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arXiv:cond-mat/0703211

A Proposed Casimir-Like Effect Between Contaminants in Ideal Bose-Einstein Condensates

Alexander Oshmyansky

Published Mar 8, 2007• 1 citation
arXivHTMLPDF

Abstract

It is hypothesized that, within Bose-Einstein condensates, contaminants will form a potential that effects the energy state of a condensate. While assuming a system governed by the Gross-Pitaevskii equation, contaminants are modelled as boundary conditions for the wave function of the condensate. It is then found that the energy of the system depends directly upon the distance between contaminants. Energy is minimized as two particles either come together or move apart depending on the nature of the condensate. This is due to the presence of induced standing waves in the condensate between two contaminants, similar to the attractive effect caused by standing electromagnetic waves in a vacuum, the Casimir effect. Quantum calculations are also done to determine the expected strength of the "contaminant in condensate" effect.

DOI
10.48550/arxiv.cond-mat/0703211

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It is hypothesized that, within Bose-Einstein condensates, contaminants will form a potential that effects the energy state of a condensate. While assuming a system governed by the Gross-Pitaevskii equation, contaminants are modelled as boundary conditions for the wave function of the condensate. It is then found that the energy of the system depends directly upon the distance between contaminants. Energy is minimized as two particles either come together or move apart depending on the nature of the condensate. This is due to the presence of induced standing waves in the condensate between two contaminants, similar to the attractive effect caused by standing electromagnetic waves in a vacuum, the Casimir effect. Quantum calculations are also done to determine the expected strength of the "contaminant in condensate" effect.
In this paper the interaction between contaminants of the Bose-Einstein condensed system at finite temperature is discussed by using the Thermal Field Dynamics.The system energy and Casimir force between the contaminants are obtained,the relationship of the force with temperature and distance is also discussed.These results will help us further understand the physical effect of contaminants in the Bose-Einstein condensed body and provide certain reference value to Casimir effect and the Bose-Einstein condensation experimental study.
Abstract The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross–Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross–Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.
Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.
We consider the Casimir force between two vortices due to the presence of density fluctuations induced by turbulent modes in a Bose–Einstein condensate. We discuss the cases of unbounded and finite condensates. Turbulence is described as a superposition of elementary excitations (phonons or BdG modes) in the medium. Expressions for the Casimir force between two identical vortex lines are derived, assuming that the vortices behave as point particles. Our analytical model of the Casimir force is confirmed by numerical simulations of the Gross–Pitaevskii equation, where the finite size of the vortices is retained. Our results are valid in the mean-field description of the turbulent medium. However, the Casimir force due to quantum fluctuations can also be estimated, assuming the particular case where the occupation number of the phonon modes in the condensed medium is reduced to zero and only zero-point fluctuations remain.
Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive 1∕r1∕r1∕r interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate ``atomic'' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N2a∕au{N}^{2}a∕{a}_{u}N2a∕au​ and $\ensuremath{\gamma}∕{N}^{2}$, where NNN is the particle number, aaa the scattering length, au{a}_{u}au​ the ``Bohr'' radius, and $\ensuremath{\gamma}$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.