Topological Matter in Artificial Gauge Fields

Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also show how this gauge field can be used to design waveguides in which sound propagates with robustness against disorder as a consequence of the change in topological polarization that occurs along a domain wall. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may potentially be exploited for the design of sound amplification by stimulated emission of radiation (SASERs, the mechanical analogs of lasers.)

In superfluid 4He, due to strong interactions, the density profile of a vortex line, as computed with Quantum Monte Carlo, deviates from what predicted by Gross–Pitaevskii (GP) mean-field. We find that the basic features of this density modulation are recovered in wave–packets of a single rotonic excitation. This suggests to correct the current GP-based view of a vortex reconnection event as a source of phonon waves, by including emission of rotons. Experiments at low temperature of quantum evaporation should be able to detect these non-thermal rotons.

Ultracold atoms are a versatile system to study the fascinating phenomena of gauge fields and topological band structures. By Floquet driving of optical lattices, the topology of the Bloch bands can be engineered. In this poster, we present experimental schemes for momentum-resolved Bloch state tomography, which allow mapping out the Berry curvature and obtaining the Chern number. Furthermore, we discuss the dynamics of the wave function after a quench into the Floquet system. We observe the appearance of dynamical vortices, which trace out a closed contour, the topology of which can be directly mapped to the Chern number. Our measurements provide a new perspective on topology and dynamics and a unique starting point for studying interacting topological phases.

Spin-Orbit (SO) coupling, which links a particle's spin to its motion, has a crucial role in the electronic properties of many condensed matter systems, and it is at the basis of phenomena such as the spin-Hall effect and topological insulators. The high level of control of ultracold atoms makes them ideal candidates to engineer the spin-orbit coupling in neutral systems [1]. Here we show that by dressing three atomic internal states of a Bose-Einstein condensate (BEC) with two pairs of lasers in a double Raman configuration, such three atomic spin states of the BEC become coupled and a triple-well in the 2D lowest band of the single atom dispersion relation is obtained. The distance between the centres, heights of the barriers, and the energy bias of the triple well in momentum state can be engineered by an appropriate manipulation of the laser intensities and detunings while tunneling in momentum space is induced by the external trapping potential. Interaction-dependent quantum phase transitions of the BEC ground state in such a triple-well potential in momentum space are predicted. [1] Y. Zhang, M. E. Mossman, Th. Busch, P. Engels, and C. Zhang, Frontiers of Physics 11, 118103 (2016).

Motivation: Previous works aiming to modify the Fermi velocity in Dirac materials require cumbersome setups [1-3]. It is thus desirable to find new ways to tune this fundamental parameter. Our proposal is to embed different Dirac materials in a uniform electric field, something readily achievable in experiments. Systems: Topological crystalline insulator/semiconductor interface, armchair graphene nanoribbons and carbon nanotubes. Main result: The Fermi velocity is significantly reduced with increasing the transverse electric field in Dirac materials. This result has been tested via continuum (Dirac equation), tight-binding and ab initio approaches [4-5]. [1] G. Li et al., Nat. Phys. 6, 109 (2010). [2] C. Hwang et al., Sci. Rep. 2, 590 (2012). [3] D. C. Elias et al., Nat. Phys. 7, 701 (2011). [4] A. D. F. et al., Scientific Reports 7, 8058 (2017). [5] A. D. F. et al., Physica E 93, 230 (2017).

We introduce the scientific goals, the engineering progress and the new technology being developed at the new dysprosium lab being built at MIT.

When considering topological states we usually use the bulk-edge correspondence to look for their existence. In this work we will not use the bulk-edge correspondence, instead, we will construct both the edge and bulk eigenfunctions analytically. It is known that the bulk states of certain topological models can be constructed via Bloch's theorem. We will discuss a general approach to construct the bulk states of a finite system in one dimension. Then by extending Bloch's theorem, we construct the exact edge state eigenfunctions. We fully prescribe a method of obtaining the form and properties of the edge and bulk eigenfunctions for a given one-dimensional periodic model. We extend the method to two dimensions by considering the dimensionally separable Hofstadter model. We also show that this method can be utilized to consider the robustness of a model to a static impurity localized to the edge or in the two-dimensional case a line defect across the edge. We observe that the presence of a single edge impurity can have a drastic effect on the edge state of a system. On increasing the impurity strength, for certain models, the topological edge state can be replaced (or joined) by a trivial bound state of the impurity, with an energy of the order of the impurity strength.

