Ultra-low-noise phase gate and squeezed state rotation in a gain-and-loss-balanced coherently prepared atomic medium

The realization of ultra-low-noise quantum phase gates and squeezed state rotations has long been a goal in the fields of quantum optics and quantum information. In this study, we present a theoretical proposal for an ultra-low-noise quantum phase gate and squeezed state rotation using a coherently prepared atomic medium. We demonstrate that, under a suitable set of parameters, the loss and gain mechanisms within this coherently prepared atomic system can balance each other over a broad range of probe field frequencies. As a result, the noise associated with the Raman gain process can be significantly suppressed within this frequency range. Additionally, we show that the system exhibits a strong optical Kerr nonlinearity, which can facilitate a π-phase gate operation for the probe field at the quantum level with high fidelity. Furthermore, when a squeezed probe field is injected, the squeezed state of the input nonclassical field can undergo a $90^\circ$ rotation. These findings provide valuable insights into the unique properties of gain-and-loss-balanced coherently prepared atomic media, paving the way for new applications in quantum information processing and quantum metrology.