arXiv subjects

Shi-Guo Peng

Publications and source records attributed to Shi-Guo Peng.

At least 19 recordsLinked to original sources

arXiv2026

Breathing Modes as a Probe of Energy Fluctuations in a Unitary Fermi Gas

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$(2,1)$ 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 $k$, which labels the irreducible representation of the underlying SU$(1,1)$ 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.

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arXiv2025

Finding the stable mechanism of ring solitons in two-dimensional Fermi superfluids

We theoretically investigate the stable mechanism of a ring soliton in two-dimensional Fermi superfluids by solving the Bogoliubov-de Gennes equations and their time-dependent counterparts. In the uniform situation, we discover that the ring soliton is always driven away from its initial location, and moves towards the edge due to a curvature-induced effective potential. The ring soliton is impossible to remain static at any location in the uniform system. To balance the density difference between the ring soliton's two sides, a harmonic trap is introduced, which can exert an effect to counterbalances the curvature-induced effective potential. This enables the ring dark soliton to become a stable state at a particular equilibrium position r_s, where the free energy of the ring dark soliton just reaches the maximum value. Once ring soliton is slightly deviated from r_s, some stable periodic oscillations of ring soliton around r_s will turn out. Some dissipation will possibly occur to ring soliton once its minimum radius is comparable to the healing length of soliton's Friedel oscillation. This dissipation will increase the oscillation amplitude and finally make the ring soliton decay into sound ripples. Our research lays the groundwork for a more in-depth understanding of the stable mechanism of a ring dark soliton in the future.

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arXiv2025

Energy Dynamics of a Nonequilibrium Unitary Fermi Gas

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.

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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.

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arXiv2024

Macroscopic superposition of vortex states in a matter wave

Generating the vortex-state superposition in a matter wave is demanded in many quantum processes such as quantum memory and quantum metrology. Here we report the experimental generation of macroscopic superposition of vortex states in ultracold quantum gases. By transferring an optical vortex-state superposition to the center-of-mass rotational state of ultracold atoms using the Raman coupling technique, we realize two-vortex and three-vortex superposition states in quantum gases, demonstrating the high dimensionality of the vortex state. We show the controllability of the superposition states on the Bloch sphere. The lifetime of the vortex superposition state in quantum gases is as large as 25 ms, about two orders of magnitude longer than the storage time in atomic ensembles. This work paves the way for high dimensional quantum processing in matter waves.

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arXiv2024

Two atoms in a harmonic trap with spin-orbital-angular-momentum coupling

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy.

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arXiv2024

Scale invariance of a spherical unitary Fermi gas

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 work opens the possibility of studying non-equilibrium dynamics in a conformal invariant system in the future.

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arXiv2024

Dynamical excitations of one-dimensional Fulde-Ferrell pairing Fermi superfluid

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum $p$, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum $p$, and separates two kinds of single-particle excitations in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment.

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arXiv2023

Dynamic structure factor of two-dimensional Fermi superfluid with Rashba spin-orbit coupling

We theoretically calculate the dynamic structure factor of two-dimensional Rashba-type spinorbit coupled (SOC) Fermi superfluid with random phase approximation, and analyse the main characters of dynamical excitation sh own by both density and spin dynamic structure factor during a continuous phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Generally we find three different excitations, including collective phonon excitation, two-atom molecular and atomic excitations, and pair-breaking excitations due to two-branch structure of quasi-particle spectrum. It should be emphasized that collective phonon excitation is overlapped with a gapless DD type pair-breaking excitation at the critical Zeeman field hc, and is imparted a finite width to phonon peak when transferred momentum q is around Fermi vector kF. At a much larger transferred momentum (q = 4kF ), the pair-breaking excitation happens earlier than two-atom molecular excitation, which is different from the conventional Fermi superfluid without SOC effect.

