Thermal fluctuations tend to destroy long-range phase correlations. Consequently, bosons in a lattice will undergo a transition from a phase-coherent superfluid as the temperature rises. Contrary to common intuition, however, we show that nonequilibrium driving can be used to reverse this thermal decoherence. This is possible because the energy distribution at equilibrium is rarely optimal for the manifestation of a given quantum property. We demonstrate this in the Bose-Hubbard model by calculating the nonequilibrium spatial correlation function with periodic driving. We show that the nonequilibrium phase boundary between coherent and incoherent states at finite bath temperatures can be made qualitatively identical to the familiar zero-temperature phase diagram, and we discuss the experimental manifestation of this phenomenon in cold atoms.
Thermal fluctuations tend to destroy long-range phase correlations. Consequently, bosons in a lattice will undergo a transition from a phase-coherent superfluid as the temperature rises. Contrary to common intuition, however, we show that nonequilibrium driving can be used to reverse this thermal decoherence. This is possible because the energy distribution at equilibrium is rarely optimal for the manifestation of a given quantum property. We demonstrate this in the Bose-Hubbard model by calculating the nonequilibrium spatial correlation function with periodic driving. We show that the nonequilibrium phase boundary between coherent and incoherent states at finite bath temperatures can be made qualitatively identical to the familiar zero-temperature phase diagram, and we discuss the experimental manifestation of this phenomenon in cold atoms.
We study the equilibrium and nonequilibrium properties of strongly interacting bosons on a lattice in the presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose-Hubbard model and obtain the Mott insulator, Bose glass, and superfluid phases. We also study the nonequilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter, and the energy pumped into the system in this process as a function of the inverse ramp rate $\ensuremath{\tau}$. For the clean case the density of excitations goes to a constant, while the order parameter and energy relax as $1/\ensuremath{\tau}$ and $1/{\ensuremath{\tau}}^{2}$ respectively. With disorder, the excitation density decays exponentially with $\ensuremath{\tau}$, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as $\ensuremath{\tau}$ is increased.
Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms
We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long-range order. We investigate how the coherent interaction affects the properties of the steady state of the system qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long-range order. The phase diagram also exhibits an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of low particle density, we provide a precise analytical description of the time evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.
The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.
The understanding of quantum many-body physics is the key to develop new quantum technologies including novel quantum materials, high-precision sensors, and quantum computers. However, understanding the general quantum many-body physics is extremely difficult, particularly when such systems are driven far from an equilibrium state. Ultracold atoms, a clean, fully controllable, and coherent quantum many-body systems can provide useful insights into the fundamental properties of quantum matter. This thesis discusses experiments on studying nonequilibrium dynamics in driven ultracold bosonic atoms with fantastic static and dynamical controls of the inter-particle interactions through Feshbach resonances and external trapping potentials using optical lattices and digital micromirror device (DMD). With this versatile apparatus, we first study the critical dynamics across a quantum phase transition in shaken optical lattices. Across a ferromagnetic transition where the Z2 inversion symmetry is broken, we are interested in how the system evolves toward the new ground states generally with a different symmetry. Utilizing the phase imprinting technique with DMD, we show that the macroscopic coherence is maintained across the phase transition, the system undergoes a coherent population transfer of particles toward lower energy states and quantum fluctuations determine the domain structure but do not destroy the macroscopic coherence. We then present the complex correlations rising from the matter-wave version of a high-harmonic generation with oscillating interaction. This high-harmonic generation of matterwave is a result of stimulated secondary collisions. The stimulated primary collisions, two condensate atoms collide absorbing one energy quantum from the oscillating field, give rise to the first observation of Bose fireworks. The scattered atoms from the primary collisions can further collide with each other or the ground-state atoms from the condensate and such secondary collisions promote atoms to higher momentum modes. Moreover, we show the density-wave dynamics prior to the jets emission within the condensate with oscillating interactions and explain the asymmetry in the jets emission pattern based on near-field interference. Besides, we further demonstrate the spatial and temporal phase coherence of the emitted jets using matter-wave interference and connect our matter-wave jets emission to the famous Unruh radiation in relativistic physics.
At any finite temperature, the correlation function $〈{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}(\mathcal{r})\ensuremath{\psi}(0)〉$ of a two-dimensional Bose system is known to approach zero as the separation r approaches infinity. This paper is devoted to supporting the point of view that superfluid phenomena may still persist in such a system. To describe the low-temperature behavior of a condensed two-dimensional Bose system, we use a coherent-state representation of the low-lying phonon excitations. The expectation of the particle field operator $〈\ensuremath{\psi}(\mathcal{r})〉$ in a coherent phonon state of the system is shown to be a well-defined function. This function has only small fluctuations in its magnitude and, therefore, it is possible to make the usual arguments for superfluid behavior based on the existence of the condensate wave function. The large phase fluctuations of the function, when the coherentphonon states are collected into the thermal ensemble, give rise to the spatial decay of the correlation function or reduced density matrix $〈{\ensuremath{\psi}}^{+}(\mathcal{r})\ensuremath{\psi}(0)〉$. It is concluded that two-dimensional Bose systems are superfluid at sufficiently low temperatures, even in the inifinite-volume limit. An analogous argument would indicate the possibility of superconductivity in a two-dimensional Fermi system.