Time-periodic quantum states of weakly interacting bosons in a harmonic trap

• URL: http://arxiv.org/abs/2003.03684v2
• Date: Thu, 15 Oct 2020 10:33:37 GMT
• Title: Time-periodic quantum states of weakly interacting bosons in a harmonic trap
• Authors: Marine De Clerck, Oleg Evnin
• Abstract summary: We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap, and focus on states at the Lowest Landau Level (LLL) We exploit the rich algebraic structure of the problem to give an explicit construction of a large family of quantum states with energies of the form $E_0+gE_1/4+O(g2)$. As a result, any superposition of these states evolves periodically with a period of at most $8pi/g$ until, at much longer time scales of order $1/g2$, corrections to the energies of order $g
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap, and focus on states at the Lowest Landau Level (LLL). At linear order in the coupling parameter $g$, we exploit the rich algebraic structure of the problem to give an explicit construction of a large family of quantum states with energies of the form $E_0+gE_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. As a result, any superposition of these states evolves periodically with a period of at most $8\pi/g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ become important and may upset this perfectly periodic behavior. We further construct coherent-like combinations of these states that naturally connect to classical dynamics in an appropriate regime, and explain how our findings relate to the known time-periodic features of the corresponding weakly nonlinear classical theory. We briefly comment on possible generalizations of our analysis to other numbers of spatial dimensions and other analogous physical systems.

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