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Bulletin of Federal State University of Education Series Physics and Mathematics

Temporal evolution of tunneling of bose-condensed atoms in a quadrupole trap under the condition of initial equipopulation of trap pits

O. Vasilieva, Зинган Анна Петровна

Published Jan 28, 2024• 0 citations

Abstract

Aim of this work is to theoretically investigate the temporal evolution of Bose-condensed atoms in a quadrupole trap. Methodology. Theoretical studies of the interaction Hamiltonian describing the time evolution of Bose-condensed atoms in a quadrupole trap under linear tunneling conditions have been carried out. Results. Analytical solutions are obtained for a system of differential equations describing the time evolution of Bose-condensed atoms in a quadrupole trap. Research implications. The time evolution of Bose-condensed atoms in a quadrupole trap is determined by the initial phase difference, which makes it possible to phase-control the process of Bose-atom tunneling in traps.

DOI: 10.18384/2949-5067-2023-3-15-32

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Aim of this work is to theoretically investigate the temporal evolution of Bose-condensed atoms in a quadrupole trap. Methodology. Theoretical studies of the interaction Hamiltonian describing the time evolution of Bose-condensed atoms in a quadrupole trap under linear tunneling conditions have been carried out. Results. Analytical solutions are obtained for a system of differential equations describing the time evolution of Bose-condensed atoms in a quadrupole trap. Research implications. The time evolution of Bose-condensed atoms in a quadrupole trap is determined by the initial phase difference, which makes it possible to phase-control the process of Bose-atom tunneling in traps.

In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.

For a Bose-Einstein condensate in a trap with oscillating barriers, in the resonance approximation, evolution equations are derived. Their analytical solution reveals the existence of two fundamentally different types of nonlinear conservative Rabi oscillations: (i) with periodic temporal variation of moduli and phase difference of levels' amplitudes of probability, and (ii) with monotonic temporal variation of the phase difference. It is shown that the two types can be realized for the same parameters of the scheme, but for different initial conditions. Analytical predictions are confirmed by numerical solution to the Gross-Pitaevskii equation.

The particle distribution in a Bose condensate under the trapping potential and its time evolution after switching off the trapping potential suddenly are calculated. We investigate the problem from the viewpoint of quantum field theory,using a model of self-interacting neutral boson field. Within the approximation of retainng the most dominant term in the Hamiltonian after applying the Bogoliubov replacement, we can calculate analytically the particle distribution as a function of space and time coordinates.

Abstract The results of investigation of the photodissociation dynamics of triatomic Bose-condensed ultracold molecules (trimers) with the formation of atoms and diatomic (dimer) pairs are presented. The interaction Hamiltonian is proposed, and a system of nonlinear equations is constructed that describes the evolution of atoms and molecules. Integrals of motion are obtained, and a nonlinear differential equation is derived for the time evolution of the atomic density with the use of these integrals. The solutions of this equation in various approximations imply that, depending on the initial conditions, different regimes of time evolution of the system are possible: periodic and aperiodic regimes.