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arXiv:2507.12852 · Physical Review A

Energy dynamics of a nonequilibrium unitary Fermi gas

Xiangchuan Yan, Jing Min, Dali Sun, Shi-Guo Peng, Xin Xie, Xizhi Wu, Jiqi Li, Wenxing Yang, Kaijun Jiang

Published Apr 24, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the energy dynamics of a unitary Fermi gas driven away from equilibrium. The energy is injected into the system by periodically modulating the trapping potential of a spherical unitary Fermi gas, and due to the existence of SO(2,1) symmetry, the breathing mode is excited without dissipation. Through the long-lived breathing oscillation, we precisely measure the energy evolution of the nonequilibrium system during the trap modulation. We find the trapping potential and internal energies increase with modulation time and simultaneously oscillate nearly $\textrm{180}^{\textrm{o}}$ out of phase. At large modulation amplitudes, the energy-injection efficiency is strongly reduced due to the trap anharmonicity. Unlike the equilibrium system, the measured energy evolution agrees well with predictions of the dynamic virial theorem. Our work provides valuable insights into the energy injection and redistribution in a non-equilibrium system, paving a way for future investigations of nonequilibrium thermodynamics.

DOI
10.1103/1jfx-yntk

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•Oct 26, 2020•0 citations
We investigate the energy dynamics of a unitary Fermi gas driven away from equilibrium. The energy is injected into the system by periodically modulating the trapping potential of a spherical unitary Fermi gas, and due to the existence of SO(2,1) symmetry, the breathing mode is excited without dissipation. Through the long-lived breathing oscillation, we precisely measure the energy evolution of the nonequilibrium system during the trap modulation. We find the trapping potential and internal energies increase with modulation time and simultaneously oscillate nearly 180o\textrm{180}^{\textrm{o}}180o out of phase. At large modulation amplitudes, the energy-injection efficiency is strongly reduced due to the trap anharmonicity. Unlike the equilibrium system, the measured energy evolution agrees well with predictions of the dynamic virial theorem. Our work provides valuable insights into the energy injection and redistribution in a non-equilibrium system, paving a way for future investigations of nonequilibrium thermodynamics.
A unitary Fermi gas in an isotropic harmonic trap is predicted to show scale and conformal symmetry that have important consequences in its thermodynamic and dynamical properties. By experimentally realizing a unitary Fermi gas in an isotropic harmonic trap, we demonstrate its universal expansion dynamics along each direction and at different temperatures. We show that as a consequence of SO(2,1) symmetry, the measured release energy is equal to that of the trapping energy. We further observe the breathing mode with an oscillation frequency twice the trapping frequency and a small damping rate, providing the evidence of SO(2,1) symmetry. In addition, away from resonance when scale invariance is broken, we determine the effective exponent γ that relates the chemical potential and average density along the BEC-BCS crossover, which qualitatively agrees with the mean field predictions. This Letter opens the possibility of studying nonequilibrium dynamics in a conformal invariant system in the future.
SO(2,1) dynamical symmetry makes a remarkable prediction that the breathing oscillation of a scale-invariant quantum gas in an isotropic harmonic trap is isentropic and can persist indefinitely. In two dimensions, this symmetry is broken due to quantum anomaly in the strongly interacting range, and consequently the lifetime of the breathing mode becomes finite. The persistent breather in a strongly interacting system has so far not been realized. Here, we experimentally achieve the long-lived breathing mode in a three-dimensional unitary Fermi gas, which is protected by the SO(2,1) symmetry. The nearly perfect SO(2,1) symmetry is realized by loading the ultracold Fermi gas in an isotropic trap and tuning the interatomic interaction to resonance. The breathing mode oscillates at twice the trapping frequency even for large excitation amplitudes. The ratio of damping rate to oscillation frequency is as small as 0.002, providing an interacting persistent breather. The oscillation frequency and damping rate are nearly constant for different atomic densities and temperatures, demonstrating the robustness of the SO(2,1) symmetry in three dimensions. The factors that lead to the residual damping have also been clarified. This work opens the way to study many-body nonequilibrium dynamics related to the dynamical symmetry.
