong response in that quantity and can drive the system far from its equilibrium steady state. A simple classical example is a well-insulated greenhouse, which can be heated up significantly even by weak sunlight, due to the approximate conservation of the energy within the greenhouse. A quantum platform with many conserved quantities is provided, for example, by integrable models. I will present the theory of weakly open and driven integrable systems on the one-dimensional Heisenberg XXZ model. The integrability-breaking perturbations due to driving and coupling to the environment will be of Lindblad or Floquet form. Firstly, I will argue that in above situations the concept of the generalized Gibbs ensemble can be approximately but efficiently used to describe the non-equilibrium steady state and approach to it. Secondly, I will show that, as in the greenhouse example, certain perturbations can activate huge heat and spin currents since these are approximate conservations of our model. Latter finding could be tested with trapped-ions experiments or by activating heat and spin pumping in realistic materials.

Bimodal (micro)cavities offer a rich spectrum of emission properties. Especially the switching of steady state intensities has gathered substantial interest due to potential technical applications as optical flip-flop memories, and tunable sensitive switches. We show that the largest effective gain selects the coherent emission mode for weak pumping. However, akin to condensation of massive bosons, it is the inter-mode kinetics, that select the coherent emission mode for strong pumping, thus inducing a switching from the high effective gain mode $h$ to the low effective gain mode $l$ [1]. Our description of mode switching is a generalization of the theory of Bose selection [2] and emphasizes the connection to the Bose condensation of massive bosons. We derive an analytical criterion for the mode selection. Our theory is in excellent agreement with both numerical and experimental data for a semiconductor quantum-dot based bimodal micropillar. Additionally we present the phase diagram that reveals the generic behavior of a bimodal laser system. Recent experiments with a photon number resolving transition edge sensor allows to analyze the full photon statistics of the system and the origin of the observed superthermal photon bunching [3]. [1] Pump-power-driven mode switching in a microcavity device and its relation to Bose-Einstein condensation HAM Leymann, D Vorberg, T Lettau, C Hopfmann, C Schneider, M Kamp, ... Physical Review X 7 (2), 021045 [2]Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems D Vorberg, W Wustmann, R Ketzmerick, A Eckardt Physical review letters 111 (24), 240405 [3] Exploring the Photon-Number Distribution of Bimodal Microlasers E Schlottmann, M von Helversen, HAM Leymann, T Lettau, F Krüger, ... arXiv preprint arXiv:1709.04312

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments [1]. The Schrödinger equation for the total state of system and environment is considered in a coherent state representation with respect to the environmental degrees of freedom. This equation is reformulated by employing the Feshbach partitioning technique for open quantum systems [2] based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger [3] equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator. [1] V. Link and W. T. Strunz, Phys. Rev. Lett. 119, 180401 (2017) [2] D. Chruściński and A. Kossakowski, Phys. Rev. Lett. 111, 050402 (2013) [3] W. T. Strunz, L. Diósi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)

Qubits strongly coupled to a photonic crystal can give rise to many exotic physical scenarios, including the realization of certain quantum many-body models and single photon and multi-photon bound states which are localized around the qubits. Here, we consider two qubits connected to a superconducting, microwave photonic crystal. We demonstrate that this system allows for controllable interactions between the two qubits and observe a fourth-order two photon virtual process indicating strong coupling between the photonic crystal and qubits. In this presentation, we focus on the theoretical modeling of this experimental system and compare experimental and theoretical results. By treating the photonic crystal as a one-dimensional hopping model, we find quantitative agreement with the experimental data, including two-photon results.

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for optimal entanglement bounds or for environment-assisted entanglement protection.

