We investigate the quantum squeezing of slow-light solitons generated in a $\mathrm{\Lambda }$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). Starting from the Heisenberg-Langevin and Maxwell equations governing the quantum dynamics of atoms and probe laser field, we derive a quantum nonlinear Schrödinger equation controlling the evolution of the probe-field envelope. By using a direct perturbation approach to diagonalize the effective Hamiltonian (where the atomic variables have been eliminated), we carry out a detailed calculation on the quantum fluctuations of a slow-light soliton, expanded as a superposition of the complete and orthonormalized set of eigenfunctions obtained by solving the Bogoliubov-de Gennes (BdG) equations describing the quantum fluctuations. We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.

中文翻译：

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慢光孤子的量子压缩

我们研究了慢光孤子的量子压缩 $\mathrm{\Lambda }$在电磁感应透明 (EIT) 条件下工作的 形三级原子系统。从控制原子量子动力学和探测激光场的海森堡-朗之万和麦克斯韦方程开始，我们推导出控制探测场包络演化的量子非线性薛定谔方程。通过使用直接微扰方法对有效哈密顿量（其中原子变量已被消除）进行对角化，我们对慢光孤子的量子涨落进行了详细计算，扩展为完整和正交化的本征函数集的叠加通过求解描述量子涨落的 Bogoliubov-de Gennes (BdG) 方程获得。我们表明，由于 EIT 效应造成的巨大克尔非线性，可以在短传播距离内​​实现对慢光孤子的显着量子压缩。这里报告的结果有助于理解慢光孤子的量子特性，并有助于在实验上通过 EIT 在冷原子气体中实现光压缩。