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Low Temperature Physics

Multipole degrees of freedom in physics of high-spin quantum atomic gases

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

Published Aug 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1063/10.0005559

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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.
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.
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 study several problems in Bose-Einstein condensates with internal degrees of freedom, and we find that this kind of condensates, which are usually referred to as spinor condensates, exhibit several phenomena that are qualitatively different from scalar (i.e. spinless) condensates. We analyze the ground state of a condensate with the constraint of maintaining a constant value of the total spin, and we find a number of different structures depending on the value of the total spin and the applied external magnetic field. We also study a certain type of measurement on spinor condensates in an attempt to distinguish between the so-called coherent and singlet states. We find that this kind of measurement cannot distinguish between the two states in question. We then consider a different experiment based on the interference between spinor condensate. It turns out that interference experiments cannot be used to distinguish between coherent and singlet states either. One of the interesting results regarding interference between two spinor condensates is that both the offset and visibility of the interference fringes vary from shot to shot, even if the initial conditions are identical in all the runs of the experiment. We then turn to the problem of condensing a gas of effectively spin 1/2 atoms. We argue that if spin relaxation mechanisms are slow enough, the condensate displays the phenomenon of fragmentation. The main difference of the fragmented state that we study and other fragmented states discussed in the literature is that this one is not caused by interatomic interactions, but rather by the constraint on the total spin of the system. We investigate the consequences of performing the experiment in a toroidal trap, and we find that, under certain conditions, the system spontaneously builds up a macroscopic value of orbital angular momentum. We finally discuss several problems related to the external Josephson effect. We derive simple equations of motion for the case of a two-component condensate that are identical to the extensively analyzed Bloch equations. We also find equilibrium points of the motion that are unstable in the spinless case.
The monograph is devoted to the main aspects of theoretical description of quantum many-body systems with Bose-Einstein or Fermi-Dirac statistics. We provide a review of modern methods of theoretical research, both analytical and numerical, as well as experimental realizations of unique effects and phenomena in quantum systems. The main attention is given to the theoretical study of exotic states in degenerate gases of atoms and quasiparticles. We develop a methology to accurately determine chemical potentials and other thermodynamic characteristics of ideal Bose and Fermi gases. These allow us to describe the ultraslow-light phenomenon in ultracold atomic gases in the framework of the microscopic approach that accounts for the internal degrees of freedom of bound states. The formalism relies on the linear response theory applied for the case of weak perturbation by the external elecromagnetic field. We also study Bose-Einstein condensation of photons in ideal atomic gases in different regimes of degeneracy of atomic and photonic components. A special attention is given to the Bogoliubov method of quasiaverages and related theory of a weakly interacting Bose gas with condensate. We extend the Bogoliubov theory to examine the spinor condensate and its magnetic states, as well as the condensate of heteronuclear Fermi-Fermi molecules. We also study a spatially periodic state of Bose-Einstein condensate, which can serve as a model for supersolid state of matter and develop the hydrodynamic theory of the latter. We outline the main statements of the Fermi liquid theory including the Pomeranchuk stability conditions of the normal state. It is shown that the violation of stability conditions results in certain phase transitions associated with the breaking of translational symmetry and rotational symmetry in the momentum space. We review a progress in the theoretical description of ultracold Fermi gases consisting of neutral atoms in the presence of the optical lattice spatial modulation. In case of multicomponent systems, a number of unique magnetically-ordered states are theoretically studied and predicted. We also develop a theory of highly dispersive spinful excitons in cobaltite compounds that explains certain unusual magnetic properties and effects in the resonant inelastic X-ray scattering on these materials.
Abstract We theoretically study a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also reexamine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential. We also obtain three-branch excitation spectrum of the broken-axisymmetry state. We show that this state can be prepared at three different regimes of applied magnetic field. Finally, we present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.
The achievement in cooling alkali atomic gases, such as 87^{87}87Rb, 23^{23}23Na and 7^{7}7Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a k2k^2k2-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut