Shedding Quantum Light on Strongly Correlated Materials

In the past decade, the concept of time crystals was introduced as a possible new dynamical phase of matter. Whilst initial proposals have been proven to be impossible, the idea remained. In this talk, I would like to give a brief overview of time crystals and discuss their characteristics. I will then discuss a system of coupled driven-dissipative bosonic modes and show that this system exhibits a series of phase transitions between regular dissipative phases and time crystalline ones.

Exciton-polaritons in microcavities are an excellent platform for the study of driven-dissipative phase transitions [1]. In particular, the investigation of fluctuations near the critical point is an open problem both from the experimental as well as theoretical perspectives. In this work, we study experimentally and theoretically a non-resonantly pumped polariton system in the trapped geometry close to the condensation transition. The condensate is formed using a ring- shaped pump which allows trapping the polaritons inside the ring [2]. In the nonequilibrium steady-state, as the driving is increased across the phase transition, we observe strong density fluctuations including the condensate hopping between different modes of the trapping potential [3]. This is somewhat analogous to the quantum fluctuations causing switching between different multi-stable states [4]. We quantify the behavior of these critical density fluctuations and compare them with those characteristics of equilibrium condensates in a trap. It is worth noting that in laser physics, critical phase fluctuations have been revealed to be responsible for the onset of “random telegraph noise” [2] characterized by a laser field undergoing jump-like fluctuations in amplitude, phase or frequency. We show that moving further away from the condensation threshold is stabilizing the condensate into one single mode. This emphasizes the usefulness of polariton condensate as a source of a stable single-mode coherent light. REFERENCES [1] I Carusotto, C. Ciuti, Rev. Mod. Phys. 85, 299, 2013 [2] Dreismann, A., Cristofolini, P., Balili, R., Christmann, G., Pinsker, F., Berloff, N.G., Hatzopoulos, Z., Savvidis, P.G. and Baumberg, J.J., Proceedings of the National Academy of Sciences, 111(24), 8770-8775 (2014) [3] Sun, Y., Yoon, Y., Khan, S., Ge, L., Steger, M., Pfeiffer, L.N., West, K., Türeci, H.E., Snoke, D.W. and Nelson, K.A., 2018. Phys. Rev. B, 97(4), (2018) [4] Rodriguez, S.R.K., Casteels, W., Storme, F., Zambon, N.C., Sagnes, I., Le Gratiet, L., Galopin, E., Lemaître, A., Amo, A., Ciuti, C. and Bloch, J., 2017. Phys. Rev Letters, 118(24), 247402 (2017) [5] J. H. Eberly, K. Wódkiewicz, and B. W. Shore, Phys. Rev. A 30, 2381

A physical system interacting with an environment relaxes to an equilibrium or a non-equilibrium steady state on time scales much longer than the relaxation time. In the steady state the system no longer evolves in time due to its coupling to the environment and *all* associated physical observables reach a constant value. This characteristic is inherent to classical and quantum open systems. We study and find the conditions under which oscillations in an open quantum system persist at long-timescales. We introduce classes of these conditions, ranging from the ones induced by symmetries to others of different nature.

Quantum many-body systems in the presence of drive and dissipation are some of the more difficult problems to solve numerically. Algorithms based on tensor networks have found great success in the context of closed quantum systems, and open systems in one-dimension, however their extension to two-dimensional open quantum systems has only recently come to fruition. This poster presents an adaptation of the infinite projected entangled pair operator (iPEPO)-based tensor network algorithm detailed in Ref. [1] that instead leverages the variational uniform matrix product state (VUMPS) algorithm [2] to contract infinite two-dimensional tensor networks. Near critical points, the VUMPS algorithm has been shown to perform significantly faster compared to the corner transfer matrix renormalisation group (CTMRG) method utilised in the original proposal [3], therefore we expect the VUMPS adaptation to inherent this computational speed up, while remaining stable and providing accurate results when compared to a known numerically exact method. This tensor network algorithm can be used to obtain the steady states and transient dynamics of two-dimensional quantum lattice models evolving according to the Lindblad equation. 1. C. Mc Keever and M. H. Szymańska, Phys. Rev. X 11, 021035 (2021) 2. V. Zauner-Stauber et al. Phys. Rev. B 97, 045145 (2018) 3. M. T. Fishman et al. Phys. Rev. B 98, 235148 (2018)