Many-body open quantum systems have attracted increasing attention in recent years. From a theoretical viewpoint, these systems call for new effective methods for the simulation of the dynamics and of the nonequilibrium steady state (NESS). In this contribution, we will discuss our recent progress in the development of a projector Monte Carlo approach, called Driven Dissipative Quantum Monte Carlo (DDQMC), to stochastically sample the time evolution of the density matrix as dictated by the Liouville-von-Neumann equation. For closed, Hamiltonian systems, various quantum Monte Carlo approaches have been the election tool to stochastically sample system properties, both at zero and finite temperature. Modeling the ground state properties at zero temperature in particular, is made possible by stochastically sampling the time evolution of the imaginary-time Schrödinger equation, with a class of methods generally known as projector Monte Carlo [1]. The Liouvillian dynamics towards the steady state shares with the imaginary-time Schrödinger equation the fact that, in the long-time limit, the eigenstate with the smallest-real-part-eigenvalue will dominate. In the Liouvillian case, this corresponds to the NESS. It is therefore natural to attempt an extension of projector Monte Carlo techniques to the simulation of the NESS properties. However, the complex-valued density matrix follows an oscillatory dynamics which may easily result in the well known sign problem affecting most Monte Carlo algorithms. Recently, a new projector Monte Carlo approach -- called Full Configuration Interaction Quantum Monte Carlo (FCIQMC) -- has been developed for quantum chemistry simulations, and was found to alleviate significantly the sign problem [2]. We present a proof of principle of the possibility to apply FCIQMC to the real-time evolution of the Liouville-von-Neumann equation towards the NESS. We demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional spin lattice governed by the Heisenberg XYZ Hamiltonian. The results are compared to those obtained by exact calculations. DDQMC holds promise as a computationally effective tool to address open quantum system independently of their dimensionality. [1] C. J. Umrigar, J. Chem. Phys. 143, 164105 (2015). [2] G. H. Booth, et al., J. Chem. Phys. 131, 054106 (2009); F. R. Petruzielo, et al., Phys. Rev. Lett. 109, 230201 (2012); J. S. Spencer, et al., J. Chem. Phys. 136, 054110 (2012).

We study an open quantum system of cold atoms illuminated by an external plane wave, which drives the dipolar transition between two energy levels. In this set up, the cold atoms map to a two-level spin system with long range interactions and nonlocal dissipation. We determine at the mean-field level the long-time phase diagram of the system as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations and phase bistabilities. We investigate some of these phases in more detail and explain how nonlocal dissipation plays a role in the long time dynamics. Furthermore, we discuss what features would survive in the full quantum regime.

Already in 2010, a Bose-Einstein condensate (BEC) of photons has been created at room temperature within a dye-filled microcavity being pumped by a laser [1]. The dye plays insofar a double role as it provides the thermalization of the photon gas via its specific absorption and emission spectrum and introduces at the same time an effective photon-photon interaction by changing its refractive index mainly due to thermal lensing [2]. We show, that these effects can be described consistently by using an open-dissipative Gross-Pitaevski approach as it is widely used in the community of exciton-polariton condensates [3,4]. In our context this means to set up a pair of coupled mean-field equations, one for the coherent condensate wave function and one for the diffusion of temperature in the dye solution. With this mean-field approach at hand we perform a linear stability analysis for a homogeneous photonic BEC. At first, we determine the steady state, from which we deduce a photon-photon interaction strength agreeing with the experimental value [2,4]. Afterwards, we analyze small deviations from the BEC steady state, yielding both the Bogoliubov spectrum and its damping. In particular, we show that the Goldstone theorem turns out to be valid even for such an open-dissipative photonic system. Finally, we note that our mean-field modelling yields for experimenal realistic parameters a stable BEC steady state as both pumping and dissipation are included. [1] J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature 468, 545 (2010) [2] J. Klaers, J. Schmitt, T. Damm, F. Vewinger, and M. Weitz, Appl. Phys. B 105, 17 (2011) [3] M. Wouters and I. Carusotto, Phys. Rev. Lett. 99, 140402 (2007) [4] D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz and J. Klaers, Nature Photonics 11, 565 (2017)

In the absence of disorder, periodically driven many-body systems are generically expected to be ergodic and to thermalize to an infinite-temperature ensemble. Here we find an exception to this rule by considering an infinite chain of coupled identical kicked rotors. We numerically study the classical dynamics of the system and identify three distinct regions, which are respectively localized, diffusive, and super-diffusive. The above phases are characterized using the diffusion constant and the exponent $\alpha$ with $\langle p^2\rangle\propto t^\alpha$, where $p$ is the average angular momentum of coupled rotors. We have also investigated the effect of initial conditions for the angles of the rotors, to determine the different phases. We have found that the parametric resonance point shifts from linear to quadratic stable point as the number of kicks is increased for small initial temperature. On the other hand, if the initial temperature is increased substantially the linear stability disappears and the system becomes marginally stable.

The study of driven-dissipative open quantum systems prompted the emergence of a plethora of interesting new physics inaccessible to their equilibrium counterparts [S. Diehl et al., Nat. Phys. 4, 878 (2008)]. Combining Floquet's theorem with the general Liouvillian approach to open quantum systems [M. Grifoni and P. Hänggi, Phys. Rep. 304, 229 (1998)] provides powerful tools to investigate such systems beyond the adiabatic limit. Here, we present a general method to calculate the quasistationary state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) with arbitrary coherent driving strength and modulation frequency of system parameters. Applying this method, we extend our previous results based on the Floquet scattering theory [M. Pletyukhov et al., Phys. Rev. A 95, 043814 (2017)] for a two level system with time-dependent parameters which show the breakdown of the adiabaticity condition even for a slow time modulation. Secondly, we apply our method to a driven $\Lambda$-system exhibiting electromagnetically induced transparency (EIT) and observe how the time modulation modifies the latter phenomenon. Our focus however lies on the third application -- the single-mode Kerr nonlinearity model -- where driving is considered across the point of the dissipative phase transition [A. Le Boite et al., Phys. Rev. A 95, 023829 (2017)]. In this talk I discuss the behaviour of observables in the quasistationary regime going beyond the range of driving parameters studied previously.

In one dimension, electron-phonon interactions lead to the well known Peierls instability. In this talk we address the fate of this instability under non-equilibrium conditions created by imposing a finite voltage across the system.

Ultracold atomic gases confined in optical lattices have proven to be an ideal playground for the simulation of quantum many-body physics. Optical cavities can mediate infinite-ranged interactions between the atoms and also allow for in-situ monitoring of the system. When short- and long-range interactions compete, new quantum phases can emerge, involving both coherent emission and spatial ordering of the atoms. We are interested in the case where dissipation plays a major role and ask how the out-of-equilibrium effects will modify the phase diagram.

Recent experiments in quantum optics provide an ideal platform to study nonequilibrium quantum phase transitions. In particular, the stimulated Raman coupling between a single-mode cavity and cold trapped atoms was recently used to realize the Dicke model and observe its second-order phase transition. In these experiments, the atoms are affected by single-atom decay and dephasing that cannot be taken into account in the framework of the common mean-field approximation. We include these effects by an appropriate cumulant expansion of the Lindblad master equations and find significant modifications to the stability diagram of the system. Our analysis may shed light on discrepancies between previous theoretical predictions and current experimental findings.

We investigate the propagation of light and the induced quantum correlations in an ultracold dilute atomic cloud. The atoms interact between each other, through real and virtual photons, leading to a ``cooperative'' scattering of light, where macroscopic degrees of freedom emerge. Our system consists in a laser of classical light interacting with a dilute cloud of two-level atoms. We compute the master equation using ``exact'' simulations thanks to the python module QuTiP (1) and semiclassical simulation with the truncated BBGKY hierarchy. (2) The truncation is taken by means of a cluster expansion to include two-atoms connected correlations. We analyze the propagation of quantum correlations in the cloud and we also study the fluorescence power spectrum, that yields signatures of quantum coherences between the atomic dipoles (collective effects in the Mollow triplet). I'll present results of quantum cooperativity in the fluorescence spectrum, which scale with the resonant optical thickness -- additional sidebands and asymmetry in the Mollow triplet. (3) (1) J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013). (2) L. Pucci, A. Roy and M. Kastner, Simulation of quantum spin dynamics by phase space sampling of Bogoliubov-Born-Green-Kirkwood-Yvon trajectories Phys. Rev. B, 93, 174302 (2016) (3) L. Pucci, A. Roy, T. S. do Espirito Santo, R. Kaiser, M. Kastner and R. Bachelard, Quantum effects in the cooperative scattering of light by atomic clouds Phys. Rev. A, 95, 053625 (2017)

We study dynamical and steady-state dissipative quantum phase transitions of a driven Bose Hubbard model between an incoherent Mott-like insulating phase and a non-equilibrium superfluid. We highlight the crucial role of pumping scheme and the unique features that emerge in the driven-dissipative case as compared to the well known equilibrium quantum criticality. These results might be relevant for the upcoming generation of circuit QED arrays experiments aiming at realizing Mott Insulator of Polaritons and its transition into a non-equilibrium superfluid.