Controlling quantum states by temporally periodic driving is actively studied with the use of the Floquet theory. In such driven systems we can realize exotic properties which cannot be exhibited in undriven equilibrium states. In this study we analyze the Schwinger model, (1+1)-dimensional quantum electrodynamics (QED), under temporally periodic electric field. Since the Schwinger model is a relativistic theory with fermions, we can expect chiral anomaly. We show that the periodic external field plays a role to shift the energy dispersions oppositely for right- and left-handed fermions, which is nothing but the spectral flow nature of the chiral anomaly, and that this leads to temporally oscillating chiral condensate.

We report on two dierent approaches to the quantum simulation of Hall-like systems subjected to an articial gauge eld. Adopting an innovative scheme we engineer an hybrid two dimensional lattice characterized by a \real" dimension, provided by a 1D optical lattice, and a \synthetic" dimension encoded in the internal degrees of freedom of 173Yb. In the rst experiment [1] the synthetic dimension is mapped by performing a Raman coupling between the hyperne states (F = 5=2) of the ground state of 173Yb. In this kind of experimental setup we observed chiral edge states, as well as their \skipping" trajectories. In the second major experiment [2] we demonstrate a new method to synthesize spin-orbit interaction which exploits the ultranarrow clock transition between the 1S0 and the long-lived 3P0 state in degenerate 173Yb atoms. For the rst time we characterize the dependence of the amplitude of the chiral current on the magnetic ux, providing a direct evidence of the inversion of the chiral current sign when the magnetic ux increases above . In second experiment the presence of spin-orbit coupling has been detected by means of clock transition spectroscopy, as proposed in [3], also taking advantage of a 642 km-long optical ber link infrastructure connecting LENS to the Italian National Metrology Institute (INRiM).

Topological insulators in the AIII symmetry class lack experimental realization. Moreover, fractionalization in one-dimensional topological insulators has not been yet directly observed. Our work might open possibilities for both challenges. We propose a one-dimensional model realizing the AIII symmetry class which can be realized in current experiments with ultracold atomic gases. We further report on a distinctive property of topological edge modes in the AIII class: in contrast to those in the well studied BDI class, they have non-zero momentum. Exploiting this feature we propose a path for the detection of fractionalization. A fermion added to an AIII system splits into two halves localized at opposite momenta, which can be detected by imaging the momentum distribution.

Optical lattices filled with ultra-cold atomic gases can be thought of as a counterpart of solid state systems, where the optical lattice plays the role of the ionic potential, while ultra-cold atoms act as the charge carriers. Recent development in experimental techniques allowed to investigate correlation functions and transport phenomena in such systems. We study the Bose-Hubbard model in the quantum rotor approach, which allows us to take into account spatial dependencies, such as dimensionality, lattice geometry, and influence of the gauge potentials. We calculate conductivity of bosons in a two-dimensional lattice in synthetic magnetic field. In such scenario, two types of conductivity can be distinguished, intra- and inter-band. The interband contribution, usually omitted in analysis of multiband systems, appears to have a crucial role in the transport properties as its values are a few orders of magnitude greater than the intraband one.

Inspired by the recent experimental advances in the study of ultracold atoms trapped in optical lattices, we consider models of fermions hopping in ladder geometries and subject to artificial magnetic fluxes such as [1, 2, 3]. By applying the concept of resonances in chiral currents [2], we find a parameter (momentum component of the current in Fourier space), distinguishing between trivial and quantum Hall (QH) phases in non-interacting cases. We aim for evidence about fractional QH phases: In case of nearest-neighbor Hubbard interactions, we identify a gap in the spin sector of the corresponding Luttinger liquid leading to a resonant state at fractional filling factor v =1/2. We support our analytic results with matrix product sates (MPS) simulations [3]. References: [1] L. Mazza, M. Burrello et. al, New J. Phys. Volume 17, 105001 (2015) [2] E. Cornfeld and E. Sela, Phys. Rev. B Volume 92, 115446 (2015) [3] A. Haller, M. Rizzi and M. Burrello, arXiv:1707.05715 (2017)

Charge pumps in 1D systems can be used to probe the topology 2D systems by associating a cyclic Hamiltonian parameter with an artificial quasi-momentum. We use this mapping to investigate topological phase transitions in the presence of interactions.

