Session S02: Many Body and Nonequilibrium Systems

Emergence of local equilibrium in a boundary-driven quantum chaotic system

Quantum chaos is expected to be sufficient to allow even single eigenstates of a many-body Hamiltonian to achieve thermal equilbrium. Here we investigate the role of quantum chaos in reaching local equilbrium for a classic non-equilibrium scenario: a system in contact with two reservoirs held at different chemical potentials. To realize quantum chaotic behavior in our model we study a two-parameter family of Brownian circuits acting on a chain of spin-1/2s or qubits, such that the only conserved quantity is the total z component of the spin. We find that, for all parameters of the model, the time-averaged correlation functions agree and are close to local equilibrium; however, computing the total entropy of the system shows that there are, in fact, three distinct phases of the driven problem, with local equilibrium only emerging in the quantum chaotic region of parameter space. Our results suggest a generic picture for the emergence of local equilibrium in current driven quantum chaotic systems, as well as provide insights into methods to stabilize highly-entangled many-body states out of equilibrium.   

Pairing in the Peierls/Su-Schrieffer-Heeger(SSH) model: From light spinful bipolarons to self-trapping of hard-core pairs and repulsive bipolarons

It is widely accepted that strong particle-phonon coupling generally makes the resulting polarons and bipolarons heavy, with masses increasing smoothly with the coupling strength with no self-trapping transitions. This is the characteristic behaviour in the Holstein and Fr{\"o}hlich models. Here, we study the one-dimensional Peierls/Su-Schrieffer-Heeger(SSH) model necessary for describing coupling of hopping to breathing-mode distortions in certain oxides, polyenes and quantum simulators based on ultracold lattice systems. We show that the Peierls interactions bind polarons into light bipolarons, which could undergo Bose-Einstein condensation at high temperatures. This proves that phonon-mediated high-Tc superconductivity is possible. We also find that for particles with hard-core statistics, interactions mediated by Peierls phonons are repulsive. The interplay of hard-core statistics and phonon-mediated hopping leads to a transition characterized by flattening of the bipolaron dispersion, suggestive of self-trapping. The repulsive phonon-mediated interactions also lead to a repulsively bound bipolaron state appearing above the two-polaron continuum. These results provide a specific path to utilize Peierls coupling to control superconductivity and quantum transport.   

Dynamical phase transitions in a collective Heisenberg model simulated with harmonically trapped ultracold fermions

The collective Heisenberg spin model is a textbook model for magnetism and superconductivity. It describes localized spins interacting via long-range exchange interactions. We discuss a quantum simulation of this model using tens of thousands of potassium atoms trapped in a three-dimensional harmonic oscillator, without an optical lattice. Using a Feshbach resonance to tune the interactions between spin-up and spin-down potassium atoms to be weak, mode-changing collisions can be suppressed during the time of the experiment. Atoms remain in their initial single-particle eigenmodes, which form a lattice in mode space. We study spin dynamics initiated with a $\pi/2$ pulse, and observe competition between interactions and an inhomogenous effective magnetic field (due to a real-space field curvature, which maps onto a mode-space field gradient). Varying both the strength of interactions and of inhomogeneity, we observe a dynamical phase transition between ferromagnetic dynamics and ungapped paramagnetic dynamics. We find excellent agreement with calculations based on a mean-field treatment of a collective Heisenberg model, with all-to-all couplings.   

Universal behaviors for the dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates

We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is sweeped. Three distinct dynamical regions are identified corresponding to different sweeping time scales ($\tau$), manifested by the excitation probability $\mathcal{P}$ and the heat density $\mathcal{Q}~$. We show that the adiabatic region of $~\mathcal{P}$ $\sim$ $\mathcal{Q}$ $\sim$ $\tau^{-2}~$ follows from the Landau-Zener theory, while the non-adiabatic universal region of $~\mathcal{P}$ $\sim$ $\mathcal{Q}$ $\sim$ $\tau^{-1}~$ in the thermodynamic limit is described by the Kibble-Zurek mechanism. The dynamical Kibble-Zurek scaling is postulated for a finite-size system in the latter region and several experimentally falsifiable features are predicted. The region of the fastest time scale is found to be non-universal and far-from-equilibrium with $\mathcal{P}$ and $\mathcal{Q}$ essentially being constants independent of $\tau$.   

