arXiv subjects

Shizhong Zhang

Publications and source records attributed to Shizhong Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Universal Transport Properties of Continuous Quantum Gases

The Drude weight characterizes ballistic transport in quantum many-body systems. Although analytical calculations of Drude weights have been extensively studied in integrable models, their direct connections to finite-temperature macroscopic state functions remain unestablished, especially for continuous multicomponent quantum gases. In the present work, we use generalized hydrodynamics and the thermodynamic Bethe ansätz to calculate exactly the Drude weights for one-dimensional continuous integrable systems, including the Lieb-Liniger and Bose-Fermi mixture models. We derive universal exact relations between Drude weight matrix components and key thermodynamic densities (particle density, enthalpy, entropy). Analytic expressions for Drude weight are obtained across different physical regimes, i.e. strong- and weak-coupling regimes in addition to universal scaling laws near the quantum phase transitions. To bridge theory and experiment, we simulate two experimental protocols, linear potential quench and bipartitioning quench, to enable reliable measurements of the Drude weights. Using these protocols, we calculate the charge and energy Drude weight for Lieb-Liniger gas and compare with recent measurements reported in [Science 391, 290 (2026)], showing excellent agreement with particle density and enthalpy, respectively, thus offering deeper physical insights into experimental observations. Our findings directly link ballistic transport properties to thermodynamics, providing rigorous theoretical benchmarks for future ultracold atomic gas experiments.

cond-mat.quant-gas↗

arXiv2026

Structure of the mean-field yrast spectrum of a two-component Bose gas in a ring: role of interaction asymmetry

The mean-field yrast spectrum of an SU(2)-symmetric two-component Bose gas confined to a ring geometry is known to exhibit an intricate nonanalytic structure that is absent in single-component systems. In particular, due to the interplay between the species concentration and the atomic interactions, a sequence of plane-wave states can emerge as yrast states at fractional values of the angular momentum per particle. This behavior stands in sharp contrast to the single-component case, where plane-wave states occur only at integer angular momenta. In this paper, we investigate how the structure of the yrast spectrum in a two-component Bose gas is modified by interaction asymmetry. By numerically solving the coupled Gross-Pitaevskii equations for propagating soliton states, we compute the mean-field yrast spectrum and, in particular, determine the critical curves associated with the emergence of various plane-wave yrast states. We find that both the behavior of these critical curves and the mechanisms by which plane-wave yrast states arise depend sensitively on the relative strengths of the inter- and intra-component interactions. When the intra-component interaction is weaker, the plane-wave yrast states replace soliton states through a continuous evolution, as in the SU(2)-symmetric case, although the conditions for their existence become more restrictive. In contrast, when the intra-component interaction is stronger, plane-wave yrast states may emerge by overtaking soliton states via branch crossings, and their stability is significantly enhanced. Our results have important implications for the existence and stability of persistent currents in asymmetric, two-component Bose gases.

cond-mat.quant-gas↗

arXiv2025

Generalized Onsager reciprocal relations of charge and spin transport

In spin-orbit-coupled systems the charge and spin transport are generally coupled to each other, namely a charge current will induce a spin current and vice versa. In the presence of time-reversal symmetry $T$, the cross-coupling transport coefficients describing how one process affects the other are constrained by the famous Onsager reciprocal relations. In this paper, we generalize the Onsager reciprocal relations of charge and spin transport to systems that break the time-reversal symmetry but preserve a combined symmetry of $T$ and some other symmetry operation $O$. We show that the symmetry or antisymmetry of the cross-coupling transport coefficients remains in place provided that the operator $O$ meets certain conditions. Among many candidate systems where our generalized Onsager relations apply, we focus on a conceptually simple and experimentally realized model in cold atomic systems for explicit demonstration and use these relations to predict highly non-trivial transport phenomena that can be readily verified experimentally.

cond-mat.quant-gas↗

arXiv2025

Observation of Brownian Motion of a Bose-Einstein Condensate

We report on the experimental observation of classical Brownian motion in momentum space by a Bose-Einstein condensate (BEC) of Rubidium atoms prepared in a hexagonal optical lattice. Upon suddenly increasing the effective atomic mass, the BEC as a whole behaves as a classical rigid body with its center-of-mass receiving random momentum kicks by a Langevin force arising from atom loss and interactions with the surrounding thermal cloud. Physically, this amounts to selective heating of the BEC center-of-mass degree of freedom by a sudden quench, while with regard to the relative coordinates, the BEC is stablized by repulsive atomic interactions, and its internal dynamics is suppressed by forced evaporative cooling induced by atom loss. A phenomenological theory is developed that well explains the experimental data quantitatively.