Recent cold atom experiments have realized artificial gauge fields in periodically modulated optical lattices [1,2]. We study the dynamics of atomic clouds in these systems by performing numerical simulations using the full time-dependent Hamiltonian and comparing these results to the semiclassical approximation. Under constant external force, atoms in optical lattices with flux exhibit an anomalous velocity in the transverse direction. We investigate in detail how this transverse drift is related to the Berry curvature and Chern number, taking into account realistic experimental conditions. [1] G. Jotzu et al., Nature 515, 237 (2014). [2] M. Aidelsburger et al., Nature Phys. 11, 162 (2015).

Quantum fluids such as ultracold condensate of bosonic atoms has long been suggested as an important candidate for sonic black hole. Existence of such analogue black hole, their event horizon, and related Hawking radiation was recently confirmed experimentally. In this work we report a study of such sonic black hole in the pseudo-spin-1/2 Bosons, the related modification of the sonic horizon as well as the analogue space-time metric.

The main feature of topological phases is the presence of robust boundary states, which appear for example in the form of chiral edge states in Chern insulators and open Fermi arcs on the surfaces of Weyl semimetals. Recently, new higher-order topological phases were proposed in the form of corner and hinge states. Even though, noninteracting, topological systems can be straightforwardly described by fully periodic systems, the understanding of the corresponding boundary states has almost exclusively relied on numerical studies. We devised a generic recipe for constructing D-dimensional lattice models whose d-dimensional boundary states, located on edges, surfaces, corners, hinges and so forth, can be obtained exactly. The solvability of these states is rooted in the underlying lattice structure and does not as such depend on fine-tuning, which allows us to track their evolution throughout various phases and across phase transitions. On my poster, I present the generic method with which to find these exact solutions and provide explicit examples of chiral, edge states, Fermi arcs, corner states and topologically protected hinge states. This is based on Phys. Rev. B 96, 085443 (2017) and arXiv: 1712.07911.

Higgs and Goldstone modes are possible collective modes of an order parameter upon spontaneously breaking a continuous symmetry. Whereas the low-energy Goldstone (phase) mode is always stable, additional symmetries are required to prevent the Higgs (amplitude) mode from rapidly decaying into low-energy excitations. In high-energy physics, where the Higgs boson has been found after a decades-long search, the stability is ensured by Lorentz invariance. In the realm of condensed–matter physics, particle–hole symmetry can play this role and a Higgs mode has been observed in weakly-interacting superconductors. However, whether the Higgs mode is also stable for strongly-correlated superconductors in which particle–hole symmetry is not precisely fulfilled or whether this mode becomes overdamped has been subject of numerous discussions. Experimental evidence is still lacking, in particular owing to the difficulty to excite the Higgs mode directly. Here, we observe the Higgs mode in a strongly-interacting superfluid Fermi gas. By inducing a periodic modulation of the amplitude of the superconducting order parameter $\Delta$, we observe an excitation resonance at frequency $2\Delta/h$. For strong coupling, the peak width broadens and eventually the mode disappears when the Cooper pairs turn into tightly bound dimers signalling the eventual instability of the Higgs mode.

In condensed matter physics, gauge theories are often considered as an “emergent” phenomenon. They appear as an effective description of the collective behavior of some interacting systems at low energy. However, we could also reverse this methodology: taking gauge theories and some other degrees of freedom as initial inputs, it may give rise to exotic orders that correspond to the collective behavior of some underlying model. That is, instead of the gauge theory, the order is emerging. In this presentation, I will attempt to give examples of this scenario by considering ordinary $O(n)$ rotors coupled with, typically discrete, gauge theories. This produces various “emergent” orders. I will discuss the meaning of these orders from a perspective of statistical physics, in the hope that they can be realistic under the rapid development of engineering artificial gauge fields.

When non-interacting Bose-Einstein condensate is confined to a quasi one-dimensional channel it will spread due to dispersion as dictated by the Schrödinger equation. The spreading rate can be affected by changing the interaction between the atoms via the Feshbach resonance. If the interaction is set to just the right value, the attraction between atoms exactly compensates the dispersion. In this case the BEC doesn't spread and we get a bright matter-wave soliton. The maximum number of atoms in a soliton is limited by the frequency of the channel and the interaction between atoms. By setting the inter-atom interaction to different attractive values we are able to create soliton trains with different number of solitons from elongated BECs.

