This work is a companion paper to X.-Y. Gao et al., Phys. Rev. Lett. 134, 153402 (2025), where we discuss the nonequilibrium two-body loss dynamics of a single-component ultracold Fermi gas and its possible thermalization. This paper provides detailed information on the derivation and analysis of the inelastic quantum Boltzmann equation (IQBE) used to describe the system. We demonstrate that the Mellin transform is a powerful tool for solving and approximating the IQBE for free-space systems. In this case, the particle-number dynamics are beyond the description of the widely used phenomenological two-body equation. For harmonically trapped systems, we propose a fast-flowing approximation to simplify the numerical evaluation of the IQBE. We verify the approximation in an analogous quasi-one-dimensional system and apply it to three-dimensional calculations, obtaining satisfactory agreement with recent experimental results. Furthermore, we compare the nonequilibrium results with those obtained using a thermal ansatz in both situations, providing a systematic understanding of the antievaporation phenomena observed in such systems.
This work is a companion paper to X.-Y. Gao et al., Phys. Rev. Lett. 134, 153402 (2025), where we discuss the nonequilibrium two-body loss dynamics of a single-component ultracold Fermi gas and its possible thermalization. This paper provides detailed information on the derivation and analysis of the inelastic quantum Boltzmann equation (IQBE) used to describe the system. We demonstrate that the Mellin transform is a powerful tool for solving and approximating the IQBE for free-space systems. In this case, the particle-number dynamics are beyond the description of the widely used phenomenological two-body equation. For harmonically trapped systems, we propose a fast-flowing approximation to simplify the numerical evaluation of the IQBE. We verify the approximation in an analogous quasi-one-dimensional system and apply it to three-dimensional calculations, obtaining satisfactory agreement with recent experimental results. Furthermore, we compare the nonequilibrium results with those obtained using a thermal ansatz in both situations, providing a systematic understanding of the antievaporation phenomena observed in such systems.
Two-body inelastic collisions arising from chemical reactions are prevalent in ultracold fermionic and bosonic molecular gases. Although recent advancements have achieved quantum degeneracy in these systems, loss dynamics are typically modeled phenomenologically using rate equations that often assume thermalization during chemical reactions. In this study, we employ the inelastic quantum Boltzmann equation to analyze particle loss, temperature evolution, and momentum distributions in single-component Fermi gases from first principles. Our results demonstrate that the conventional particle-number rate equation accurately describes the dynamics in trapped systems but fails to capture the behavior in homogeneous systems. Notably, under pure p-wave inelastic collisions and zero elastic collisions, we find that systems prepared near or above quantum degeneracy remain in a thermal state, whereas systems initialized deep within degeneracy exhibit nonequilibrium dynamics. Our theoretical predictions align well with recent experimental observations in trapped systems, and our claim can be further verified in atomic systems with induced two-body loss in box potentials.
We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than 0.47TF, up to the strong coupling regime, where TF is the Fermi temperature.
Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al. [1], in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis [2], nonequilibrium mass transport [1], dynamical fermionization [3], and transient phenomena such as quantum distillation or dynamical quasicondensation [4]. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems [1] and in determining the asymptotic state after a quantum quench [5]. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics [6]. [1] Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013) [2] Sorg et al., Phys. Rev. A 90, 033606 (2014) [3] Vidmar et al., Phys. Rev. B 88, 235117 (2013) [4] Vidmar et al., Phys. Rev. Lett. 115, 175301 (2015) [5] Mei et al., arXiv:1509.00828 [6] Hauschild, Pollmann, FHM, arXiv:1509.00696
Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the N-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.
In this thesis, we study the coherence and the dynamics of ultracold atomic quantum gases, with a particular regard on Fermi gases. For what concerns the coherence, we study a Fermi gas confined on a ring threaded by an artificial gauge field. First, we show that the persistent current flowing in the ring can be used as probe for the different regimes of the BCS-BEC crossover. We propose a readout protocol for our results, based on the co-expansion of the gas trapped on the ring and a reference gas placed in the center of the ring itself. Next, we show that using the same expansion protocol we can extract information about the phase of the quantum gas. At intermediate times, the expanding cloud provides information about the first order coherence of the Fermi gas. In few-body systems, we can also access the number of particles in the system. At long times, we extract information about the many-body coherence coherence of the gas. Subsequently we focus on the dynamics of a strongly interacting two-component Fermi gas trapped in a harmonic potential. We consider a spin-separated state and then we follow the dynamics until long times. At short times, the dynamics is superdiffusive with dynamical exponents of the Kardar-Parisi-Zhang universality class. At intermediate times, the dynamics is dominated by damped spin oscillations unveleing a spin-drag effect. At long times, we observe thermalization. Ultimately, we study a multicomponent Bose gas in the strongly interacting regime. We first provide the exact solution for the wavefunction and we discuss its symmetry. Afterwards, we study the response of the gas to an artificial gauge field, with particular regard to the period of the persistent current as a function of the gauge flux.
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including collective modes and transport coefficients, but often proves intractable due to computational costs associated with multidimensional integrals describing collision processes. Here, we present a method to resolve this bottleneck, enabling the study of a broad class of many-body systems that appear in fundamental science contexts and technological applications. Specifically, we demonstrate that a Gaussian mixture model can accurately represent equilibrium distribution functions, thereby allowing efficient evaluation of collision integrals. Inspired by cold atom experiments, we apply this method to investigate the collective behavior of a quantum Bose-Fermi mixture of cold atoms in a cigar-shaped trap, a system that is particularly challenging to analyze. We focus on monopole and quadrupole collective modes above the Bose-Einstein transition temperature, and find a rich phenomenology that spans interference effects between bosonic and fermionic collective modes, dampening of these modes, and the emergence of hydrodynamics in various parameter regimes. These effects are readily verifiable experimentally. Published by the American Physical Society 2024