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arXiv2023

Dynamic virial theorem at nonequilibrium and applications

We show that a variety of nonequilibrium dynamics of interacting many-body systems are universally characterized by an elegant relation, which we call the dynamic virial theorem. The out-of-equilibrium dynamics of quantum correlations is entirely governed by Tan\textquoteright s contact. It gives rise to a series of observable consequences and is closely related to experiments with ultracold atoms. Especially, we show that the dynamic virial theorem provides an experimentally accessible verification of maximum energy growth theorem [Qi et al., Phys. Rev. Lett. 126, 240401 (2021)], which is encoded in the evolution of the atomic cloud size during expansion. In addition, the dynamic virial theorem leads to a simple thermodynamic relation of strongly interacting quantum gases in the framework of two-fluid hydrodynamic theory, which holds in a wide range of temperature. This thermodynamic relation is a kind of the out-of-equilibrium analog of Tan's pressure relation at equilibrium. Our results provide fundamental understanding of generic behaviors of interacting many-body systems at nonequilibrium, and are readily examined in experiments with ultracold atoms.

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arXiv2022

Spin-orbital-angular-momentum-coupled quantum gases

We briefly review the recent progress of theories and experiments on spin-orbital-angular-momentum (SOAM)-coupled quantum gases. The coupling between the intrinsic degree of freedom of particles and their external orbital motions widely exists in universe, and leads to a broad variety of fundamental phenomena both in the classical physics and quantum mechanics. Recent realization of synthetic SOAM coupling in cold atoms has attracted a great deal of attention, and stimulates a large amount of considerations on exotic quantum phases in both Bose and Fermi gases. In this review, we present a basic idea of engineering SOAM coupling in neutral atoms, starting from a semiclassical description of atom-light interaction. Unique features of the single-particle physics in the presence of SOAM coupling are discussed. The intriguing ground-state quantum phases of weakly interacting Bose gases are introduced, with emphasis on a so-called angular stripe phase, which has yet been observed at present. It is demonstrated how to generate a stable giant vortex in a SOAM-coupled Fermi superfluid. We also discuss topological characters of a Fermi superfluid in the presence of SOAM coupling. We then introduce the experimental achievement of SOAM coupling in $^{87}$Rb Bose gases and its first observation of phase transitions. The most recent development of SOAM-coupled Bose gases in experiments is also summarized. Regarding the controllability of ultracold quantum gases, it opens a new era, on the quantum simulation point of view, to study the fundamental physics resulted from SOAM coupling as well as newly emergent quantum phases.

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arXiv2022

Dynamic structure factor of one-dimensional Fermi superfluid with spin-orbit coupling

We theoretically calculate the density dynamic structure factor of one-dimensional Fermi superfluid with Raman-type spin-orbit coupling, and analyze its main dynamical character during phase transition between Bardeen-Cooper-Schrieffer superfluid and topological superfluid. Our theoretical results display four kinds of single-particle excitations induced by the two-branch structure of single-particle spectrum, and the cross single-particle excitation is much easier to be seen in the spin dynamic structure factor at a small transferred momentum. Also we find a new roton-like collective mode emerges at a fixed transferred momentum $q \simeq 2k_F$, and it only appears once the system enters the topological superfluid state. The occurrence of this roton-like excitation is related to switch of global minimum in single-particle spectrum from $k=0$ to $k \simeq 2k_F$.

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arXiv2022

Universal scattering phase shift in the presence of spin-orbit coupling

Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the scattering phase shifts for cold atoms in the presence of spin-orbit coupling. We first construct the asymptotic form of the two-body wave function when two fermions get as close as the interaction range, and consider perturbatively the correction of the spin-orbit coupling up to the second order, in which new scattering parameters are introduced. Then for elastic collisions, the scattering phase shifts are defined according to the unitary scattering $S$ matrix. We show how the low-energy behavior of the scattering phase shifts is modified by these new scattering parameters introduced by spin-orbit coupling. The universality of the scattering phase shifts is manifested as the independence of the specific form of the interatomic potential. The explicit forms of the new scattering parameters are analytically derived within a model of the spherical-square-well potential. Our method provides a unified description of the low-energy properties of scattering phase shifts in the presence of spin-orbit coupling.

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arXiv2022

Molecular state in a spin-orbital-angular-momentum coupled Fermi gas

We study the two-body bound states in a spin-orbital-angular-momentum (SOAM) coupled quantum gas of fermions. Two different configurations are considered: an attractive $s$-wave interaction exists between two spin species that are SOAM coupled; and an atom with SOAM coupled internal spins interacts state-selectively with another atom. For both cases, we identify the condition for the emergence of molecular states with finite total angular momenta.These molecular states with quantized total angular momenta correspond to the SOAM-coupling-induced vortices in the corresponding Fermi superfluid. We propose to detect the molecules through Raman spectroscopy with Laguerre-Gaussian lasers. As the molecular states can form above the superfluid temperature, they offer an experimentally more accessible route toward the study of the underlying pairing mechanism under SOAM coupling.