The fractional quantum Hall effect, which can be realized in certain two-dimensional systems at low temperature and high magnetic field, leads to many interesting properties, such as the possibility to have anyonic quasiparticles that are neither bosons nor fermions. There is currently much interest in investigating the possibilities for having fractional quantum Hall physics in lattice systems, both because it may lead to new ways to realize the effect, and because the lattice gives rise to new features and opportunities. Here, we propose a quite general approach based on conformal field theory to obtain lattice fractional quantum Hall models. The models have analytical ground states, and we use Monte Carlo simulations to compute, e.g., topological entanglement entropies and shape and statistics of anyons. We also discuss how one can interpolate between lattice and continuum fractional quantum Hall models and propose a scheme to implement a related model in ultracold atoms in optical lattices.

We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time-dependent and contains extra terms appearing due to changes in the periodic driving. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly changing direction. The effective evolution of the spin is then associated with non-Abelian geometric phases reflecting the geometry of the extended Floquet space. The developed formalism is general and also applies to other periodically driven systems, such as shaken optical lattices with a time-dependent shaking strength, a situation relevant to the cold atom experiments.

The dynamics in solid state systems is not only governed by the band structure but also by topological defects of the Eigenstates. A paradigmatic example are the Dirac points in graphene. For this system with a two-atomic basis the linear dispersion relation at the Dirac points is accompanied by a vortex of the azimuthal phase of the Eigenstates. In a time-of-flight (ToF) expansion the Eigenstates interfere and the resulting signal contains information about the azimuthal phase. We present a versatile detection scheme that uses off-resonant lattice modulation to extract the azimuthal phase from the ToF signal. This detection scheme is applicable to a variety of two-band systems and can be extended to general multi-band systems.

The effect of disorder on zero temperature phase diagram of two dimensional Bose Hubbard model has been studied in presence of artificial gauge field. Employing single site gutzwiller mean field theory, we incorporate the effect of disorder which shows the presence of Bose glass phase which impedes the direct transition from mott insulator to superfluid phase. Incorporating nearest neighbour interaction, at nearest neighbour strength, VN = 0:02, the density wave states first starts to appear. Applying disorder in this regime shows the co-existence of Bose glass and disordered solid phase depending on the nature and distribution of the disorder. Furthermore, we report the effect of synthetic magnetic field on Bose glass phase.

We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with zig-zag, bearded and armchair boundaries. In contrast with the fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states are tunable. Additionally, when a non-trivial gap is induced, we find that some of the edge states are topologically protected and also tunable. Our results may explain the origin of the novel edge states recently observed in photonic lattices.

We study ultra-cold bosonic atoms in optical lattice with gauge potentials. In order to describe these systems, we use Bose-Hubbard model in quantum rotor approximation. This allows us to include influence of spatial correlation – necessary in correct description of lattices with non-zero Chern number such as Haldane model. We calculate the optical Hall conductivity and present its dependence on the temperature and model parameters. We identify two main transport channels and excitation related to them. The results show that the spectral properties of the Berry curvature influences the transverse transport.

The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.

Recent theoretical and experimental studies have shown that it is possible to simulate artificial magnetic fields with ultracold atoms in optical lattices [1]. In particular, the possibility to implement chiral, topologically protected edge states analogous to those found in the context of quantum Hall physics has been demonstrated both for fermionic and bosonic atoms [2,3]. In this work, we propose an alternative strategy to implement robust edgelike states (ELS) with an ultracold atom carrying orbital angular momentum (OAM) in a diamond-chain optical lattice. The existance of these states is due to quantum interference effects, and they can be intuitively constructed as combinations of three-site spatial dark states (SDS). These states are very robust against different types of deffects [4] and form a zero-energy flat band. For states with one unit of OAM, the l=1 case, the tunneling amplitudes depend both on the spatial localization and the winding number of the local states, and they may become complex depending on the relative position of the sites [5]. The ELS implemented in this manifold can display global chirality. In addition, the angular momentum degree of freedom opens a gap in the band structure that is not present in the absence of OAM, resembling the effect of a net flux through the plaquettes [6]. Finally, in the limit of unit filling and strong interactions we study the mapping of the system into a spin-1/2 model with two-body nearest neighbour interactions [7]. References [1] M. Aidelsburger, S. Nascimbene, N. Goldman, arXiv 1710.00851. [2] M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Science 349, 1510-1513 (2015). [3] B. K. Stuhl, H.I. Lu, L.M. Aycock, D. Genkina, and I.B. Spielman, Science 349, 1514-1518 (2015). [4] G. Pelegrí, J. Polo, A. Turpin, M. Lewenstein, J. Mompart, and V. Ahufinger, Phys. Rev. A 95, 013614 (2017). [5] J. Polo, J. Mompart, and V. Ahufinger, Phys. Rev. A 93, 033613 (2016). [6] A. A. Lopes and R. G. Dias, Phys. Rev. B 84, 085124 (2011). [7] G. Pelegrí et al, in preparation.

