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Physica Scripta

Dynamics of the atom-polyatomic molecule conversion with quantum decoherence

Chenglong Yang, Qi Zhang, B. Cui

Published Apr 9, 2024• 1 citation
Publisher

Abstract

Abstract Based on the mean-field approximation and the two-mode Bose–Hubbard model, we investigate the dynamical properties of atom-polyatomic molecule conversion systems under dissipation and dephasing. For such a many-body system problem, we partition phase space based on the states of fixed points, study the movement of fixed points and the transition to attractors in an open system. Additionally, for all the atoms that constitute a molecule, depending on whether the species of these atoms are identical or not, we introduce the innovative concepts of unbiased and biased systems. We discover that in biased conversion systems under particle losses, the evolution trajectories are distributed on a three-dimensional Bloch sphere with an internal structure. There exists a significant difference from the two-dimensional Hilbert space of an unbiased system. Finally, we discuss the sweeping rate of the time-varying magnetic field applied externally to the conversion system, and analyze a feasible scheme for the quantum coherent synthesis of triatomic molecules.

DOI
10.1088/1402-4896/ad3c9e

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Abstract Based on the mean-field approximation and the two-mode Bose–Hubbard model, we investigate the dynamical properties of atom-polyatomic molecule conversion systems under dissipation and dephasing. For such a many-body system problem, we partition phase space based on the states of fixed points, study the movement of fixed points and the transition to attractors in an open system. Additionally, for all the atoms that constitute a molecule, depending on whether the species of these atoms are identical or not, we introduce the innovative concepts of unbiased and biased systems. We discover that in biased conversion systems under particle losses, the evolution trajectories are distributed on a three-dimensional Bloch sphere with an internal structure. There exists a significant difference from the two-dimensional Hilbert space of an unbiased system. Finally, we discuss the sweeping rate of the time-varying magnetic field applied externally to the conversion system, and analyze a feasible scheme for the quantum coherent synthesis of triatomic molecules.
Based on the mean-field approximation and the phase-space analysis, we study the dynamics of atom-molecule conversion systems subject to particle losses. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schr\"odinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundaries, which separate different dynamical regimes, have been established and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored. By numerically solving the master equation, we show that the mean-field approximation is a good approach to study the dynamics of this atom-molecule conversion system.
In this paper, we investigate quantum manipulations in an open atom-molecule conversion system. Through the transformation for the basis of the system, a set of time-dependent equations are derived under mean field approximation. We find that transitions between different dynamic areas of the system can be realized through manipulating an external rotating magnetic field, which corresponds to the tunneling rate in the equation. Through investigating the phase space of the system, we design an efficient method to combine pure cold molecule and pure molecular state so that it can be reached with much shorter time. Furthermore, manipulation of laser signal modulation, external diving and the distance-selective diffusion are also discussed in this paper.
The dynamics of an atom-molecule-conversion system subject to dephasing noises is studied in this paper. Using a dephasing master equation and mean-field theory, we derive a Bloch equation for the system, and this equation is compared with the Bloch equation derived by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy truncation approach. Fixed points of the system are calculated by solving both the Bloch equation and the master equation. Comparison between these two calculations suggests that while at short times the mean-field theory (MFT) is a good approximation for the atom-molecule-conversion system, a high-order hierarchy truncation approach is necessary for the system on a long time scale. Although the MFT cannot predict the fixed points correctly, its predictions for the stability of the fixed points are consistent with the BBGKY theory for a wide range of parameters.
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.
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.
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.