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Low Temperature Physics

Dynamic electrostriction of a Bose condensate and of a system of neutral atoms

Arnold M. Kosevich

Published Oct 1, 2005• 13 citations
Publisher

Abstract

It is shown that the condensate of a Bose gas of neutral atoms has electrical properties that are reflected in the dynamics of the condensate and do not reduce to a trivial polarization of the atomic gases in an external electric field. The concept of an isotropic atomic quadrupole moment whose distribution creates a distribution of the macroscopic electric potential 〈φ〉 in a system of neutral atoms is used. The nonuniform distribution of atoms that arises in a sound wave, for example, will produce an electric field whose behavior is determined by the dynamics of 〈φ〉.

DOI
10.1063/1.2126942

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It is shown that the condensate of a Bose gas of neutral atoms has electrical properties that are reflected in the dynamics of the condensate and do not reduce to a trivial polarization of the atomic gases in an external electric field. The concept of an isotropic atomic quadrupole moment whose distribution creates a distribution of the macroscopic electric potential 〈φ〉 in a system of neutral atoms is used. The nonuniform distribution of atoms that arises in a sound wave, for example, will produce an electric field whose behavior is determined by the dynamics of 〈φ〉.
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.
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.
A study is made of the electric polarization of quantized vortices in a superfluid Bose liquid and their interaction with electric field. Two types of vortex polarization are considered, both of which are due to the centrifugal forces exerted on the atoms of the liquid in their azimuthal motion around the vortex line. First, under the influence of these forces the atoms acquire dipole moments (inertial polarization in the absence of external field), and a nonuniform symmetric distribution of the polarization density arises around the vortex line. Here the vortex does not have an integral dipole moment, but each element of the vortex line possesses a quadrupole moment. Second, the centrifugal forces lead to a nonuniform distribution of the atomic density around the vortex line, and therefore the polarization density of the liquid in an external electric field is also nonuniform near the vortex line, and an individual element of the vortex line acquires an effective dipole moment proportional to the field (inductive polarization). Analytical expressions are obtained for the polarization density around rectilinear and ring-shaped vortex lines, and the effective dipole and quadrupole moments of such vortices are calculated. The distribution of ponderomotive forces acting on a superfluid liquid containing a quantized vortex in an electric field is analyzed, and the corrections to the vortex energy due to the field are found. Numerical estimates of these effects are made for the case of HeII.
We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is estimated. Quantum equations for the evolution of medium polarization are constructed for the first time. The mathematical method we developed allows studying the effects of interactions on the evolution of polarization. The developed method may be applied to various physical systems in which dynamics is affected by DDI. A problem of elementary excitations in BEC, either affected or not affected by the uniform external electric field, is addressed using our method. We show that the evolution of polarization in BEC leads to the formation of a novel type of elementary excitations. Also, we consider the process of wave generation in polarized BEC by means of monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov's modes and polarization modes by the dipole beam.