Quantum many-body analysis of a spin-2 bosons with two-body inelastic decay

TL;DR

This work analyzes the quantum many-body dynamics of spin-2 bosons undergoing two-body inelastic loss, modeled as an open quantum system with a Lindblad master equation under a single-mode approximation. The authors prove that the steady states are statistical mixtures of maximal total-spin states $|F=2N,F_z angle$, reflecting the magnetization induced by loss channels that forbid the $\,\mathcal{F}=4$ collision. Numerical simulations for $^{87}$Rb with and without a quadratic Zeeman term $q$ reveal that, absent $q$, the system relaxes to a fully magnetized steady state, while a quench in $q$ can yield a nonclassical, Schrödinger-cat-like magnetization distribution, evidenced by parity features in the $Q_m^{(N)}$ distributions. These results demonstrate how dissipation can sculpt nontrivial quantum states in small spinor condensates and suggest routes to realize cat-like magnetization in experiments, potentially with other atomic species such as $^{23}$Na$.$

Abstract

Bose-Einstein condensates (BECs) of $^{87}\textrm{Rb}$ atoms with a hyperfine spin of 2 are open quantum systems, where the atoms are lost through two-body inelastic collisions. In this dissipation process, a collision channel with total spin of 4 is forbidden by angular momentum conservation, which results in magnetization of the atoms remaining in the condensate. Here, we investigate the quantum many-body properties of spin-2 bosons that undergo two-body atomic loss. We show that the system finally reaches a steady state, which is a mixture of the states with maximum total spins. In addition, we find that a non-classical steady state can be obtained by quenching the quadratic Zeeman coefficient.

Figures (2)

• Figure 1: Time evolution for $q = 0$. (a) Average particle number $\langle \hat{N} \rangle$ and normalized total magnetization $F^2_\textrm{norm}$. (b) Particle number distribusions $P_N$ at $t = 0, 0.132$, and $1.76~\mathrm{s}$. (c) Distribusions $Q_m^{(N)}$ of the $z$-magnetization at $t = 0.132$ and $1.76~\mathrm{s}$. The upper and lower panels show the distributions in the subspaces $N=6$ and $N=16$, respectively. The dotted lines correspond to Eq. (\ref{['mean_field_coefficient_35.5']}).
• Figure 2: Time evolution for $q / \hbar = 90.6~\textrm{Hz}$ with and without quenching of $q$. In the case with quenching, $q$ is suddenly changed to 0 at $t = 14.3~\textrm{ms}$. (a) Transverse magnetization $S_\perp$ with quenching (solid line) and without quenching (dotted line). (b) Average particle number $\langle \hat{N} \rangle$ (blue or dark-gray lines) and normalized total magnetization $F^2_\textrm{norm}$ (red or light-gray lines) with quenching (solid lines) and without quenching (dotted lines). (c) Particle number distribution at $t = 1.76~\textrm{s}$ with quench (filled boxes) and without quench (striped boxes). (d) Distribution $Q_m^{(N)}$ of $z$-magnetization for $N = 6$ and $N = 16$ at $t = 1.76 \textrm{s}$. The dotted lines show Eq. (\ref{['mean_field_coefficient_35.5']}).