An optical cavity may be used to influence or induce phases of matter. We discuss how a charge-density wave phase in a 1-dimensional chain of spinless fermions is enhanced through the coupling to the quantized photon field. At the critical point between the Luttinger liquid and the charge-density wave, we find strong light-matter entanglement such that Mean-Field approaches fail to capture the relevant physics even in the thermodynamic limit. Additionally, we investigate how a cavity (or, more generally speaking, surface plasmon polaritons) coupled to a dipole electronic transition may enhance superconductivity both in the vacuum and the driven case.

The Kardar-Parisi-Zhang (KPZ) universality offers a description of a wide array of non-equilibrium systems, such as growing interfaces in liquid crystals, cell colonies and burning paper, to name a few. Over the past few years, a great body of theoretical work has established the possibility of realising both the 1D and 2D KPZ universality using the phase of exciton-polariton condensates in semiconductor microcavities, with the first experimental demonstrations in 1D having recently been announced [1]. Platforms for studying KPZ in 2D are highly sought after, and while the mapping from polariton condensates to the 2D KPZ equation was shown, these analyses also discovered practical problems for observing the signatures of the KPZ universality in such systems, such as requiring impossibly large system sizes [2] or being destroyed by proliferating vortices [3]. One way around these problems lies in instead using the optical parametric oscillator (OPO) regime of microcavity polaritons, where it was shown that a mapping onto 2D KPZ also occurs, and for specific values of the external drive strength can be expected to become observable for any system size [4]. In our recent work [5], we demonstrated numerically that the signatures of 2D KPZ in the polariton OPO are observable in both spatial correlations and the distribution of phase fluctuations, and are robust against the appearance of vortices. This result, alongside the recent progress observing KPZ in polariton experiments, highlights polariton OPO as a possible experimental platform for studying the 2D KPZ universality in the near future. [1] Q. Fontaine et al., arXiv:2112.09550 (2021) [2] E. Altman et al., Phys. Rev. X 5, 011017 (2015) [3] G. Wachtel et al., Phys. Rev. B 94, 104520 (2016) [4] A. Zamora et al., Phys. Rev. X 7, 041006 (2017) [5] A. Ferrier et al., Phys. Rev. B 105, 205301 (2022)

The interaction of infrared-active molecular vibrations with quantized field modes of optical cavities leads to the formation of light-matter hybrid states known as vibrational polaritons[1], which are conveniently probed experimentally by means of infrared spectroscopy[2]. Naturally, only a small number of molecular vibrational states hybridizes with resonantly tuned cavity modes, whereas a major fraction forms a manifold of purely molecular ``dark states''. In this contribution, we discuss the quantum dynamics and spectroscopy of strongly coupled rovibrational molecular ensembles in a multi-mode infrared cavity model extending recent work by Vib\'ok and coworkers[3]. Based on an adiabatic separation of ``slow'' rotational and ``fast'' vibro-polaritonic degrees of freedom, we interpret the light-matter hybrid system from a non-adiabatic perspective and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly-excited vibro-polaritonic states in a multidimensional angular coordinate branching space[4]. The VPCIs provide effective population transfer channels between upper and lower polariton surfaces characterized by rich interference patterns in rotational densities. From the non-adiabatic perspective, the manifold of degenerate ``dark states'' turns into a manifold of degenerate ``dark adiabatic surfaces'' located in the multi-dimensional angular coordinate space. Spectroscopically, we identify light-matter hybrid states containing molecular rovibrational and cavity photonic contributions, which emerge due to the non-trivial topology of the upper and lower vibro-polaritonic surfaces. The role of experimentally ubiquitous spontaneous emission from cavity modes in non-ideal optical cavities manifests as intensity reduction and broadening of peaks with substantial photonic contributions. Our study provides a starting point for the dynamics and spectroscopy of rovibrational molecular ensembles on crystalline surfaces strongly-coupled to optical cavity modes. [1] T. W. Ebbesen. Acc. Chem. Res. 49, 2403 (2016). [2] A. Shalabney et al. Nat. Commun. 6, 5981 (2015). [3] T. Szidarovszky et al. J. Chem. Phys. 154, 064305 (2021). [4] E. W. Fischer, P. Saalfrank. Accepted at J. Chem. Phys. (2022), Doi:10.1063/5.0098006.