Directly accessing energy fluctuations in interacting quantum many-body systems remains a long-standing challenge, especially far from equilibrium. Here we show that in scale-invariant quantum gases with SO(2,1)(2,1)(2,1) dynamical symmetry, the amplitude of the breathing mode provides a direct and quantitative probe of energy fluctuations. We establish an exact and universal relation between the oscillation amplitude and the energy fluctuation, with a dimensionless ratio fixed solely by the Bargmann index kkk, which labels the irreducible representation of the underlying SU(1,1)(1,1)(1,1) algebra and thereby determines the structure of the many-body spectrum and dynamics. As a consequence, this relation is fully dictated by symmetry and remains independent of microscopic details and excitation protocols. Furthermore, we show that the excitation of breathing-mode states follows a universal statistical distribution governed by a single parameter, independent of the specific driving protocol. Our findings demonstrate that energy fluctuations, typically encoded in the many-body spectrum, can be directly accessed through collective dynamics, offering a symmetry-based route to probe nonequilibrium energy statistics in strongly interacting quantum systems.
Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.
We report an observation of a dynamical super Efimovian expansion in a strongly interacting Fermi gas by engineering time dependent external harmonic trap frequencies. When the trap frequency is tailored as [1/4t^{2}+1/t^{2}λlog^{2}(t/t_{*})]^{1/2}, where t_{*} and λ are two controllable parameters, and the change is faster than a critical value, the expansion of such a quantum gas shows novel dynamics that share the same characteristics as the super Efimov effect. A clear double-log periodicity with discrete geometric scaling emerges for the cloud size in the expansion. The universality of such scaling dynamics is verified both in the noninteracting and in the unitarity limit of Fermi gas. Moreover, the measured energy scaling reveals that the potential and internal energy also show double-log periodicity with a π/2 phase difference, but the total energy is monotonically decreased. Observing super Efimovian evolution represents a paradigm in probing universal properties and allows us in a new way to study many-body nonequilibrium dynamics with experiments.
Strongly correlated quantum systems display a myriad of complex, fascinating behaviour. The competition between charge, spin, orbital, or lattice degrees of freedom and their respective energy scales gives rise to rich and complex emergent phases. More recently, the non-equilibrium properties of correlated quantum many-body systems have come into the focus of active research, with remarkable advances. While the advent of tensor network based simulations on the theoretical side has allowed access to the full time-evolution of the quantum state as it traverses the Hilbert space, the experimental progress in the ultracold atom community has allowed physicists to enter the paradigm of analog quantum simulation. Their tunability and isolation from the environment makes them ideal platforms to emulate and study open problems in condensed matter physics and go beyond the simulational capabilities of state of the art classical simulations. In this thesis, we explore the dynamics of correlated Fermi gases. We develop and present different facets of applicability of radiofrequency modulation techniques to drive the system out of equilibrium. We begin by considering a homogeneous, three-dimensional Fermi gas in the BCS-BEC crossover and develop an off-resonant radiofrequency transfer scheme to excite the Higgs mode of the superfluid. In a subsequent study we investigate the tunability of the coherence between Cooper pairs by tuning the duration of interaction ramps of the internal interaction strength. These works highlight the possibility to externally tune and stabilise complex quantum many-body states away from equilibrium. Using quasi-exact matrix product state simulations, we study the response of an attractively interacting, one-dimensional Fermi-Hubbard model to weak radiofrequency perturbations. We reveal the emergence of two distinct dynamical regimes in the time evolution and are able to relate it back to the underlying excitation spectrum of the system. Finally, we explore the possibility to perform quantum quenches through radiofrequency π-pulses, achieving nearly complete population transfer between different interacting fermionic states. We reveal non-trivial dynamical effects in the pair correlation of the final state, as well as the excitation of a collective trap mode of the system.