We investigate theoretically a one-dimensional ideal Bose gas that is driven into a steady state far from equilibrium via the coupling to two heat baths: a global bath of temperature $T$ and a ``hot needle'', a bath of temperature $T_h\gg T$ with localized coupling to the system. Remarkably, this system features a crossover to finite-size Bose condensation at temperatures $T$ that are orders of magnitude larger than the equilibrium condensation temperature. This counterintuitive effect is explained by a suppression of long-wavelength excitations resulting from the competition between both baths. Moreover, for sufficiently large needle temperatures ground-state condensation is superseded by condensation into an excited state, which is favored by its weaker coupling to the hot needle. Our results suggest a general strategy for the preparation of quantum degenerate nonequilibrium steady states with unconventional properties and at large temperatures.

We study the decoherence of a spin in a quantum dot due to its hyperfine coupling to a fluctuating bath of nuclear spins. We calculate the spectrum and time evolution of the coherence factor using a Monte Carlo sampling of the exact eigenstates obtained via the algebraic Bethe Ansatz. The exactness of the obtained eigenstates allows us to study the full crossover from strong to weak external magnetic field in a full quantum mechanical treatment. We find a large non-decaying fraction in the zero-field limit which is explained by Bose-Einstein-condensate-like physics. We compare our results to a simple semiclassical picture and find surprisingly good agreement. Finally, we discuss the effect of weakly coupled spins and show that they will eventually lead to complete decoherence. References: A Faribault and D Schuricht, Phys. Rev. Lett. 110, 040405 (2013); Phys. Rev. B 88, 085323 (2013).

The transport properties of electrons are theoretically studied in a one-dimensional setup, when inter-band transitions couple to the light field of a cavity mode that is close to its vacuum. It is shown that light-matter interaction can allow for a significant enhancement of steady-state charge currents in two bands that interact via emission and absorption of dressed photons. The analysis is performed by using non-equilibrium Green’s function methods and quantum Master equation techniques. Moreover, we apply Matrix Product States techniques in order to study conductivity enhancement in general cavity-coupled interacting disordered many-body models. Here, the focus lies on the change of the diffusion properties for electrons/holes due to light-matter coupling, for which we show first results.

We study the low-frequency dynamics of the periodically driven Su-Schrieffer-Heeger model as a prototypical model of a Floquet topological insulator. We show, both analytically and numerically, that in the low frequency limit, $\Omega\to0$, the topological invariants of the system exhibit universal fluctuations. While the topological invariants in this limit nearly vanish on average, over a small range of frequencies, we find that they follow a Gaussian distribution with a width that scales as $1/\sqrt{\Omega}$. We explain this scaling based on a diffusive structure of the winding numbers of the Floquet-Bloch evolution operator at low frequency. We also find that the maximum quasienergy gap remains finite and scales as $\Omega^2$. Thus, we argue that the adiabatic limit of a Floquet topological insulator is highly structured, with universal fluctuations persisting down to very low frequencies.

We consider a Bose-Einstein condensate coupled to a single mode of an optical cavity. The cavity-atom interaction provides a one-dimensional dynamic optical lattice potential for the ultracold atomic condensates because of the matter-field coupling. With the help of the resulting tight binding model, we discuss how an artificial gauge field can be created in this system dynamically and how from the cavity transmission spectrum, properties of such a gauge field can be identified. Acknowledgements - This work is supported by CSIR Fellowship (P.S.) and DAE-SRC(BRNS) Outstanding Investigator Fellowship (S.G.)).

