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ON THEORY OF BOSE-EINSTEIN CONDENSATION OF PARTICLES WITH ARBITRARY INTEGER SPIN

Abdus Salam

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The Bogoliubov theory of weakly interacting Bose gas is generalized to Bose-Einstein condensates (BEC) of particles with arbitrary integer spin in a magnetic eld. On the basis of the Bogoliubov method of quasiaverages, an equation for the condensate wave function is obtained. The ground state properties, thermodynamic stability, and excitation spectra of such BEC are studied. The obtained results are compared to spin-1 Bose condensate.

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The Bogoliubov theory of weakly interacting Bose gas is generalized to Bose-Einstein condensates (BEC) of particles with arbitrary integer spin in a magnetic eld. On the basis of the Bogoliubov method of quasiaverages, an equation for the condensate wave function is obtained. The ground state properties, thermodynamic stability, and excitation spectra of such BEC are studied. The obtained results are compared to spin-1 Bose condensate.
The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.
We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to TcT_{c}Tc​ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.
Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the framework of the considering interaction Hamiltonian it is shown that the ground state spin structure and spin part of the chemical potential is determined by the renormalized interaction, being defined by the contribution of the virtual large momenta. The ferromagnetic structure of the ground state, and the equation of the phase, density, and spin dynamics are obtained from Gross-Pitaevskii equations.
We generalize the perturbation theory of weakly interacting bosons to Bose-Einstein condensates with hyperfine spin F=1.F=1.F=1. Analytical expressions of second-order self-energies beyond the mean-field approximation are derived at zero temperature. We further extend the perturbation theory to the finite-temperature case, and derive the corresponding self-energies. We evaluate these self-energies near the poles of the first-order (mean-field) Green's functions within the on-shell approximation, and expand the results in powers of wave number in the long-wavelength limit. Excitation spectra for each mode are obtained analytically at low temperatures. We also derive the ground-state energy and thermodynamic quantities such as free energy 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.