Entanglement and correlations in an exactly-solvable model of a
Bose-Einstein condensate in a cavity
- URL: http://arxiv.org/abs/2311.08138v1
- Date: Tue, 14 Nov 2023 13:06:39 GMT
- Title: Entanglement and correlations in an exactly-solvable model of a
Bose-Einstein condensate in a cavity
- Authors: Ofir E. Alon and Lorenz S. Cederbaum
- Abstract summary: The model can be seen as a generalization of the harmonic-interaction model for a trapped BEC coupled to a bosonic bath.
As an application we investigate a specific case of basic interest for itself, namely, non-interacting bosons in a cavity.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: An exactly solvable model of a trapped interacting Bose-Einstein condensate
(BEC) coupled in the dipole approximation to a quantized light mode in a cavity
is presented. The model can be seen as a generalization of the
harmonic-interaction model for a trapped BEC coupled to a bosonic bath. After
obtaining the ground-state energy and wavefunction in closed form, we focus on
computing the correlations in the system. The reduced one-particle density
matrices of the bosons and the cavity are constructed and diagonalized
analytically, and the von Neumann entanglement entropy of the BEC and the
cavity is also expressed explicitly as a function of the number and mass of the
bosons, frequencies of the trap and cavity, and the cavity-boson coupling
strength. The results allow one to study the impact of the cavity on the bosons
and vice versa on an equal footing. As an application we investigate a specific
case of basic interest for itself, namely, non-interacting bosons in a cavity.
We find that both the bosons and the cavity develop correlations in a
complementary manner while increasing the coupling between them. Whereas the
cavity wavepacket broadens in Fock space, the BEC density saturates in real
space. On the other hand, while the cavity depletion saturates, and hence does
the BEC-cavity entanglement entropy, the BEC becomes strongly correlated and
eventually increasingly fragmented. The latter phenomenon implies single-trap
fragmentation of otherwise ideal bosons, where their induced long-range
interaction is mediated by the cavity. Finally, as a complimentary
investigation, the mean-field equations for the BEC-cavity system are solved
analytically as well, and the breakdown of mean-field theory for the cavity and
the bosons with increasing coupling is discussed. Further applications are
envisaged.
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