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arXiv:2203.08922 · Physics Letters A

Persistent revivals in a system of trapped bosonic atoms

Carlos Diaz-Mejia, Javier de la Cruz, Sergio Lerma-Hernández, Jorge G. Hirsch

Published Dec 6, 2023• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physleta.2023.129262

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We study the collapse and revival of interference patterns in the momentum distribution of atoms in optical lattices using a projection technique to properly account for the fixed total number of atoms in the system. We consider the common experimental situation in which weakly interacting bosons are loaded into a shallow lattice, which is suddenly made deep. The collapse and revival of peaks in the momentum distribution is then driven by interactions in a lattice with essentially no tunneling. The projection technique allows to us to treat inhomogeneous (trapped) systems exactly in the case that noninteracting bosons are loaded into the system initially, and we use time-dependent density-matrix renormalization group techniques to study the system in the case of finite tunneling in the lattice and finite initial interactions. For systems of more than a few sites and particles, we find good agreement with results calculated via a naive approach, in which the state at each lattice site is described by a coherent state in the particle occupation number. However, for systems on the order of ten lattice sites, we find experimentally measurable discrepancies to the results predicted by this standard approach.
We present a theoretical method to study a trapped gas of bosonic two-level atoms interacting with a single mode of a microwave cavity. This interaction is described by a trilinear Hamiltonian that is formally completely equivalent to the one describing parametric down-conversion in quantum optics. A system of differential equations describing the evolution, including the long-time behavior, of not only the mean value but also the variance of the number of excited atoms is derived and solved analytically. For different initial states the mean number of excited atoms exhibits periodically reappearing dips, with an accompanying peak in the variance, or fractional collapses and revivals. Closed expressions for the period and the revival time are obtained.