We study collective effects in the fluctuation-induced forces between a system of correlated neutral two-level atoms and a surface. We find that the total Casimir-Polder force on the atoms can be modified via the mutual correlations between the atomic dipoles, showing in particular that a collection of atoms that is super- or sub-radiant with regard to spontaneous emission experiences an enhanced or suppressed collective vacuum-induced force respectively. This demonstrates the potential of collective phenomena as a new tool to selectively tailor vacuum forces.

We explore the influence of dissipation on a paradigmatic driven-dissipative model where a collection of two level atoms interact with both quadratures of a quantum cavity mode. The closed system exhibits multiple phase transitions involving discrete and continuous symmetries breaking and all phases culminate in a multicritical point. In the open system, we show that infinitesimal dissipation erases the phase with broken continuous symmetry and radically alters the model's phase diagram. The multicritical point now becomes brittle and splits into two tricritical points where first- and second-order symmetry-breaking transitions meet. A quantum fluctuations analysis shows that, surprisingly, the tricritical points exhibit anomalous finite fluctuations, as opposed to standard tricritical points arising in $^3He-\text{}^4He$ mixtures.

In recent years the phenomenon of nonequilibrium Bose-Einstein condensation (BEC) has been studied extensively. One of the most recent and most prominent systems is a photon Bose-Einstein condensate [1]. The core of the system is a dye solution filling the microcavity in which the photons are harmonically trapped. Due to cyclic absorption and reemission processes of photons the dye leads to a thermalization of the photon gas at room temperature. Furthermore, due to a nonideal quantum efficiency, those cycles yield in addition a heating of the dye solution, which results in a change of the refractive index and, thus, in an effective photon-photon interaction [2]. In order to describe this thermooptic effect at a mean-field level, we use an open-dissipative Schrödinger equation coupled to a diffusion equation for the temperature of the dye solution [3]. In our contribution we calculate analytically the lowest-lying collective frequencies and damping rates via a linear stability analysis for a harmonically trapped photon BEC. Due to the open-dissipative character of the system its energy is not conserved and, thus, it is not possible to investigate its dynamical properties within a variational approach by using an action. Instead, we work out an approximation which is based on determining the equations of motion for the lower moments under the assumption that both the condensate wave function and the temperature distribution are Gaussian shaped. As a result of the photon-temperature coupling the collective frequencies and damping rates turn out to depend on the diffusive properties of the dye solution. In particular, we examine whether the Kohn theorem is valid, i.e. whether the dipole-mode frequency is the same as the trap frequency [4,5]. [1] J. Klaers, F. Vewinger, and M. Weitz, Nature 468, 545 (2010) [2] J. Klaers, J. Schmitt, T. Damm, F. Vewinger, and M. Weitz, Appl. Phys. B 105, 17 (2011) [3] D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz and J. Klaers, Nature Photonics 11, 565 (2017) [4] A. L. Fetter and D. Rokhsar, Phys. Rev. A 57, 1191 (1998) [5] H. Al-Jibbouri and A. Pelster, Phys. Rev. A 88, 033621 (2013)

