Roles of Polarization and Detuning in the Noise-induced Relaxation Dynamics of Atomic-Molecular Bose Condensates

TL;DR

This work analyzes noise-induced relaxation in a resonant atom–molecule Bose–Einstein condensate described by a two-channel Feshbach model, comparing mean-field (MF) and Bogoliubov backreaction (BBR) approaches. Relaxation of polarization and coherence is characterized by longitudinal and transverse times $T_z$ and $T_{x-y}$, whose behavior depends on the initial polarization $|s^0_z|$ and detuning $\epsilon_b$, with noise on the coupling $\tilde{g}$ and detuning driving damping and dephasing. Near resonance, population transfer accelerates while coherence indicators (von Neumann entropy $S_V$, fidelity $F$, Husimi distribution $H$, and quantum Fisher information $Q$) reveal enhanced coherence, even as other measures like the conversion efficiency $\Gamma$ and condensate fraction $C_+$ peak, signaling robust relaxation dynamics. The study also explains a positive-detuning shift of the resonance arising from magnetic-field fluctuations and phase noise, offering a comprehensive set of observable signatures for experiments on noisy atom–molecule conversion. These results provide a framework for controlling coherence and population dynamics in bimodal condensates under realistic noise.

Abstract

We study the relaxation process of a resonant Bose gas under the influence of Gaussian white noise. We characterize the system dynamics in terms of the polarization or imbalance between the atoms and molecules, and the system coherence. The relaxation times corresponding to these two quantities are studied both using a mean-field model, and a Born Green Kirkwood Yvon hierarchy that takes into account the higher-order correlations. The role of the initial polarization and the Feshbach detuning are investigated. It is found with an increasing initial population imbalance, the longituidinal relaxation time (that governs the dyanamics of the polarization) grows, while the transverse relaxation time (that governs the dynamics of the coherence) decays. As for the varying Feshbach detuning, it is observed that the longituidinal relaxation time reaches its minima and its transverse counterpart reaches its maxima near the resonance. We also study how the initial polarization and the detuning affect physical quantities like drift speed, condensate fraction, fidelity and entanglement entropy etc, and find the results to be fully consistent with the behavior of the relaxation dynamics of the system.

Figures (15)

• Figure 1: A few initial states (brown) and the final equilibrium point (purple, south pole oriented state) are indicated on the Bloch sphere, where $\theta$ and $\phi$ denote the polar and azimuthal angles, respectively.
• Figure 2: Two types of outward motions for A-BEC ($N_a$) and M-BEC ($2N_b$).
• Figure 3: Effect of absolute initial polarization ($\lvert s^0_z\rvert$) variation with longitudinal relaxation time ($T_{z}$) where MF (), and $\Delta^0_{xx}$ () are denoted by their respective colors.
• Figure 4: Effect of activation of variance ($\Delta^0_{ii}$) on longitudinal relaxation time ($T_{z}$) driven by detuning ($\epsilon_b$) variation where MF (), $\Delta^0_{xx}$ (), and $\Delta^0_{yy}$ () are denoted by their respective colors.
• Figure 5: Effect of absolute initial polarization ($\lvert s^0_z\rvert$) variation with transverse relaxation time ($T_{x\text{-}y}$) where MF (), $\Delta^0_{xx}$ (), and $\Delta^0_{yy}$ () are denoted by their respective colors.