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arXiv2021

Dynamical generation of solitons in one-dimensional Fermi superfluids with and without spin-orbit coupling

We theoretically generalize a systematic language to describe the phase-imprinting technique to investigate the dynamical generation of solitons in a one-dimensional Raman-type spin-orbit-coupled Fermi superfluid. We check our method with the simulation of time-dependent Bogoliubov-de Gennes equations and find that our method not only can generate stable dark and even gray solitons in a conventional Fermi superfluid by controlling the transferred phase jump but also is feasible to create a stable dark soliton in both BCS and topological states of a spin-orbit-coupled Fermi superfluid. We also discuss the physical implication of our method.

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arXiv2021

Generating Giant Vortex in a Fermi Superfluid via Spin-Orbital-Angular-Momentum Coupling

Spin-orbital-angular-momentum (SOAM) coupling has been realized in recent experiments of Bose-Einstein condensates [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)], where the orbital angular momentum imprinted upon bosons leads to quantized vortices. For fermions, such an exotic synthetic gauge field can provide fertile ground for fascinating pairing schemes and rich superfluid phases, which are yet to be explored. Here we demonstrate how SOAM coupling stabilizes vortices in Fermi superfluids through a unique mechanism that can be viewed as the angular analog to that of the spin-orbit-coupling-induced Fulde-Ferrell state under a Fermi surface deformation. Remarkably, the vortex size is comparable with the beam waist of Raman lasers generating the SOAM coupling, which is typically much larger than previously observed vortices in Fermi superfluids. With tunable size and core structure, these giant vortex states provide unprecedented experimental access to topological defects in Fermi superfluids.

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arXiv2020

Angular Stripe Phase in Spin-Orbital-Angular-Momentum Coupled Bose Condensates

We propose that novel superfluid with supersolid-like properties - angular stripe phase - can be realized in a pancake-like spin-1/2 Bose gas with spin-orbital-angular-momentum coupling. We predict a rich ground-state phase diagram, including the vortex-antivortex pair phase, half-skyrmion phase, and two different angular stripe phases. The stripe phases feature modulated angular density-density correlation with sizable contrast and can occupy a relatively large parameter space. The low-lying collective excitations, such as the dipole and breathing modes, show distinct behaviors in different phases. The existence of the novel stripe phase is also clearly indicated in the energetic and dynamic instabilities of collective modes near phase transitions. Our predictions of the angular stripe phase could be readily examined in current cold-atom experiments with $^{87}$Rb and $^{41}$K.

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arXiv2019

Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

We present a comprehensive derivation of a set of universal relations for spin-orbit-coupled Fermi gases in three or two dimension, which follow from the short-range behavior of the two-body physics. Besides the adiabatic energy relations, the large-momentum distribution, the grand canonical potential and pressure relation derived in our previous work for three-dimensional systems {[}Phys. Rev. Lett. 120, 060408 (2018){]}, we further derive high-frequency tail of the radio-frequency spectroscopy and the short-range behavior of the pair correlation function. In addition, we also extend the derivation to two-dimensional systems with Rashba type of spin-orbit coupling. To simply demonstrate how the spin-orbit-coupling effect modifies the two-body short-range behavior, we solve the two-body problem in the sub-Hilbert space of zero center-of-mass momentum and zero total angular momentum, and perturbatively take the spin-orbit-coupling effect into account at short distance, since the strength of the spin-orbit coupling should be much smaller than the corresponding scale of the finite range of interatomic interactions. The universal asymptotic forms of the two-body wave function at short distance are then derived, which do not depend on the short-range details of interatomic potentials. We find that new scattering parameters need to be introduced because of spin-orbit coupling, besides the traditional $s$- and $p$-wave scattering length (volume) and effective ranges. This is a general and unique feature for spin-orbit-coupled systems. We show how these two-body parameters characterize the universal relations in the presence of spin-orbit coupling. This work probably shed light for understanding the profound properties of the many-body quantum systems in the presence of the spin-orbit coupling.

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