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Journal of Experimental and Theoretical Physics

Dynamics of Bose-Condensed Ultracold Atoms and Trimer Molecules with the Formation of Atomic–Molecular Pairs

Зинган Анна Петровна, Olga F. Vasilieva, P. I. Khadzhi

Published Nov 1, 2019• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s1063776119090073

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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.
We theoretically examine the neutral atom-molecule analogue of the anomalous quantum correlations between degenerate electrons, i.e., Cooper pairs, that are responsible for superconductivity. Based on rogue dissociation of triatomic molecules (trimers) into opposite-momentum pairs of atoms and diatomic molecules (dimers) via a photoassociation or Feshbach resonance, we find a superfluid transition to a Bose-Einstein condensate of trimers dressed by atom-dimer Cooper pairs, at a critical temperature in reach of present ultracold technology.
A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic-molecular conversion in a Bose-Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined, to a considerable extent, by the initial density of particles and by the initial phase difference. Depending on initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.
The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is 1∕21∕21∕2 (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.
A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic-molecular conversion in a Bose-Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.