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arXiv:2305.14043 · Journal of Physics A Mathematical and Theoretical

Zero sound in a quantum gas of spin-3/2 atoms with multipole exchange interaction

M. S. Bulakhov, A. S. Peletminskii, Yu. V. Slyusarenko

Published Sep 21, 2023• 1 citation
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Abstract

Abstract In the context of quantum gases, we obtain a many-body Hamiltonian for spin-3/2 atoms with general multipole (spin, quadrupole, and octupole) exchange interaction by employing the apparatus of irreducible spherical tensor operators. This Hamiltonian implies the finite-range interaction, whereas, for zero-range (contact) potentials parameterized by the s-wave scattering length, the multipole exchange interaction becomes irrelevant. Following the reduced description method for quantum systems, we derive the quantum kinetic equation for spin-3/2 atoms in a magnetic field and apply it to examine the high-frequency oscillations known as zero sound.

DOI
10.1088/1751-8121/acfc0a

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Abstract In the context of quantum gases, we obtain a many-body Hamiltonian for spin-3/2 atoms with general multipole (spin, quadrupole, and octupole) exchange interaction by employing the apparatus of irreducible spherical tensor operators. This Hamiltonian implies the finite-range interaction, whereas, for zero-range (contact) potentials parameterized by the s-wave scattering length, the multipole exchange interaction becomes irrelevant. Following the reduced description method for quantum systems, we derive the quantum kinetic equation for spin-3/2 atoms in a magnetic field and apply it to examine the high-frequency oscillations known as zero sound.
We provide the general arguments that quantum atomic gases of interacting high-spin atoms represent a physical system in which the multipole (hidden) degrees of freedom may be manifested. Their manifestation occurs when the interatomic interaction is of non-local type. For a local interaction described by the s-wave scattering length, the multipole degrees of freedom do not reveal themselves. To illustrate our findings, we theoretically examine the phenomenon of Bose–Einstein condensation in an interacting gas of spin-1 atoms in an external magnetic field. This study is based on the SU(2) invariant Hamiltonian, which has a bilinear structure in the spin and quadrupole operators along with the scalar term. It is shown that depending on the conditions imposed on the interaction amplitudes (stability conditions), the ground state of the system may exhibit three different phases: quadrupolar, ferromagnetic, and paramagnetic. The basic thermodynamic characteristics affected by hidden degrees of freedom are found for all phases.
This article follows up on arxiv:2511.15938, in which we developed an Hamiltonian renormalization scheme to construct a quantized theory of Fermi liquids. Here, we apply this formalism to a low-temperature atomic Fermi gas where the short-range interactions are fully parametrized by the s-wave scattering length aaa. We benchmark our renormalized theory by recovering known perturbative results on the static properties of the Fermi gas, such as the Lee-Huang-Yang expansion of the equation of state, the Galitskii expansion of the momentum distribution, and the Gor'kov-Melik Barkhudarov preexponential correction to the critical temperature. We then turn to the transport dynamics and demonstrate the presence of a preexponential correction to the speed of zero sound when including corrections of second order in aaa. Finally, we develop an efficient numerical method to solve the transport equation exactly, and we apply it to study the crossover from the collisionless to the hydrodynamic regime in the density and polarisation response functions.
We develop an analytical approach for the description of an atomic Bose gas at unitarity. By focusing in first instance on the evaluation of the single-particle density matrix, we derive several universal properties of the unitary Bose gas, such as the chemical potential, the contact, the speed of sound, the condensate density and the effective interatomic interaction. The theory is also generalized to describe Bose gases with a finite scattering length and then reduces to the Bogoliubov theory in the weak-coupling limit.
Motivated by the recent success of optical trapping of alkali-metal bosons, we have studied the zero sound modes of dilute Fermi gases with arbitrary spin-fff, which are spin-SSS excitations (0< S< 2f)(0<~S<~2f)(0< S< 2f). The dispersion of the mode (S) depends on a single Landau parameter F(S){F}^{(S)}F(S), which is related to the scattering lengths of the system through a simple formula. Measurement of (even a subset of) these modes in finite magnetic fields will enable one to determine all the interaction parameters of the system.
Abstract We obtain and justify a many-body Hamiltonian of pairwise interacting spin-1 atoms, which includes eight generators of the SU(3) group associated with spin and quadrupole degrees of freedom. It is shown that this Hamiltonian is valid for non-local interaction potential, whereas for local interaction specified by s -wave scattering length, the Hamiltonian should be bilinear in spin operators only (of the Heisenberg type). We apply the obtained Hamiltonian to study the ground-state properties and single-particle excitations of a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate (BEC) taking into account the quadrupole degrees of freedom. It is shown that the system under consideration can be in ferromagnetic, quadrupole, and paramagnetic phases. The corresponding phase diagram is constructed and discussed. The main characteristics such as the density of the grand thermodynamic potential, condensate density, and single-particle excitation spectra modified by quadrupole degrees of freedom are determined in different phases.