Spontaneous Emission in a System of Atomic Matter Wave Emitters

One of the most fundamental examples of an open quantum system is the exponential decay of an excited two-level atom, described by the Wigner-Weisskopf model. However, the Markov approximation underlying this model can be violated under certain conditions, and recent experiments on optical decay in photonic band-gap (PBG) materials have indeed started to find deviations from its predictions. We present an experimental realization \footnote{L. Krinner, arxiv 1712.07791} of a model \footnote{I. de Vega et. al, Phys. Rev. Lett. 101, 260404, 2008}\footnote{M. Stewart et. al, Phys. Rev. A 95, 013626, 2017} for an ``artificial atom'' emitting atomic matter-wave rather than optical radiation, in which the vacuum coupling and the excited-state energy can be controlled at will. The experiments are performed using an optical lattice geometry, which provides arrays of such artificial atoms. We are able to observe Markovian and strongly non-Markovian dynamics in this system, including exponential and partly reversible oscillatory decay, atom re-absorption, as well as a bound state for emission below the band edge of the mode continuum, which is a direct analog of the long-predicted atom-photon bound state in PBG-materials.   

Quench-Induced Phase Separation Dynamics in Two-Component Bose Einstein Condensates

We investigate the many-body quench dynamics of a binary Bose-Einstein condensate crossing the miscibility-immiscibility threshold and vice versa. For particle balanced mixtures the increasement of the interspecies repulsion leads to the filamentation of the density of each component. These filaments are found to be strongly correlated exhibiting domain-wall structures. Following the reverse quench scenario multiple dark-antidark solitary waves are spontaneously generated and subsequently decay. In the case of particle imbalanced mixtures fragmented domain-wall-bright complexes arise which appear to be strongly entangled. Finally, we utilize single-shot simulations to relate our findings to possible experimental realizations.   

Long-time expansion of a Bose-Einstein condensate: Does the interacting many-particle system show Anderson localization?

We numerically explore the long-time expansion of a one-dimensional Bose-Einstein condensate (BEC) in a disorder potential employing the Gross-Pitaevskii equation. We address the fundamental question whether unique signatures of Anderson localization are observable in the presence of particle-particle interactions. We compare different expansion scenarios in which particle-particle interactions are selectively switched on or off. Using typical experimental parameters, we show that the time scale for which the nonequilibrium dynamics of the interacting system begins to diverge from that of the noninteracting system exceeds the observation times up to now accessible in the experiment. We find evidence that the long-time evolution of the wave packet is characterized by (sub)diffusive spreading and a growing effective localization length suggesting that interactions destroy Anderson localization. \\ $[1]$ S. Donsa et al., Phys. Rev. A \textbf{96} (4), 043630 (2017).   

Transport properties across the many body localization transition in quasiperiodic and random systems

We will present our comparative study of non-equilibrium dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity and the return probability and study their average low-frequency and long-time power-law behavior, respectively. We find that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. We analyze the distributions of the DC conductivity and test the activated dynamical scaling ansatz in both models. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.   

Nonequilibrium Quantum Phase Transition in a Hybrid Atom-Optomechanical System

We consider a hybrid quantum many-body system formed by a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. The adiabatic elimination of the light field yields an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. At a critical atom-membrane interaction, we find a nonequilibrium quantum phase transition from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, the energy of the lowest collective excitation vanishes, and a strong atom-membrane entanglement arises. The effect occurs when the atoms and the membrane are nonresonantly coupled.   

Dynamics of spin systems realized in trapped ions, atoms, and molecules from numerical cluster methods

Interaction quenches drive interesting dynamics such as long-lived nonequilibrium quantum states and dynamical quantum phase transitions. We utilize numerical linked cluster expansions and moving-average cluster expansions (MACE) to calculate the quench dynamics of the magnetization and correlations in two-dimensional transverse field Ising and XXZ models evolved from a product state. Such dynamics are directly probed in ongoing experiments in ultracold atoms, molecules, and ions. Both numerical methods give more accurate results at short-to-moderate times than exact diagonalization for an equivalent computational system size. In addition, MACE and exact results coincide up to an error term which is provably constrained by a modified Lieb-Robinson bound. This furnishes a rare example of a numerical algorithm with a rigorous error bound. Beyond these quenches, we study dynamical quantum phase transitions in spin systems (as indicated by nonanalytic Loschmidt echo) and give preliminary results.