cond-mat.quant-gas↗

arXiv2025

Unconventional spin Hall effect in PT symmetric spin-orbit coupled quantum gases

We theoretically study the intrinsic spin Hall effect in PT symmetric, spin-orbit coupled quantum gases confined in an optical lattice. The interplay of the PT symmetry and the spin-orbit coupling leads to a doubly degenerate non-interacting band structure in which the spin polarization and the Berry curvature of any Bloch state are opposite to those of its degenerate partner. Using experimentally available systems as examples, we show that such a system with a two-component Fermi gas exhibits an intrinsic spin Hall effect akin to that found in the context of electronic materials. For a two-component Bose gas, however, an unconventional spin Hall effect emerges in which the spin polarization and the currents are coplanar and the spin Hall conductivity displays a characteristic anisotropy. We propose to detect such an unconventional spin Hall effect in harmonically trapped systems using dipole oscillations and perform extensive numerical simulations to validate the proposal. Our work paves the way for quantum simulation of the solid-state intrinsic spin Hall effect and experimental explorations of unconventional spin Hall effects in quantum gases.

cond-mat.quant-gas↗

arXiv2024

Persistent breather and dynamical symmetry in a unitary Fermi gas

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 2D, 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 3D 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 keep nearly constant for different atomic densities and temperatures, demonstrating the robustness of the SO(2,1) symmetry in 3D. The factors that lead to the residual damping have also been clarified. This work opens the way to study many-body non-equilibrium dynamics related to the dynamical symmetry.

cond-mat.quant-gas↗

arXiv2024

Nonlinear spin dynamics induced by feedback under continuous Larmor frequency distributions

Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce self-sustained oscillations at the base Larmor frequency due to nonlinearity. These features have driven the development of single-species and multiple-species spin masers. The latter, with multiple discrete Larmor frequencies, provides significant advantages for precision measurement by mitigating uncertainties in precession frequencies due to long-term drifts in experimental conditions. The self-sustained oscillations of single-species and multiple-species spin masers correspond to limit cycles and quasi-periodic orbits of the stable nonlinear dynamics of the systems respectively; the correspondence is elucidated in a recent study on a related spin system featuring two discrete intrinsic Larmor frequencies under dual bias magnetic fields. Here, we extend the study to the case that the intrinsic Larmor frequencies of individual spins of the system, given rise to by an inhomogeneous bias magnetic field, form a continuum. We show that generically the stable dynamics of the system includes limit cycles, quasi-periodic orbits, and chaos. We establish the relation between the synchronization frequency of limit cycles and the field inhomogeneity and derive an equation determining the stability of limit cycles. Furthermore, detailed characteristics of different dynamical phases, especially the robustness of limit cycles and quasi-periodic orbits against experimental fluctuations, are discussed. Our findings not only encompass the case of discrete Larmor frequencies, but also provide crucial insights for precision measurement and the exploration of continuous time crystals and quasi-crystals.

quant-ph↗

arXiv2024

Feedback-Induced Nonlinear Spin Dynamics in an Inhomogeneous Magnetic Field

Nonlinear effects are the root of interesting phenomena such as masers and lasers, and play a significant role in science and engineering. In spin systems, nonlinear spin dynamics is crucial for the prediction of complex dynamical behavior such as self-organizing oscillation, with applications ranging from spin masers and time crystals to precision measurement. However, when a spin system operates in a static magnetic field, how the inhomogeneity of the field affects its dynamics is a primary concern. Here we study the dynamics of a collection of spins with multiple Larmor frequencies for modeling a static inhomogeneous magnetic field, and reveal that due to the nonlinearity induced by a feedback scheme, the spin system exhibits much richer stable dynamical phases, including quasi-periodic orbits and chaos besides the usual limit cycles emerged in previous works. These phases are generally applicable to coupled nonlinear spin systems, even with more than two intrinsic Larmor frequencies or in continuum cases. Furthermore, we discuss their robustness against the experimental noises and the feasibility of realization in several spin systems. Our findings contribute to future observation of nonlinear dynamical phases and prospective applications in precision measurement.

cond-mat.quant-gas↗

arXiv2024

Emergent $s$-wave interactions in orbitally active quasi-two-dimensional Fermi gases

