Active Optomechanics

Cavity optomechanics studies the interaction between optical and mechanical modes through radiation pressure. Traditional approaches are passive, relying on external laser manipulation. Active optomechanics, however, introduces optical gain, directly linking mechanical motion to lasing dynamics. This offers advantages in simplicity and the ability to directly observe system-intrinsic properties. This study uses numerical simulations to explore active optomechanics, examining both macroscopic systems (many atoms) and microscopic systems (a single atom). Understanding this interaction is crucial for advancing technologies such as integrated photonic circuits, quantum communication, and highly sensitive biosensors. The research aims to characterize the influence of mechanical oscillations on lasing properties in both classical and quantum regimes, thereby paving the way for the development of novel optomechanical light sources with tailored characteristics.

Existing research in cavity optomechanics extensively covers passive systems, where external lasers control the optomechanical coupling. These systems have demonstrated impressive results, such as ground-state cooling of mechanical oscillators and highly sensitive force/displacement transduction. Various optomechanical devices have been developed, including mirrors, membranes, microcavities, and nanorods. However, passive systems are limited by technical noise from the probe laser and require complex stabilization, hindering the detection of high-frequency mechanical vibrations. Active cavity optomechanics, or optomechanical lasing, offers a promising alternative. Recent work has demonstrated its potential with vertical-external-cavity surface-emitting lasers, showing enhanced photon-phonon interaction and high-speed wavelength sweeping. However, a comprehensive analysis of mechanical oscillation's impact on lasing dynamics has been lacking, especially in the quantum regime where photon and phonon numbers are small.

The researchers numerically investigated active optomechanics using two distinct models. For macroscopic systems, they employed a set of Heisenberg-Langevin equations to describe the light-matter interaction within the optical cavity and a second-order differential equation (spring-mass oscillator model) for the mechanical oscillator. The radiation pressure force from the intracavity field drives the mechanical oscillator. The self-consistent solution was achieved by numerically solving the coupled equations. The stability of steady-state solutions was assessed through linear stability analysis. The power spectral density of the intracavity field was simulated using the Wiener-Khinchin theorem to analyze the impact of mechanical oscillation on laser spectral broadening and frequency stability. The efficiency of optical energy transfer to the mechanical oscillator was also investigated by tracking energy conversion from the laser light to the elastic potential energy in the spring-mass system. For microscopic systems (single-atom optomechanical microlaser), a full quantum-mechanical treatment was applied. The Heisenberg-Langevin equations were replaced by a master equation for the density operator of the system, accounting for the quantum nature of photons and phonons. The photon and phonon numbers were calculated from the density matrix, and higher-order correlation functions (second-order correlation functions) were computed to characterize photon and phonon statistics, revealing the presence of nonclassical features. The system was modeled using the Lindblad master equation, and the simulations involved solving this equation for the density matrix to obtain the relevant quantities such as photon and phonon numbers and correlation functions.

In the macroscopic regime, the mechanical oscillation of the movable mirror introduces multiple unstable steady-state regimes in the lasing phase, significantly broadens the laser spectrum, and degrades laser frequency stability. The extent of these effects strongly depends on the cavity Q factor. A high Q factor enhances the intracavity photon number, boosting the radiation pressure force and, consequently, amplifying the impact of mechanical fluctuations on the lasing dynamics. The frequency shift of the laser light is linearly dependent on the intracavity photon number and the cavity pulling effect. The spectral broadening can be predicted by the Schawlow-Townes formula in the low Q limit. The efficiency of energy transfer from the laser light to the mechanical oscillator is dependent on the pump rate and cavity Q factor, approaching unity for high Q factor cavities. For the microscopic (single-atom) system, the study revealed the emission of nonclassical photons and the generation of nonclassical photon-phonon pairs, demonstrating clear deviations from the behavior of a conventional one-atom microlaser. The spectrum of photons exhibits multiple peaks due to the well-resolved transitions between states. The second-order correlation function for photons shows antibunching, while that for phonons indicates bunching. Importantly, the cross-correlation function between photons and phonons violates the Cauchy-Schwarz inequality, providing evidence for nonclassical photon-phonon pair generation. This is a notable achievement, given the significant frequency difference between photons and phonons.

This study provides a comprehensive numerical investigation of active optomechanics, encompassing both macroscopic and microscopic systems. The results highlight the unique characteristics and capabilities of active optomechanics. Unlike passive systems, active optomechanics offers a simpler setup and provides direct insights into the intrinsic system properties. The ability to generate nonclassical photon-phonon pairs in the microscopic system opens new avenues for quantum communication and control. The observation of multiple unstable regimes in the macroscopic system demonstrates the significant impact of mechanical oscillations on lasing dynamics, particularly at high cavity Q factors. These findings have significant implications for the development of integrated photonic devices and quantum technologies.

This research successfully extends cavity optomechanics to an active regime, revealing the substantial influence of mechanical oscillations on macroscopic laser properties and the generation of nonclassical photon-phonon pairs in a single-atom microlaser. Future research could explore experimental implementations of these findings, focusing on optimizing material choices and cavity designs to enhance the optomechanical coupling strength and minimize thermal noise. Investigating multimode active optomechanical systems and exploring advanced control techniques to exploit the nonclassical correlations generated would be highly beneficial.

The study relies on numerical simulations. While the models are well-established, experimental verification is needed to fully validate the results. The macroscopic model assumes a classical mechanical oscillator, neglecting potential quantum effects at very low temperatures. The single-atom model simplifies the atomic structure and interactions. Exploring more complex atomic systems and including other relevant noise sources in the models could provide more realistic simulations.