Transition Metal Dichalcogenides (TMDCs), such as MoS2$_2$, MoSe2$_2$, WS2$_2$, WSe$_2$, are van der Waals layered semiconductors. The reduced dimension of their atomically thin monolayer form leads to much reduced dielectric screening of the electronic particles and also gives rise to very strong light-matter interaction. The optical properties of these material are dominantly governed by excitons with giant oscillator strength, which are fundamentally bosonic quasi-particles composed of Coulomb correlated electron-hole pair. In our lab, by fabricating TMDC heterobilayer, interlayer excitons with large dipole moment (0.5-1 nm*e) can be formed with electron and hole residing in different layers [1]. The spatial distribution of these particles can be modified by the Moiré potential landscape which is a function of the stacking angle of the bilayer. And more importantly, though the interlayer excitons usually bear weak oscillator strengths, the dipolar excitons composed of both the intralayer and interlayer excitonic components merit both large oscillator strength and dipole moment, which can possibly trigger very large excitonic non-linearity [2, 3]. By depositing the heterobilayer inside an optical micro-cavity, the strong coupling between cavity photons and the dipolar excitons can lead to strongly interacting dipolaritons. These structures are expected to host polaritonic blockade, Bose-Einstein condensation, Mott insulating phases, Bose-Hubbard physics, and even provide a solution to the future on-chip quantum simulators based on these condensed matter systems [4]. 1 Cristofolini, P., et al. C. Science, 2012, 336(6082): 704-707. 2 Zhang, L., et al. Nature, 2021. 591(7848): p. 61-65; 3 Li, W., et al. Nature materials, 2020, 19(6): p. 624-629. 4 Kennes, D.M., et al. Nature Physics, 2021, 17(2): 155-163.

We analytically study the localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. The quasi-continuum approximation reduces calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximation, we reduce the problem to the motion of the fictitious Newtonian particle in the potential well. We show that there exist running waves in the form of supersonic kinks and solitons and calculate their velocities and profiles. We show that the nonstationary smooth waves which are small perturbations on the homogeneous non-zero background are described by Korteweg-de Vries equation, and those on zero background – by modified Korteweg-de Vries equation. We also study the effect of dissipation on the running waves in JTL and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found. Finally in the framework of Stocks expansion we study the nonlinear dispersion and modulation stability in the discrete JTL.

We study the phenomena emergent from embedding a topological chain (TC) in a cavity under different conditions of the light-matter coupling. When the electromagnetic mode interacts with all the sites in the chain, the system reveals a second-order phase transition coming with a photon Gaussian state rendering. The nature of the resulting state allows for identifying the topological phase by measuring different experimentally accessible photon observables such as the Fano factor and the cavity quadrature fluctuations. Moreover, we show that typical quantum information entropies can be readily obtained from the cavity observables. Additionally, we show that selectively embedding sites of a TC provide an efficient resource to shift the localization of, or even the creation of new, topological qubits depending on the TC-cavity coupling geometry.