We investigate the scattering properties and bound states of a quasi-two-dimensional (q2D) spin-polarized Fermi gas near a $p$-wave Feshbach resonance. Strong confinement promotes the out-of-plane spatial wave functions to a discrete, gapped orbital degree of freedom. Exchange-antisymmetric orbital pair wave functions are predicted to give rise to low-energy q2D interactions with $s$-wave symmetry. Using radiofrequency (rf) spectroscopy, we observe the signature power-law scaling and the dimensional-crossover feature anticipated for the emergent $s$-wave channel. Additionally, we demonstrate that two types of low-energy dimers, with either $s$-wave and $p$-wave symmetry, could be formed via rf spin-flip association from an orbital mixture. These findings illustrate how gapped orbital degrees of freedom can provide additional control over scattering symmetries in strongly confined ultracold gases.

cond-mat.quant-gas↗

arXiv2024

Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases

Low-dimensional ultracold gases are created in the laboratory by confining three-dimensional (3D) gases inside highly anisotropic trapping potentials. Such trap geometries not only provide access to simulating one-dimensional (1D) and two-dimensional (2D) physics, but also can be used to study how the system crosses over towards a 3D system in the limit of weak confinement. In this work, we study the signature in radio-frequency (RF) spectroscopy for both the 1D-to-3D and the 2D-to-3D crossovers, in spin-polarized Fermi gases. We solve the two-body scattering T-matrix in the presence of strong harmonic confinement and use it to evaluate the two-body bound state and the RF spectroscopy transfer rate in the high frequency limit, covering both the quasi-low-dimensional and 3D limits. We find that in order to understand the dimensional crossover for spin-polarized Fermi gases with p-wave interactions, one needs to take into account an emergent s-wave interaction.

cond-mat.quant-gas↗

arXiv2024

Hydrodynamic equations for a U(N) invariant superfluid

In this paper, we develop the appropriate set of hydrodynamic equations in a U(N) invariant superfluid that couple the dynamics of superflow and magnetization. In the special case when both the superfluid and normal velocities are zero, the hydrodynamic equations reduce to a generalized version of Landau-Lifshitz equation for ferromagnetism with U(N) symmetry. When both velocities are non-zero, there appears couplings between the superflow and magnetization dynamics, and the superfluid velocity no longer satisfies the irrotational condition. On the other hand, the magnitude of magnetization is no longer a constant of motion as was the case for the standard Landau-Lifshitz theory. In comparison with the simple superfluid, the first sound and second sounds are modified by a non-zero magnetization through various thermodynamic functions. For U(2) invariant superfluid, we get both (zero-) sound wave and a spin wave at zero temperature. It is found that the dispersion of spin wave is always quadratic, which is consistent with detailed microscopic analysis. In the Appendix, we show that the hydrodynamic equation for a U(N) invariant superfluid can be obtained from the general hydrodynamic equation with arbitrary internal symmetries.

cond-mat.quant-gas↗

arXiv2024

Fragmented Condensate in a Two-Component Bose Gas with $p$-wave Interactions

In this Letter, we discuss the effects of $p$-wave attractive interaction in a spin-$1/2$ Bose gas. With a repulsive $s$-wave background interaction, we show that for weak $p$-wave attraction, one obtains a standard Bose-Einstein condensate at zero momentum with spins fully polarized. Upon increasing the $p$-wave attraction, a fragmented condensate state with singlet pair formation and $p$-wave correlation emerges. We determine the transition point and investigate the properties of the fragmented condensate using an ansatz wave function. We construct the relevant Gross-Pitaevskii equations for the fragmented condensate and show that the sound velocities are anisotropic and may vanish in specific directions. Based on the many-body wave function, we also discuss the low-energy spin excitations of the system.

cond-mat.quant-gas↗

arXiv2023

Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries

Orbital degrees of freedom play an essential role in metals, semiconductors, and strongly confined electronic systems. Experiments with ultracold atoms have used highly anisotropic confinement to explore low-dimensional physics, but typically eliminate orbital degrees of freedom by preparing motional ground states in strongly confined directions. Here we prepare multi-band systems of spin-polarized fermionic potassium ($^{40}$K) in the quasi-one-dimensional (q1D) regime and quantify the strength of atom-atom correlations using radio-frequency spectroscopy. The activation of orbital degrees of freedom leads to a new phenomenon: a low-energy scattering channel that has even particle-exchange parity along the q1D axis, as if the underlying interactions were s-wave. This emergent exchange symmetry is enabled by orbital singlet wave functions in the strongly confined directions, which also confer high-momentum components to low-energy q1D collisions. We measure both the q1D odd-wave and even-wave "contact" parameters for the first time, and compare them to theoretical predictions of one-dimensional many-body models. The strength and spatial symmetry of interactions are tuned by a p-wave Feshbach resonance and by transverse confinement strength. Near resonance, the even-wave contact approaches its theoretical unitary value, whereas the maximum observed odd-wave contact remains several orders of magnitude below its unitary limit. Low-energy scattering channels of multi-orbital systems, such as those found here, may provide new routes for the exploration of universal many-body phenomena.

