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Excitation spectrum and electrical properties of the condensate of Bose atoms

Arnold M. Kosevich, B. I. Verkin

Published Jan 1, 2005• 0 citations
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Abstract

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.

DOI
10.5488/cmp.8.4.773

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•Jan 1, 2001•5 citations
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.
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 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〉.
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 theory determining the electric and magnetic properties of vortex states in Bose-Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov-Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross-Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.
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.
A theory determining the electric and magnetic properties of vortex states in Bose–Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov–Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross–Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.