Bath-free squeezed phonon lasing via intrinsic ion-phonon coupling

Abstract: We present a theoretical model for realizing squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs. Our approach leverages the intrinsic ion-phonon interactions, where two trapped ions, each interacting with a shared vibrational mode, are driven on both red- and blue-sideband transitions. This enables the creation of a squeezed state of motion through the dynamic coupling between the ions' internal states and the phonon mode. Unlike traditional methods that require bath engineering, our model demonstrates that squeezed lasing can be achieved through a direct manipulation of ion-phonon interactions, with no external reservoirs required. We explore the steady-state behavior of the system, analyzing the onset of lasing, gain-loss balance, and the role of the squeezing parameter in shaping the phonon field's statistical properties. Furthermore, we show how external coherent drives can stabilize phase coherence and achieve controlled quadrature squeezing, offering a simple yet effective method for achieving squeezed lasing in quantum mechanical systems. Our findings provide new insights into the realization of squeezed states in phonon-based systems, with potential applications in quantum metrology and information processing.