The quantum nature of light possesses many astonishing properties rendering it a promising candidate for novel spectroscopy methods of complex many body phenomena, quantum information processing and subwavelength lithography. Usually its quantum nature is described in the frequency domain and even for broadband quantum states of light a quasi-continuous-wave picture with a well-defined carrier frequency is still applicable. In this picture the Wigner function is used for a phase-space visualization of the states as well as for accessing their physical properties via the classical averaging of the corresponding quantities over the phase space. Extending this approach to pulsed ultrabroadband quantum light would lead to a quite involved description in terms of a large set of single-frequency or shaped temporal modes, where each mode has to be characterized separately. An alternative approach is to consider the quantum fields directly in the time domain. For example, considering the time-resolved behavior of the photonic ground state one can show that vacuum fluctuations of its electric field can be detected using the linear electro-optic effect [1,2]. In the corresponding setup a few-femtosecond near-infrared probe pulse is sent through a thin electro-optic crystal where it interacts with the vacuum in the mid-infrared (MIR) range and then analyzed. Furthermore, it is possible to formulate a consistent time-domain theory of the generation and time-resolved detection of few-cycle and subcycle pulsed squeezed states [3]. A slightly modified version of the setup enables the detection of the probability distribution of the analyzed probe field for arbitrary phase shifts, thus enabling a full quantum tomography of its state [4]. This should pave the way to the extraction of the phase-space distributions of the sampled MIR field with an extreme (subcycle) temporal resolution and to the development of ultrafast quantum spectroscopy of strongly correlated systems based on ultrashort pulses of quantum light. [1] C. Riek et al., Science 350, 420 (2015). [2] A.S. Moskalenko et al., Phys. Rev. Lett. 115, 263601 (2015). [3] M. Kizmann et al., Nat. Phys. 15, 960 (2019). [4] M. Kizmann et al., Laser Photonics Rev. 16, 2100423 (2022).

Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. Here we investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator. Using unbiased numerical matrix product state methods for time-dependent spectral functions, we find that driving of the correlated charge-density wave insulator leads not only to a renormalization of the excitation spectrum as predicted by an effective Floquet Hamiltonian, but also to a cosine-like in-gap feature. This is not obtained for a charge density wave model without interactions. A mean-field treatment provides a partial explanation in terms of doublon excitations. However, the full picture needs to take into account strong correlation effects. arXiv:2205.09557

The realisation of QED within materials makes the following question experimentally and technologically relevant: How are the interactions between the constituents of matter (electrons) affected by preparing the force carrier (photon) in different quantum states? In this work, we address this question by developing the necessary quantum-field-theoretical approach, extending standard scattering and many-body theory. We find that an additional scattering structure emerges which reflects the Hilbert-space distribution of the carrier quantum state. We demonstrate that this emergent structure can dramatically affect collective phenomena using the example of superconductivity mediated by cavity photons prepared in pure Fock states.

Rotational misalignment or twisting of two mono-layers of graphene strongly influences its electronic properties. Structurally, twisting leads to large periodic supercell structures, which in turn can support intriguing strongly correlated behaviour. Here, we propose a highly tunable scheme to synthetically emulate twisted bilayer systems with ultracold atoms trapped in an optical lattice. In our scheme, neither a physical bilayer nor twist is directly realized. Instead, two synthetic layers are produced exploiting coherently-coupled internal atomic states, and a supercell structure is generated via a spatially-dependent Raman coupling. To illustrate this concept, i present a synthetic square bilayer lattice and show that it leads to tunable quasi-flatbands and Dirac cone spectra under certain magic supercell periodicities.

Quantum spin models coupled to bosonic modes are relevant to diverse problems such as cavity quantum electrodynamics or low-dimensional magnetic structures coupled to an environment. Already in thermal equilibrium, the numerical solution of spin-boson models is a challenging task. Using a recently-developed wormhole quantum Monte Carlo method for retarded spin interactions, we present high-accuracy results for a variety of problems: (i) We demonstrate that the method reproduces the mean-field transition in the U(1)-symmetric Dicke model to high precision. (ii) For a single spin that is coupled to a sub-ohmic bosonic bath in an SU(2)-symmetric way, we find a quantum phase transition between a critical phase predicted by the perturbative renormalization group (RG) and a localized strong-coupling phase. As the bath dimensionality can be tuned continuously, we provide direct numerical evidence for the collision and annihilation of two RG fixed points, with a surprising duality between the two fixed-point solutions and numerical evidence for the unconventionally slow RG flow close to the collision. (iii) For the one-dimensional Heisenberg chain, we demonstrate that any finite coupling to an ohmic bath stabilizes long-range antiferromagnetic order. This is in stark contrast to the isolated chain where spontaneous breaking of the SU(2) symmetry is forbidden by the Mermin-Wagner theorem. All in all, our results demonstrate the power of the novel wormhole quantum Monte Carlo approach, which permits future applications to spin-boson models relevant to cavity quantum electrodynamics.