On the issue of zero point energy in Bose–Einstein condensates

A.A. Borghardt, D.Ya. Karpenko

We show that the free relativistic wave equation which describes the particle without or with rest mass has more than one part of energy spectrum. One part of energy spectrum is beginning with rest energy and it is not limited by above. This part of spectrum is called by us as normal. Another part of energy spectrum is beginning with the zero energy . This part of spectrum is called by us as anomalous since the zero energy corresponds to the infinite group velocity.The presence of the zero in the energy spectrum permits to consider the Bose-Einstein condensation. We show that the heat capasity has the finite discontinuity at the condensation temperature. The last means that we have the phase transition at the condensation point.

Masahito Veda, Hiroki Sait

Among the species that have Bose-condensed, lithium 7 and rubidium 85 form unique condensates in that atoms interact attractively and that the energy barrier that stabilizes the gaseous Bose-Einstein condensates originates from the zero-point motion of atoms. This paper reviews some unique features of these new states of matter that are distinguished from those of other species with repulsive interactions. These include the density instability, macroscopic quantum tunneling, intermittent implosion, shellstructure formation, and partial quantization of circulation. 1. METASTABILITY AND DENSITY INSTABILITY OF THE CONDENSATE Atoms with attractive interactions are believed not to undergo Bose-Einstein condensation in the uniform 3D system. It is therefore appropriate to begin by discussing why attractive Bose-Einstein condensates (BEes) have been realized in trapped systems [1, 2]. A trapped BEe has three characteristic energies, namely, the kinetic, potential and interaction energies. The kinetic energy arises from the uncertainty principle, and is proportional to R-2 where R is the linear dimension of BEe. The trapping potential is usually harmonic, and therefore the potential energy is proportional to R2. The mean-field interaction energy is proportional to NoaR-3, where No and a denote the number of condensate atoms and the s-wave scattering length, respectively. The interaction energy and hence a are negative for attractive systems. The sum of these three energies F = No(AR-2 + BR2 CNolaIR-3), where A, B, Care positive constants, gives the total energy of the system which has a metastable minimum if No is smaller than a certain critical value Nc.lt is at this local minimum where a metastable BEe is believed to be formed. If No is larger than Nc' there is no metastable minimum and the condensate is bound to collapse to the R = 0 state, which is a metallic phase. It is clear from the above argument that the zero-point energy due to confinement serves as a kinetic obstacle against collapse, allowing the metastable BEe to be formed. For the case of attractive interactions, the lowest-energy collective mode is the

Ph. Nozières

Adelchi Fabrocini

Zeng‐Bing Chen, Yong-De Zhang

We demonstrate that two coupled Bose-Einstein condensates (BECs) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BECs are weakly coupled and confined in an asymmetric double-well trap. When the ``charging energy'' of the system is much larger than the Josephson energy and the system is biased near a degeneracy point, the two BECs represent a qubit with two states differing only by one atom. The realization of the BEC qubits in realistic BEC experiments is briefly discussed.