Strontium opens new perspectives for Hamiltonian engineering because it is an alkaline-earth element with narrow intercombination lines, metastable excited electronic states, and ten collisionally-stable SU(N)-symmetric nuclear spin states. We have built a new versatile Sr machine with quantum gas microscope capability. After precooling on a broad blue transition, we collect 107 atoms at 2 µK in a narrow-line red MOT, load them into a 1064 nm dipole trap, and evaporatively cool them to obtain either a BEC or a degenerate Fermi gas of ~105 atoms. We have now also observed for the first time the doubly-forbidden 1S0 - 3P2 transition in 87Sr by direct laser excitation, which opens up possibilities for quantum computation and gauge field engineering.

The properties of prototypical examples of one-dimensional free fermionic systems undergoing a sudden quantum quench between a gapless state characterized by a linear crossing of the energy bands and a gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis, we observe an anomalous non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions. We show that the latter is governed by a Klein-Gordon equation with a mass related to the gap opening mechanism and an additional source term, which depends on the gap as well. The competition between the two terms explains the presence of the non-monotonous behavior. We conclude by arguing the stability of the phenomenon in the cases of non-sudden quenches and higher dimensionality.

The discovery of fractional quantum Hall effect (FQHE) in 2D electron gas gave rise to immense interest in topological phases of matter. One of the most intriguing features of FQH state is fractionally charged excitations which embody anyonic statistics. Nowadays, experiments in optical lattices allow much more controllable study of many-body systems, therefore allowing regimes that are impossible to realise in semiconductor based experiments. Historically, FQHE comes from condensed matter systems, which can be characterized by a very large number of particles, as a consequence, theoretical studies were focused only on infinite or periodical Hamiltonians. However, few of the unanswered questions remain: can FQHE states be realised in minuscule lattices, containing only several sites in diameter, and what additional effects would open boundaries produce? These questions are interesting not only from the fundamental point of view, but are crucial for the design of a experiment in optical lattices. Using numerical diagonalization of interacting Harper-Hofstadter Hamiltonian we were able to observe localisation of fractional charge excitations in a square lattice using two different techniques.

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)]. The poster discusses the behaviour of observables in the quasistationary regime going beyond the range of driving parameters studied previously.

Exotic states of matter, including high-Tc superconductors, and topological phases, have long been a focus of condensed matter physics. With the recent advent of artificial spin-orbit coupling in ultracold gases, and the remarkable experimental control and enhanced interactions provided by optical lattices, a broad range of novel strongly correlated systems are quickly becoming experimentally accessible. One system of particular interest, given its potential impact on spintronics and quantum computation, is the attractive Fermi gas with spin-orbit coupling in a 2D optical lattice. Here we examine the combined effects of Rashba spin-orbit coupling and interaction in this system, with particular focus on the unique pairing, charge, and spin properties of the ground state, which is computed using the numerically exact auxiliary-field quantum Monte Carlo technique. We also study the behavior of edge currents, which are a potential precursor of various topological phenomena, such as Majorana fermions. In addition to illuminating the behavior of this exotic charge ordered superfluid state, our results serve as high-accuracy benchmarks for the coming generation of precision experiments with ultra-cold gases. Finally, we provide an outlook on future directions, including the addition of a Zeeman field to induce a spin polarization, in order to investigate finite-momentum pairing states and topological superconductivity.

We propose a novel scheme for a quantum heat pump powered by rapid time-periodic driving. We focus our investigation on a system consisting of two coupled driven quantum dots in contact with fermionic reservoirs at different temperatures. Such a configuration can be realized in a quantum-gas microscope. Theoretically we characterize the device by describing the coupling to the reservoirs using the Floquet-Born-Markov approximation.