cond-mat.quant-gas↗

arXiv2022

Three-body recombination in a single-component Fermi gas with $p$-wave interaction

We study the three-body recombination of identical fermionic atoms. Using a zero-range model for the $p$-wave interaction, we show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $α_{\rm rec} \propto v^{5/2}R^{1/2} k_T^4 (1+ C k_T^2 l_{\rm d}^2)$ for large and positive scattering volume $v$. Here $R$ is the $p$-wave effective range, $k_T^2$ gives the average thermal kinetic energy of the colliding atoms, and $l_{\rm d}$ is the size of the $p$-wave dimer. The leading term is different from the usually stated $v^{8/3}$-scaling law, but is consistent with an earlier two-channel calculation. For the subleading term, we compute the constant $C$ by solving the relevant three-body problem perturbatively when the parameter $γ\equiv R/v^{1/3}$ is small. The additional $C k_T^2 l_{\rm d}^2$ term provides important corrections for the temperature and interaction dependence of $α_{\rm rec}$, especially close to resonance when $k_T l_{\rm d}$ is relatively large.

cond-mat.quant-gas↗

arXiv2022

Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity

The transport properties of one-dimensional Fermi gases at low-temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipation one needs to examine interactions beyond the LL model. In this work we provide a simple model which allows for a direct microscopic calculation of the bulk viscosity, namely the one dimensional spin polarized p-wave Fermi gas. We calculate the bulk viscosity in both the high- and low-temperature limits. We find that the bulk viscosity is finite and consistent with the requirement of scale symmetry, in spite of the inherent integrability of the microscopic model. We argue how integrability does not forbid a finite bulk viscosity, and compare our work to previous kinetic theory calculations.

cond-mat.quant-gas↗

arXiv2021

Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry

In this Letter, we investigate the effects of a time-dependent, short-ranged interaction on the long-time expansion dynamics of Fermi gases. We show that the effects of the interaction on the dynamics is dictated by how it changes under a conformal transformation, and derive an explicit criterion for the relevancy of time-dependent interactions in both the strongly and non-interacting nearly scale invariant quantum gases. In addition, we show that it is possible to engineer interactions that give rise to non-exponential thermalization dynamics in trapped Fermi gases. To supplement the symmetry analysis, we also perform hydrodynamic simulations to show that the moment of inertia of the trapped gas indeed follows a universal time-dependence determined jointly by the conformal symmetry and time-dependent scattering length $a(t)$. Our results should also be relevant to the dynamics of other systems that are nearly scale invariant and that are governed by a non-relativistic conformal symmetry.

cond-mat.quant-gas↗

arXiv2020

Dynamical Kosterlitz-Thouless Theory for Two-Dimensional Ultracold Atomic Gases

In this letter we develop a theory for the first and second sound in a two-dimensional atomic superfluid across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic equations which incorporate the dynamics of the quantised vortices, rather than the conventional ones for a three-dimensional superfluid. As far as the sound dispersion equation is concerned, the modification is essentially equivalent to replacing the static superfluid density with a frequency dependent one, renormalised by the frequency dependent "dielectric constant" of the vortices. This theory has two direct consequences. First, because the renormalised superfluid density at finite frequencies does not display discontinuity across the superfluid transition, in contrast to the static superfluid density, the sound velocities vary smoothly across the transition. Second, the theory includes dissipation due to free vortices, and thus naturally describes the sound-to-diffusion crossover for the second sound in the normal phase. With only one fitting parameter, our theory gives a perfect agreement with the experimental measurements of sound velocities across the transition, as well as the quality factor in the vicinity of the transition. The predictions from this theory can be further verified by future experiments.

cond-mat.quant-gas↗

arXiv2020

Manipulation of heteronuclear spin dynamics with microwave and vector light shift

We report the observation and manipulation of heteronuclear spin dynamics in a spin-1 mixture of ultracold $^{87}$Rb and $^{23}$Na atoms. The dynamics is driven by the interspecies spin-dependent interaction and shows a pronounced dependence on magnetic fields with influences from both linear and quadratic Zeeman shifts. Similar to the well-studied homonuclear cases, the interspecies spin dynamics can be controlled by tuning the quadratic Zeeman shift with far-detuned microwave fields. In addition, we successfully realize spin dynamics control with vector light shifts which act as a species-selective effective magnetic field on $^{87}$Rb atoms. Both methods show negligible loss of atoms thus will be powerful techniques for investigating spin dynamics with fast temporal and high spatial resolutions.

cond-mat.quant-gas↗