Quenching to unitarity: Quantum dynamics in a three-dimensional Bose gas

Abstract

We study the dynamics of a dilute Bose gas at zero temperature following a sudden quench of the scattering length from a noninteracting Bose condensate to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rates. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be well understood within a simple, analytic two-body model. We derive a quantitative prediction for the evolution of Tan's contact, which increases linearly at short times. We also study the three-body losses at finite densities. Consistent with experiments, we observe lifetimes which are long compared to the dynamics of large momentum modes.Ultracold atomic physics offers unique opportunities to study strongly correlated systems due to the tunability of the interatomic interaction, parameterized by the s-wave scattering length, a, via Fano-Feshbach resonances [1]. Particularly interesting are quantum gases at unitarity, where a is much larger than any other length scale in the system. Such systems are predicted to exhibit universal behaviour, which depends only on the mean interparticle separation. Here the physics is highly nonperturbative, with no obvious small parameter. Investigations to date have predominantly focused on the Fermi gas, where three-body recombination is naturally suppressed by statistical repulsion [2]. Over the last decade, a general consensus seems to have emerged on many issues surrounding the unitary Fermi gas [3][4][5][6][7]. Theoretical understanding of the unitary Bose gas is far less developed. Although experiments in the quantum degenerate regime have been able to measure beyond mean field effects, such as the famous Lee-Huang-Yang correction [8,9] for values of na 3 7 × 10 −3 (n being the three dimensional number density), progress towards a unitary Bose gas with na 3 ≫ 1 is hampered by the catastrophic scaling of three-body loss in the system. At zero temperature, in the dilute gas, na 3 ≪ 1, with a ≫ r 0 where r 0 is the van der Waals length, the three-body recombination constant scales universally as L 3 ∝ a 4 /m [10][11][12][13][14]. This a 4 scaling renders any adiabatic transfer from the weakly interacting limit to the unitary limit impossible [15,16]. As a → ∞, although remaining dilute compared to the van der Waals length, the long-range aspects of Efimov physics become important [11][12][13][14]. One approach to limiting losses has emerged by considering non-degenerate unitary Bose gases [17,18], where the thermal de Broglie wavelength, λ T , can provide a small parameter nλ 3 T ≪ 1, and low-recombination regimes exist [19].A brazen new approach adopted in a recent experiment [20] utilizes an effectively diabatic quench in the scattering length to unitarity, with the initial gas temperature deeply degenerate. Although dimensional analysis requir...

Equilibrating dynamics in quenched Bose gases: Characterizing multiple time regimes

“…This typical timescale is associated with the oscillation period of observables as predicted by Bogoliubov theory [1,4,[9][10][11]. We see that as long as t ≪ τ interm (k), we can ignore the damping, and the system behaves as if it were described by Bogoliubov theory and its variants.…”

“…Equally of interest is the nature of metastable states, (often) so produced. Considerable theoretical attention has gone into this subject, albeit characterizing the post-quench physics entirely in terms of oscillatory behavior [4,6,7,[9][10][11].How long do these oscillations persist and how does ultimate equilibration proceed for different momentum states is a complicated problem that is the focus of the present paper. Here we discuss the different time scales associated with dissipation and equilibration in the context of the evolution of the momentum distribution n k for a three-dimensional Bose gas.…”

“…Equally of interest is the nature of metastable states, (often) so produced. Considerable theoretical attention has gone into this subject, albeit characterizing the post-quench physics entirely in terms of oscillatory behavior [4,6,7,[9][10][11].…”

Nonequilibrium states of a quenched Bose gas

“…We note, in passing, that the short-time behavior of the condensate fraction and other higher-order correlation functions in quenched Bose gases have been the focus of several recent studies [44,45,[48][49][50].…”

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

“…These solutions (and the two-and one-dimensional analogs) have played a crucial role in, to name a few examples, analyzing few-atom experiments [52][53][54], guiding and benchmarking few-body calculations [55][56][57], and interpreting the dynamics of manybody systems [58,59]. This paper determined portions of the energy spectrum of two s-wave interacting atoms under external spherically symmetric harmonic confinement with spin-orbit coupling of Rashba type.…”