Fermionic Gaussian states are completely characterized by their two-point correlation functions. These are collected in the so-called covariance matrix, which then becomes the main object in their description. We derive a time-dependent variational description of (1+1)-dimensional gauge theories using the framework of lattice gauge theories as well as fermionic Gaussian states. We compare our results to previously obtained results via matrix product states for ground-state properties and real-time dynamics. Specifically, we investigate the phase transition between the string and string-breaking phases among other properties in the massive Schwinger model and other non-Abelian generalizations

Periodic driving can be used to coherently control the properties of a many-body state and to realize new phases which are not accessible in static systems. In this context, cold fermions in optical lattices provide a highly tunable platform to investigate driven many-body systems and additionally offer the prospect of quantitative comparisons to theoretical predictions. We implement a driven Fermi-Hubbard model by periodically modulating a 3D hexagonal lattice. In the regime where the drive frequency is much higher than all other relevant energy scales, we verify that the interacting system can be described by a renormalized tunneling. Furthermore, we achieve independent control over the single particle tunneling and the magnetic exchange energy by driving near-resonantly to the interaction. As a consequence, we are able to show that anti-ferromagnetic correlations in a fermionic many-body system can be enhanced or even switched to ferromagnetic correlations. The implementation of more complex modulation schemes opens the possibility to combine the physics of artificial gauge fields and strongly-correlated systems.

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.

Without interactions, 1D charge pumps can be mapped onto 2D topological systems. The 1D superlattice then corresponds to the transversal kinetic energy. 1D charge pumps are readily realized experimentally. We add 1D repulsive interactions of Fermions and find topologically non-trivial Mott insulators and band insulators. The latter exhibit a topological phase transition which can be understood with an effective 1D model for strong superlattices and interactions.

The idea of inserting a local magnetic flux, representing the field of a thin solenoid, plays an important role in various condensed matter models, especially in the understanding of topological systems. One example is the creation and manipulation of quasiparticle or hole excitations in these systems, which are essential for fault-tolerant quantum information processing. Implementing such local fluxes in cold atom experiments promises great potential. Here, we propose an experimental scheme to realize a local flux in a cold atom setting which takes advantage of the recent developments in synthetic gauge fields and quantum microscopes. To demonstrate the feasibility of our method, we consider quantum-Hall-type lattice systems and study the dynamical creation of topological excitations. We analyze the adiabatic charge pumping by tuning the strength of the local flux.

Different topologically properties have been found static system. Different in the sense, topological properties depending on the dimension and the symmetry. Here, we explore them for periodically driven system. It has been seen that trivial system in static phase can be made topological by the application of periodic driving. Not only that, we can also have phases where the topological invariant for the bands vanishes eventhough it is topological, aka anomalous phases or Floquet topological insulator. From there, we try to realize such system in photonic system, more precisely waveguide arrays. And we calculate phase diagrams using bulk-boundary correspondence.

The realization of artificial gauge fields in optical lattice systems paves a route to the experimental investigation of various topological quantum effects. Here we propose a realistic scheme to locally control artificial gauge fields and to directly probe topological transport effects in Hofstadter optical lattice. In that case the system can be effectively described by a modified Hofstadter Hamiltonian with an additional flux in some individual plaquette. By treating this additional flux as a pump parameter, a different paradigm for quantum charge pumping can be created. Considering that varying gauge field with time gives rise to synthetic electric fields, which in turns affects the particle distribution, a gauge dependent dynamic happens here. As well as that, topological edge currents in a two-dimentional optical lattice can also be generated. Since all these effects are manifested on the spatial density distribution, with recent advances of microscopic manipulations in optical lattices, a direct detection of such topological properties could be achieved in the near future.

Ultracold atoms in optical lattices provide clean and tunable systems to realize many-body quantum physics. They can be used to simulate a variety of effects ranging from superconductivity and superfluidity to novel phases of matter. Particles trapped in an optical lattice are neutral so the Lorentz force does not affect them. A workaround resolving this issue is the introduction of an artificial gauge field that generates magnetic flux. It can be created by using laser assisted tunneling and periodic driving schemes. This also allows to realize a stronger magnetic flux per lattice plaquette than typically available in solid state experiments. In this work, we propose a driving scheme for a quasi-one dimensional ladder lattice that induces a tunable artificial magnetic flux through the lattice plaquettes. By manipulating the shaking phase for each individual site, this flux can be made inhomogeneous in space. It allows us to explore the dynamics and control capabilities of an atomic wave-packet propagating in such a lattice.