Relaxation of bosons in one dimension and the onset of dimensional crossover

Abstract

We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

Diffraction of strongly interacting molecular Bose-Einstein condensate from standing wave light pulses

“…In order to investigate at which stages and by what processes the loss occurs, we make use of a technique implementing a particular lattice pulse sequence [38]. By applying a designed lattice pulse sequence to a known initial distribution, the populations of the higher momentum modes can be 'returned' to the 0hk mode as long as coherence is maintained.…”

“…The pulse sequence is designed with particular pulse durations and intervals for a given lattice depth U 0 , aiming at maximizing the overlap between the final wavefunction and the BEC wavefunction in the 0 th mode [38]. Supposing that ψ 0 is the state of a BEC, we calculate the Bloch state after applying a pulse sequence [t 0 , t 1 , t 2 , t 3 , t 4 ] (see Figure 7a),…”

Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems

“…A far from equilibrium many-body initial state evolving under Hamiltonian dynamics, as relevant to describe an isolated quantum system, is generally expected to relax to thermal equilibrium (in the sense of observables being described by traditional ensembles of statistical mechanics) [1][2][3]. The advent of quantum simulations in low dimensions with ultracold atoms [4] and trapped ions [5] have ushered much of the progress in probing the realm of strongly interacting quantum systems isolated from the environment [6][7][8][9][10][11][12][13][14][15]. A recurring theme in these experiments [8,9,[12][13][14] is the phenomenon of prethermalization and its stability to perturbations [16][17][18].…”

“…The advent of quantum simulations in low dimensions with ultracold atoms [4] and trapped ions [5] have ushered much of the progress in probing the realm of strongly interacting quantum systems isolated from the environment [6][7][8][9][10][11][12][13][14][15]. A recurring theme in these experiments [8,9,[12][13][14] is the phenomenon of prethermalization and its stability to perturbations [16][17][18].…”

Emergent Pauli blocking in a weakly interacting Bose gas

“…When these energy scales approach the transverse level spacing, excitations in the transverse confinement are energetically possible and the system is often referred to as quasi-1D [9]. Unlike integrable dynamics, these excitations are not rapidity conserving and can lead to thermalization [10]. Thus, experimental studies of dynamics in this regime are crucial for understanding the extent at which quantum integrability survives in the presence of perturbations.…”