Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas

Abstract

We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate-to thermal-gas behaviour, both of which are characterised by universal scaling laws linking the particle-loss rate to the total atom number N . In the degenerate and thermal regimes the per-particle loss rate is ∝ N 2/3 and N 26/9 , respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.Strong interactions and correlations are at the heart of the most interesting many-body quantum phenomena. The possibility to control the interaction strength via Feshbach resonances [1] makes ultracold atomic gases an excellent setting for studies of strongly correlated behaviour. On resonance, the s-wave scattering length a, which characterises two-body contact interactions, diverges. In this so-called unitary regime the interactions are as strong as allowed by quantum mechanics, and the physics cannot explicitly depend on a, leading to the possibility of new types of universal behaviour [2][3][4][5][6].Of particular interest are the interaction-dominated degenerate unitary gases. Within the 'universality hypothesis', they have only one relevant lengthscale -the average interparticle spacing, given by the density n, which also sets the natural energy and time scales [2]:where m is the atom mass. These 'Fermi energy' and 'Fermi time' scales are applicable to both Fermi and Bose gases. In Bose gases, however, the universality can be broken by Efimov physics [7][8][9][10][11][12][13][14][15][16][17]. The Feshbach dimer molecular state, responsible for the resonance, is of size a and becomes unbound as a → ∞, but the infinite series of Efimov trimer states, each of a size 22.7 times larger than the previous one, can introduce new lengthscales into the problem. While unitary Fermi gases have been extensively explored [3][4][5], the experimental [15,16,[18][19][20][21] and theoretical [22][23][24][25][26][27][28][29][30][31][32][33][34] studies of unitary Bose gases are only recently emerging. An experimental challenge is that they exhibit rapid threebody loss and heating, which also raises fundamental questions about the extent to which they have well defined equilibrium properties [20], but the loss dynamics also offer a valuable probe of the unitary behaviour [16,[18][19][20][21]. While coherent three-body correlations [15] and Efimov trimers [16] have been observed, the decay dynamics [16,[18][19][20][21] have been consistent with universal scalings (see also [35]). All experiments so far were performe...

Pair formation in quenched unitary Bose gases

“…Although * s.musolino@tue.nl these findings, combined with studies of loss dynamics in Refs. [10][11][12], are consistent with the universality hypothesis, a macroscopic population of Efimov trimers was observed in Ref. [11].…”

“…In Refs. [10][11][12][13], this barrier was overcome through a fast quench from the weakly interacting to the unitary regime, where the establishment of a steady state was observed before heating dominates. Time-resolved studies of the single-particle momentum distribution in Ref.…”

“…II C. It is interesting to note the analogy of pair formation in the quenched unitary Bose gas to pair formation in the unitary Fermi gas [23], which is at the center of the so-called BCS-BEC crossover. When entering this crossover from the Bardeen-Cooper-Schrieffer (BCS) side, fermionic pairs, loosely bound by the medium, smoothly evolve into tightly bound molecules that are stable even without the medium, arXiv:1904.00908v2 [cond-mat.quant-gas] 11 Jul 2019 n the possible role of higher-order effects in explaining experiment for slower sweeps and longer times spent in of osace- / [10][11][12][13]. First, the magnetic field B is ramped suddenly towards the resonant value B 0 , taking the system from the weakly-interacting (na 3 < 1) to the unitary regime na 3 1 (shaded region).…”

“…Schematic representation of the experimental protocol used in Refs. [10][11][12][13]. First, the magnetic field B is ramped suddenly towards the resonant value B0, taking the system from the weakly interacting (na 3 < 1) to the unitary regime na 3 1 (shaded region).…”

Dynamics of Three-Body Correlations in Quenched Unitary Bose Gases

“…It is of interest to extend this analysis to later times beyond the range of our model and to observables depending functionally on the three-body contact. These investigations may suggest regimes of interest for experiments, which have covered, to date [12,15,41,44], a fraction of the log period studied in this Letter. Preliminary observations of the decay rate over a wider range of densities display oscillations [45].…”