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Modern Physics Letters B

Effective manipulation of cold atom-molecule conversion system

Dezheng Li, Junning Zheng, Yifei Chen, B. Cui

Published Jan 25, 2023• 0 citations
Publisher

Abstract

In this paper, a set of master equations of a cold atom-molecule system including the manipulation of an external rotating magnetic field and laser signal under a mean-field approximation was developed. We discovered that external manipulation can be characterized by a single regulating term. After considering the realizability and necessity of the regulating term for system manipulation, we separated the molecule preparation procedure into three stages: the phase transforming, descending and stable stages. In each stage, the regulating term’s qualities were analyzed. Further, we discovered that, under certain situations, this system cannot enter the pure molecular state in a stable manner, regardless of whether it is regulated or not. Finally, an approach was proposed for the rapid preparation of cold molecules.

DOI
10.1142/s0217984922502086

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In this paper, a set of master equations of a cold atom-molecule system including the manipulation of an external rotating magnetic field and laser signal under a mean-field approximation was developed. We discovered that external manipulation can be characterized by a single regulating term. After considering the realizability and necessity of the regulating term for system manipulation, we separated the molecule preparation procedure into three stages: the phase transforming, descending and stable stages. In each stage, the regulating term’s qualities were analyzed. Further, we discovered that, under certain situations, this system cannot enter the pure molecular state in a stable manner, regardless of whether it is regulated or not. Finally, an approach was proposed for the rapid preparation of cold molecules.
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.
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.
Deflection by magnetic or electric field gradients has long been used to analyze or to alter the translational trajectories of neutral gas-phase atoms or molecules. Recent work has developed sources of slow, cold molecular beams that offer means to enhance markedly the attainable deflections, which are inversely proportional to the translational kinetic energy. The sensitivity and resolution can thus be much increased, typically by factors of 10(2)-10(4). We illustrate ways to exploit this enhanced deflection capability, particularly when balancing electric and magnetic deflections. Chemical scope can be greatly extended by utilizing feeble but ubiquitous interactions, especially the induced electric dipole due to the molecular polarizability and magnetic moments resulting from molecular rotation or nuclear spins. We also examine the effect of non-Maxwellian velocity distributions produced by supersonic expansions or by quantum statistics (pertinent for ultracold beams). Generic plots are provided, employing dimensionless variables, to facilitate the design and interpretation of experiments with deflections amplified by low kinetic energy.
Abstract Atom-to-molecule conversion by the technique of optical Feshbach resonance in a magnetic lattice is studied in the mean-field approximation. For the case of a shallow lattice, we give the dependence of the atomto-molecule conversion efficiency on tunnelling strength and atomic interaction by taking a double-well as an example. We find that one can obtain a high atom-to-molecule conversion by tuning the tunnelling and interaction strengths of the system. For the case of a deep lattice, we show that the existence of the lattice can improve the atom-to-molecule conversion for certain initial states.
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.
We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3 × 10 −6 for the final transition probability while at certain time points it might increase up to 10 −3 . Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.