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Condensed Matter Physics

Excitation spectrum and electrical properties of the condensate of Bose atoms

Kosevich

Published Jan 1, 2005• 0 citations
Publisher

Abstract

It is shown that the condensate of a degenerated Bose gas consisting of neutral atoms possesses electrical properties which differ from a trivial polarization of the atoms in the electric field.A notion of an isotropic quadrupole moment (IQM) of a neutral atom is introduced.A distribution of IQM reflects a specific spatial ordering in the condensate and produces a distribution of the electric potential.Small vibrations of the Bose gas are considered and a correction to the Bogoliubov spectrum of elementary excitations in the degenerated Bose gas is obtained.An additional term in the Gross-Pitaevskii equation which is responsible for such a correction is found and a new type of the nonlinear Schr ödinger equation (NSE) is constructed.Since the Bose condensate is akin to the superfluid component in He II, a manifestation of its electrical activity could have a relation to the electrical activity of the superfluid liquid observed experimentally.

DOI
10.5488/cmp.8.4.773

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It is shown that the condensate of a degenerated Bose gas consisting \nof neutral atoms possesses electrical properties which differ from a trivial \npolarization of the atoms in the electric field. A notion of an isotropic \nquadrupole moment (IQM) of a neutral atom is introduced. A distribution \nof IQM reflects a specific spatial ordering in the condensate and produces \na distribution of the electric potential. Small vibrations of the Bose gas are \nconsidered and a correction to the Bogoliubov spectrum of elementary excitations \nin the degenerated Bose gas is obtained. An additional term in \nthe Gross-Pitaevskii equation which is responsible for such a correction is \nfound and a new type of the nonlinear Schrodinger equation (NSE) is constructed. Since the Bose condensate is akin to the superfluid component \nin He II, a manifestation of its electrical activity could have a relation to the \nelectrical activity of the superfluid liquid observed experimentally.
A possibility of polarization of the gas of hydrogen-like atoms at zero temperature in the Bose–Einstein condensate is studied at equilibrium and nonequilibrium conditions. The Gross–Pitaevskii equation is generalized for a gas of atoms considering their electronic structure. It is shown that the wave function of the system of interacting bosons in a single-particle condensate at zero temperature looks like the Glauber coherent state. With the help of the generalized Gross–Pitaevskii equation the polarization properties of atomic gas in the Bose–Einstein condensation state are investigated. It is shown that the electron stationary states in atoms of a gas in the coherent state differ from the electron stationary states in free atoms. Because of this the superfluid system can be spontaneously polarized, even if the free atoms in the stationary states have no intrinsic electric dipole moment. The polarization properties of a system of double-level hydrogen-like atoms in the Bose–Einstein condensate are studied more comprehensively. The propagation of both sound and high-frequency small disturbances in the coherent system of polarized atoms is accompanied by oscillations of polarization. The applicability of the developed idea to the analysis of electrical phenomena in superfluid helium is discussed.
We present the Gross–Pitaevskii equation for Bose–Einstein condensates (BECs) possessing the electric dipole and the electric quadrupole moments in a non-integral form. These equations are coupled with the Maxwell equations. The model under consideration includes the dipole–dipole, the dipole–quadrupole, and the quadrupole–quadrupole interactions in terms of the electric field created by the dipoles and quadrupoles. We apply this model to obtain the Bogoliubov spectrum for three-dimensional BECs with a repulsive short-range interaction. We obtain an extra term in the Bogoliubov spectrum in comparison with the dipolar BECs. We show that the quadrupole–quadrupole interaction gives a positive contribution in the Bogoliubov spectrum. Hence, this spectrum is stable.
After a brief historical introduction to Bose-Einstein condensation and Fermi degeneracy, we discuss theoretical results we have recentely obtained for trapped degenerate quantum gases by means of a thermal field theory approach. In particular, by using Gross-Pitaevskii and Bogoliubov-Popov equations, we consider thermodynamical properties of two Bosonic systems: a gas of Lithium atoms and a gas of Hydrogen atoms. Finally, we investigate finite-temperature density profiles of a dilute Fermi gas of Potassium atoms confined in a harmonic potential.
We study the propagation of electromagnetic waves in the Bose-Einstein condensate of atoms with both intrinsic dipole moments and those induced by the electric field. The modified Gross--Pitaevskii equation is used, which takes into account relaxation and interaction with the electromagnetic field. Two cases are considered: 1) when the dispersion curves of the electromagnetic wave and of the condensate excitations do not intercross and 2) when the condensate excitations' spectrum has a gap and the two dispersion curves do intercross. In the second case the two branches hybridize. It is shown that propagation of sound waves can be accompanied by oscillation of the electromagnetic field. The impact is studied of the dipole-dipole interaction on the character of electromagnetic and acoustic waves' propagation in the Bose-Einstein condensate.