Authors: A. Strathearn (contributing author), P. Kirton, D. Kilda, J. Keeling, B. W. Lovett Abstract: Modelling realistic quantum devices requires an understanding of quantum systems strongly coupled to their environment. Describing such strong coupling, and the non-Markovianity that accompanies it, analytically is extremely challenging and for consistently reliable results one must turn to numerical methods. To date, the available methods are either restricted to specific special cases or are limited in scope due to huge computational requirements. Here we present a novel and general numerical approach to efficiently describe the time evolution of a quantum system coupled to a non-Markovian environment [1]. Within the path integral description of open quantum systems, environmental degrees of freedom are integrated out to leave an influence functional of system trajectories only [2]. This influence functional then describes all dissipative and non-Markovian physics occurring in the system due to the environment, though performing the remaining path integration over system trajectories is intractable in general. Here we show that discretising the system trajectories allows the path integral to be written as a tensor network which can be efficiently contracted. We build upon augmented density tensor methods [3] in which the current state of the system and its previous history are stored in a large dimensional tensor. We show that this tensor can be efficiently represented as a \textit{matrix product state} [4], and that contracting the tensor network which represents the path integral influence functional can be carried out by iteratively propagating such a matrix product state. We demonstrate the power and flexibility of our method, which we call ``time-evolving matrix product operators'' (TEMPO), by addressing two contrasting problems. First we identify the the localisation transition in the Ohmic spin-boson model [5], both for the spin-$1/2$ and spin-$1$ cases, which is numerically challenging due to the transition being of infinite order. Next we look at the problem of a pair of interacting spins embedded in a common environment. Here we can clearly see the effects of excitations traveling between the spins through the environment; a highly non-Markovian phenomenon for which no other methods are suitable for studying. [1] A. Strathearn, P. Kirton, D. Kilda, J. Keeling and B. W. Lovett, arXiv:1711.09641v1 [2] R. P. Feynman, and F. L. Vernon, Jr., Ann. Phys. 24, 118 (1963) [3] N. Makri and D. E. Makarov. J. Chem. Phys. 102 4600 (1995) [4] R. Orus, Ann. Phys. (N.Y.) 349 117 (2014) [5] K. Le Hur in "Understanding Quantum Phase Transitions" edited by L. Carr (CRC Press 2010)

Understanding the intricate mechanisms behind the dynamics of many-body open systems is a great challenge. At the same, open many-body quantum systems present a very rich and interesting phenomenology, from non-equilibrium phase transitions to complex relaxation behaviors. In light of this, we study the time evolution of a Bose-Hubabrd model subjected to a heating mechanism via local dephasing. We describe how correlations build up and propagate at initial times and we show how dissipation does not affect different correlations equally. Our investigations are based on a state-of-the-art number conserving matrix product states algorithm for density operators and a fermionic quasiparticle representation describing excitations as doublons and holons. Reference Bernier, Jean-Sebastien, Ryan Tan, Lars Bonnes, Chu Guo, Dario Poletti, and Corinna Kollath. "Light-cone and diffusive propagation of correlations in a many-body dissipative system" arXiv preprint arXiv:1702.04136, accepted in Physical Review Letters.

Symmetry-Protected Topological phases of matter are now an established paradigm for condensed matter physics of closed quantum systems. Whether phenomenology of SPT phases survives when the system is driven and interacting with an external bath is still outstanding. The question can be addressed by considering non-equilibrium dynamical processes whose steady state is topologically non-trivial; in fact, such processes are now physically relevant since the great degree of control that optical tools guarantee on cold atomic systems makes it possible to engineer them. We consider as a prototypical model the Chern insulator in 2+1 dimension. A striking feature of the topological phase is the presence of the so-called boundary anomaly, namely the loss of gauge invariance in the presence of an edge, that has to be compensated by adding edge degrees of freedom. Such edge states are the celebrated topologically protected edge states. We show that such feature is present also in the driven open model, we build the effective field theory for the edge states and we discuss its robustness against some perturbations.

For open many-body quantum systems with interactions, one usually relies on numerical methods such as exact diagonalization or DMRG. By studying the steady state and the dissipative gap (if present), these methods can be effective to probe the behavior at long timescales. However, even with the most advanced numerics, it is difficult to make general predictions of short-time behavior. This research aims to use the toolbox of symmetries, both in Hilbert space and in Liouville space, to get a better understanding of the short-time effect of bulk dissipation on the Heisenberg XXZ spin chain.

The Bogoliubov method provides an approximate solution to a quantum system with sufficiently small interactions and large density. It consists of assuming a strongly occupied condensate mode plus a small depletion of noninteracting quantum fluctuations with Gaussian statistics. In a closed system the guarantee of a thermal equilibrium motivates one to put forward a Boltzmann-Gibbs distribution for the quasiparticles, regardless of the exact underlying kinetics. However, for an open system there is no such postulate and the actual distribution can be much more sensitive to the specific dynamics of the quantum fluctuations. We will show that various third-order scattering processes, which are neglected in the Bogoliubov approximation, cannot simply be omitted from the dynamics of an open system. An excitation can scatter with a condensate particle to leave two other excitations or two excitations can scatter into a condensate particle and a new excitation. At equilibrium these processes go under the name of Beliaev and Landau scattering respectively. We will show that, in a driven-dissipative context, energy and momentum conserving Beliaev-Landau channels are possible in 1D, thanks to the presence of a spectral gap when the drive is below resonance. First of all we will outline how the truncated Wigner approach, when naively applied, dramatically overestimates the effects of Beliaev-Landau scattering. Instead, we will present a consistent method, based on the construction of a hierarchy of correlations, to provide a viable way for evaluating the expected corrections beyond Bogoliubov. Furthermore, we will propose some clear experimental signatures of Beliaev-Landau physics in state-of-the-art coupled-cavity and microcavity exciton-polariton experiments. Most notably, the occupation numbers of the quantum fluctuations, as they are found in the Bogoliubov approximation, are redistributed as a consequence of spontaneous Beliaev-Landau scattering and the cavity output field exhibits non-Gaussian statistics. Reference article: M. Van Regemortel, W. Casteels, I. Carusotto, M. Wouters, Spontaneous Beliaev-Landau scattering out of equilibrium, Phys. Rev. A 96, 053854 (2017)

Many photonic systems are open and are generally considered to obey the Markov approximation, such that the Lindblad master equation provides an adequate description of the time evolution. Evolving this whole master equation explicitly is memory-consuming, though, as $D^2$ elements must be evolved for a Hilbert space dimension $D$. The method of (exact) quantum trajectories provides an alternative as only evolution of wavefunctions, containing $D$ elements, are computed. According to this method, one imagines continuous weak, selective measurements on the environment; these then correspond to stochastic updates of the wavefunction. To construct the full density matrix, one performs a Monte Carlo sampling of these stochastic trajectories. While formally exact, quantum trajectory methods applied to large systems still require a significant computational cost. The faster Truncated Wigner (TW) method is often used instead as an approximate Monte Carlo scheme. Often it yields good results, but situations are also known where it breaks down and produces unphysical results such as negative densities. We propose a class of gaussian ansatz quantum trajectory methods to close the gap between the robustness of exact quantum trajectories and the computational efficiency of the TW approach. We primarily apply this method to a Driven-Dissipative cavity with Kerr nonlinearity. As a pure Gaussian state is characterized only by its displacement $\alpha$ and its variance $\langle\hat{\delta}\hat{\delta}\rangle$ (anomalous density of fluctuations, corresponding to squeezing) , constraining the evolution of a state to the Gaussian subspace of the full Hilbert space reduces the cost for large systems by orders of magnitude. As opposed to the TW approach, every sample at every timestep corresponds by construction to a well-defined physical state. We have derived equations for these Gaussian trajectories, both for discrete jump processes (photoncounting) and for quantum state diffusion (homodyne/heterodyne detection). Using these methods, we have computed average density throughout the bistability regime and studied dephasing after the pump is set to zero and compare with other methods. Next, we look at larger systems (arrays of cavities) and use our method to investigate the heuristic phasor-method for photonic condensades.

We investigate the non-equilibrium steady state of a gas of photons in a dye-filled microcavity as it has been realized by the Weitz group. We consider the regime where the system is pumped away from the cavity center so that the pump spot predominantly overlaps spatially with excited transverse photon modes. We observe that when increasing the pump rate above a threshold, such an excited mode acquires a macroscopic occupation, i.e., becomes selected. Ramping up the pump rate further, we find that the ground mode can become selected for a given range of system parameters, resulting from an increased density of excited state molecules in the cavity center, once the excited mode gets selected. We also consider the case of a homogeneously pumped system where we observe a cascade of transitions between the selected modes. We find that a blocking mechanism between modes with a large spatial overlap effects which modes are selected before saturation takes place.

