Significance Understanding the combined effects of disorder and interactions in quantum many-body systems is a key topic of condensed matter physics. While most studies have considered a static disorder, here we investigate the relaxation dynamics of a three-dimensional Bose–Einstein condensate after switching on or off an optical disorder potential. We study, experimentally and numerically, the transient and steady-state atomic density distribution and the ability of the gas to hydrodynamically expand, directly reflecting long-range phase coherence. We find that, when the gas is exposed to disorder, long-range phase coherence breaks down one order of magnitude faster than the density distribution responds. In the opposite case, surprisingly, long-range coherence takes two orders of magnitude longer times to revive than the density relaxation.
Significance Understanding the combined effects of disorder and interactions in quantum many-body systems is a key topic of condensed matter physics. While most studies have considered a static disorder, here we investigate the relaxation dynamics of a three-dimensional Bose–Einstein condensate after switching on or off an optical disorder potential. We study, experimentally and numerically, the transient and steady-state atomic density distribution and the ability of the gas to hydrodynamically expand, directly reflecting long-range phase coherence. We find that, when the gas is exposed to disorder, long-range phase coherence breaks down one order of magnitude faster than the density distribution responds. In the opposite case, surprisingly, long-range coherence takes two orders of magnitude longer times to revive than the density relaxation.
Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from long-range coherence of the quantum system's wave function. Quantum dynamics of superfluids out of equilibrium was studied in various nonequilibrium realizations of superfluid helium, but also in turbulent relaxation of nonequilibrium, ultracold quantum gases. Such nonequilibrium states are usually created using moving objects or laser potentials, directly perturbing the system's density. However, the role of long-range phase coherence for the breakdown of quantum dynamics or the importance of coherence for the relaxation of quantum systems is still unexplored. Here, we unravel the contributions of density relaxation and coherent dynamics by studying a molecular Bose-Einstein condensate of Li atoms upon quenches of an optical speckle potential. We find that coherent dynamics breaks down one order of magnitude faster than the density of the quantum gas responds. Moreover, the system needs two orders of magnitude longer to reestablish long-range coherence and hence quantum dynamics, compared to the density response. Our results shed light on the importance of long-range coherence and the possibility of topologically robust phase excitations for the relaxation of nonequilibrium quantum systems. It thus suggests a possible route towards controlling quantum dynamics via nonequilibrium phase control.
Macroscopic coherence is an important feature of quantum many-body systems exhibiting collective behaviors, with examples ranging from atomic Bose-Einstein condensates, and quantum liquids to superconductors. Probing many-body coherence in a dynamically unstable regime, however, presents an intriguing and outstanding challenge in out-of-equilibrium quantum many-body physics. Here, we experimentally study the first- and second-order coherence of degenerate quasi-one-dimensional (1D) Bose gases quenched from repulsive to modulationally unstable attractive interaction regimes. The resulting dynamics, monitored by in situ density and matter-wave interference imaging, reveals phase-coherent density wave evolutions, clearly distinguished from iconic soliton trains previously observed in attractive gases. This arises from the interplay between noise-amplified density modulations and dispersive shock waves of broad interest in nonlinear physics, plasmas, granular systems, and beyond. At longer times, the gases become phase-scrambled, exhibiting a finite correlation length. Interestingly, following an interaction quench back to the repulsive regime, we observe that quasi-long-range coherence can be spontaneously re-established. This captivating rephasing dynamics can be attributed to the nucleation and annihilation of density defects in the quasi-1D geometry. These results shed light on out-of-equilibrium phase coherence in quantum many-body systems in a regime where beyond mean-field effects may arise and theoretical approaches have not been well-established. Attractive Bose gases are modulationally unstable yet exhibit rich nonlinear many-body behaviors, owing to the interplay between their coherence and unstable collective excitations. Here, the authors probe out-of-equilibrium dynamics in quasi-1D Bose-Einstein condensates subject to quench dynamics between repulsive and attractive interactions.
The microscopic pair structure of superfluids has profound consequences on their properties. Delocalized pairs are predicted to be less affected by static disorder than localized pairs. Ultracold gases allow tuning the pair size via interactions, where for resonant interaction superfluids shows largest critical velocity, i.e. stability against perturbations. The sensitivity of such fluids to strong, time-dependent disorder is less explored. Here, we investigate ultracold, interacting Fermi gases across various interaction regimes after rapid switching optical disorder potentials. We record the ability for quantum hydrodynamic expansion of the gas to quantify its long-range phase coherence. Contrary to static expectations, the Bose-Einstein condensate (BEC) exhibits significant resilience against disorder quenches, while the resonantly interacting Fermi gas permanently loses quantum hydrodynamics. Our findings suggest an additional absorption channel perturbing the resonantly interacting gas as pairs can be directly affected by the disorder quench.
The microscopic pair structure of superfluids has profound consequences on their properties. Delocalized pairs are predicted to be less affected by static disorder than localized pairs. Ultracold gases allow tuning the pair size via interactions, where for resonant interaction superfluids show largest critical velocity, i.e., stability against perturbations. The sensitivity of such fluids to strong, time-dependent disorder is less explored. Here, we investigate ultracold, interacting Fermi gases across various interaction regimes after rapid switching optical disorder potentials. We record the ability for quantum hydrodynamic expansion of the gas to quantify its long-range phase coherence. Contrary to static expectations, the Bose-Einstein condensate (BEC) exhibits significant resilience against disorder quenches, while the resonantly interacting Fermi gas permanently loses quantum hydrodynamics. Our findings suggest an additional absorption channel perturbing the resonantly interacting gas as pairs can be directly affected by the disorder quench.
Abstract We report on the dynamics of a Bose–Einstein condensate in one and two dimensions driven by the time-dependent harmonic trapping potential. Without the inter-particle interaction, the condensate exhibits the coherent behavior with the time-oscillating density distribution. When the inter-particle interaction is taken into consideration, the phase fluctuations, the multi-peak structure of the density distribution, and the coherence revival phenomenon, apart from the well-studied density oscillation behavior, can be observed in the condensate. Furthermore, it is demonstrated that due to the dimensional restriction these effects are more stable in the two and three-dimensional system, if compared to the one-dimensional case.
The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].