Nonequilibrium dynamics of fluctuations in an ultracold atomic mixture

Letter

Nonequilibrium dynamics of fluctuations in an ultracold atomic mixture

Apoorva Hegde, Robert Ott, Andy Xia, Valentin Kasper, Jürgen Berges, and Fred Jendrzejewski

Phys. Rev. A 107, L031302 – Published 8 March 2023

Abstract

We investigate an ultracold mixture of Bose gases interacting via spin-changing collisions by studying the dynamics of spin fluctuations. The experimental implementation employs ${}^{23}{Na}$ and ${}^{7}{Li}$ atoms, which are prepared out of equilibrium across a wide range of initial conditions. We identify three regimes in the dynamics of the system for different initial states: a long-lived metastable regime, an instability range with strong growth of fluctuations, and a regime approaching thermal equilibrium. Theoretical modeling of the data allows us to reconstruct effective potentials which characterize the different dynamical regimes of the system.

Received 28 April 2022
Accepted 9 January 2023

DOI:https://doi.org/10.1103/PhysRevA.107.L031302

Physics Subject Headings (PhySH)

Lattice gauge theory Mixtures of atomic and/or molecular quantum gases Nonequilibrium & irreversible thermodynamics Particle correlations & fluctuations Quantum field theory Quantum simulation Ultracold collisions

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyParticles & FieldsNonlinear DynamicsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Apoorva Hegde ^1,*, Robert Ott ^2,*, Andy Xia¹, Valentin Kasper³, Jürgen Berges², and Fred Jendrzejewski¹

¹Kirchhoff Institute for Physics, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
²Institut für Theoretische Physik, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
³Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Avenida Carl Friedrich Gauss 3, 08860 Barcelona, Spain

^*These authors contributed equally to this work.

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Issue

Vol. 107, Iss. 3 — March 2023

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Images

Figure 1
Dynamics of spin fluctuations induced by spin-changing collisions (SCCs). (a) The ultracold atomic mixture is coupled through SCC between sodium and lithium atoms realizing effective spin degrees of freedom. Our model involves interaction rates for SCC ( $λ$ ), density scatterings ( $χ$ ), and a relative offset $Δ$ between single-particle hyperfine states energetically separated with a magnetic field $B$ . (b) Varying initial conditions probe the mixture in three different regimes as illustrated with effective potentials (shown in a.u.): a metastable state, an instability with growth of fluctuations, and relaxation approaching equilibrium. Solid lines show numerical real-time calculations of our effective model (see [40]). (c) The fluctuations of the data (shaded blue) around mean values (red) grow in time, where gray circles show single realizations of preparation, evolution, and measurement (see the inset). Solid lines are smoothed interpolations of data points; the data correspond to ${\bar{η}}_{Na} (t_{0}) = 0.406$ . The term “fluctuation” refers to the standard deviation, shown here as a band around the mean values.
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Figure 2
Time evolution of mean and fluctuations. (a) We show the evolution of mean lithium spin transfer ${\bar{η}}_{L}$ for evolution times $t \leq 100 ms$ starting from a mean sodium imbalance of ${\bar{η}}_{Na} = 0.406$ [see the data set in Fig. 1]. The damped-oscillatory behavior of the data (red circles) is well described by our semiclassical calculation (solid line), which accommodates initial-state fluctuations. The gray area signals a systematic shift from imperfect atom detection. (b) The two-point correlation data (blue circles) shows an initial growth of fluctuations [see Fig. 1] and reaches an approximately constant value at later times. The late-time data are in approximate agreement with a thermal calculation for a temperature $T = 630 nK$ (dotted line). Error bars represent standard error on the mean. Our detection of spin fluctuations has an offset of 0.0040(1) for $Δ {\bar{η}}_{Li}$ (gray shaded area), which we added to the numerical curve in (b).
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Figure 3
Nonequilibrium regimes. (a) We indicate the different dynamical regimes with the effective (early-time) potential landscape (see the main) for different initial ${\bar{η}}_{Na}$ (see the arrows). (b) After $30 ms$ evolution time, the mean lithium imbalance ${\bar{η}}_{Li}$ reveals a sharp resonance behavior for changing initial conditions set by ${\bar{η}}_{Na}$ . (c) The fluctuation signal shows a large peak around ${\bar{η}}_{Li} \sim 0.2$ , indicating an instability regime characterized by the fast growth of fluctuations (red shaded area). We find overall good agreement with numerical real-time calculations at $30 ms$ (colored solid lines) and a late-time calculation at 150 ms (black dashed lines). On the right-hand side of the transition we find good agreement with a (classical) thermal ensemble at temperature $630 (20) nK$ (black dotted lines), which clearly fails on the left-hand side. The shaded area in (c) indicates the fluctuation offset from detection noise, which we add to the numerical curve in (c).
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