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Communications in Theoretical Physics

Chaos in coupled atom–molecular Bose–Einstein condensates

Haiming Deng, Jian‐Quan Huang, Dajun Lei, Chunzhi Jiang, Chao Kong

Published Mar 9, 2023• 0 citations
Publisher

Abstract

Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.

DOI
10.1088/1572-9494/acc2b2

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Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
We analyze the coherent multimode dynamics of a system of coupled atomic and molecular Bose gases. Starting from an atomic Bose-Einstein condensate with a small thermal component, we observe a complete depletion of the atomic and molecular condensate modes on a short time scale due to a significant population of excited states. Giant coherent oscillations between the two condensates for typical parameters are almost completely suppressed. Our results cast serious doubts on the common use of the 2-mode model for the description of coupled ultracold atomic-molecular systems and should be considered when planning future experiments with ultracold molecules.
We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory. Large-amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as N/lnN\sqrt{N}/\mathrm{ln}NN​/lnN with the total number of atoms N, rather than the expected pure N\sqrt{N}N​ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean-field theory is an initially nonexponential ``spontaneous'' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (superexponential) rate observed for the entangled state formed by spontaneous dissociation.
Nonlinear systems, including atom–field interaction, are investigated due to their fundamental applications in quantum mechanics and rapidly growing fields of quantum communication, especially secure communication with chaotic dynamics. In this paper, we study the chaotic dynamics of a system consisting of an atomic Bose–Einstein condensate interacting with a quantized radiation field in a high-quality cavity with a periodically modulated length. The frequency modulation is adapted by a periodic time-dependent atom–field coupling strength. We use a semiclassical approach to decouple the atoms and field variables and then numerically solve the corresponding nonlinear dynamical equations of the system. Generally, the dynamics of the system sensitively depends on its initial conditions, thereby long-term prediction is impossible. We show that the system demonstrates the emergence of classical dynamical chaos from quantum electrodynamics. The chaotic behavior of energy transfer in the system can be enhanced by increasing the depth of frequency modulation. The strange attractor clearly illustrates that the system presents extremely exotic dynamics over a wide range of parameters. This implies that the dynamical quantities oscillate irregularly, never exactly repeating but always remaining in a bounded region of the phase space.
We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.
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We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose–Einstein condensed state, well described by Thomas–Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.