State-of-the-art experiments with ultra-cold atoms offer a unique setting for quantum simulation of interacting many-body systems. The high degree of controllability, the novel detection possibilities and the extreme physical parameter regimes that can be reached in these "artificial solids" provide a complementary set-up as compared with natural condensed-matter systems (1,2). New forms of atomic transport, including materials with negative differential resistivity (3), driven by many-body quantum correlation effects have already been realized in the laboratory. We discuss also ratchets and quantum transport in momentum space (4), as well as the connections between classical and quantum synchronization (5). All the presented systems are potential platforms for quantum information and the investigation of the quantum-to-classical transition. (1) Atom-based analogues to electronic devices, Europhysics News 44, 6, 20 (2013), highlighting: G. Ivanov, G. Kordas, A. Komnik, S. Wimberger, Bosonic transport through a chain of quantum dots, EPJ B 86, 345 (2013) (2) G. Kordas, D. Witthaut, P. Buonsante, A. Vezzani, R. Burioni, A. I. Karanikas, S. Wimberger, The dissipative Bose-Hubbard model, EPJ ST 224, 2127 (2015) (3) R. Labouvie, B. Santra, S. Heun, S. Wimberger, H. Ott, Negative Differential Conductivity in an Interacting Quantum Gas, PRL 115, 050601 (2015) (4) G. Summy, S. Wimberger, Quantum random walk of a Bose-Einstein condensate in momentum space, PRA 93, 023638 (2016) (5) D. Witthaut, S. Wimberger, R. Burioni, M. Timme, Classical synchronization indicates persistent entanglement in quantum systems, Nat. Comm. 8, 14829 (2017).

Dmitry Krimer, Matthias Zens and Stefan Rotter Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Austria Among different hybrid quantum systems, the ones based on spin ensembles coupled to superconducting microwave cavities have recently attracted much attention. I will speak about theoretical approaches for understanding the dynamics of an ensemble of NV centers in diamond with a strong magnetic coupling to a superconducting single-mode waveguide resonator. We demonstrate [1,2], how the decoherence induced by the inhomogeneous distribution of these NV centers can be suppressed by burning of two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Furthermore, we show that engineering the spin spectral density to acquire a comb-like structure leads to coherent revival dynamics with exciting potential for the processing of quantum information [3]. All of the above non-Markovian spin-cavity dynamics was successfully captured within the framework of a linear integral Volterra equation for the cavity amplitude. In [4] we went beyond this Volterra equation approach and developed a semiclassical theoretical framework based on the Maxwell-Bloch equations to describe the physics in the nonlinear regime. The effect of amplitude bistability observed in the recent experiment is well described by our theoretical model [4]. In accordance with our theory, the experiment demonstrated a critical slowing down of the cavity population on the order of eleven hours - a timescale much longer than observed anywhere else for this effect. [1] D.O. Krimer, B. Hartl, and S. Rotter, Phys. Rev. Lett. 115, 033601 (2015) [2] S. Putz, A. Angerer, D.O. Krimer, R. Glattauer, W. J. Munro, S. Rotter, J. Schmiedmayer, and J. Majer, Nature Photonics 11, 36 (2017) [3] D. O. Krimer, M. Zens, S. Putz, and S. Rotter, Laser & Photonics Review 10, 1023 (2016) [4] A. Angerer, S. Putz, D. O. Krimer, T. Astner, M. Zens, R. Glattauer, K. Streltsov, W. J. Munro, K. Nemoto, S. Rotter, J. Schmiedmayer, and J. Majer, Science Advances 3/12 e1701626 (2017)

Virtually all interactions that are relevant for atomic and condensed matter physics are mediated by quantum fluctuations of the electromagnetic eld vacuum. Consequently, controlling the vacuum fluctuations can be used to engineer the strength and the range of interactions. Recent experiments have used this premise to demonstrate novel quantum phases or entangling gates by embedding electric dipoles in photonic cavities or waveguides, which modify the electromagnetic fluctuations. Here, we show theoretically that the enhanced fluctuations in the anti-squeezed quadrature of a squeezed vacuum state allows for engineering interactions between electric dipoles without the need for a photonic structure. Thus, the strength and range of the interactions can be engineered in a time dependent way by changing the spatial prole of the squeezed vacuum in a travelling-wave geometry, which also allows the implementation of chiral dissipative interactions. Using experimentally realized squeezing parameters and including realistic losses, we predict single atom cooperativities C of up to 10 for the squeezed vacuum enhanced interactions.