Higher order correlations in a levitated nanoparticle phonon laser

Area of Science:

• Quantum Optics
• Nanomechanics
• Optomechanics

Background:

• The optical tweezer phonon laser utilizes a silica nanosphere in a focused optical beam to generate coherent mechanical motion.
• Understanding higher-order correlations is crucial for characterizing the quantum behavior of such systems.

Purpose of the Study:

• To theoretically and experimentally investigate higher-order correlations of mechanical motion in an optical tweezer phonon laser.
• To model the nanoparticle phonon number probability distribution and its evolution across the lasing threshold.
• To compare experimental findings with theoretical predictions and existing analytical theories.

Main Methods:

• Modeling the nanoparticle phonon number probability distribution using the master equation formalism.
• Deriving up to fourth-order equal-time correlation functions from the probability distribution.
• Transforming the master equation into a nonlinear quantum Langevin equation to obtain non-equal-time correlations.
• Conducting experimental measurements of phononic correlation functions.

Main Results:

• Theoretical predictions for higher-order correlations were derived using master equation and quantum Langevin formalisms.
• Experimental measurements of phononic correlation functions were performed.
• Experimental data showed good agreement with theoretical predictions.
• A partial match was found when comparing experimental data to analytical Ginzburg-Landau theory.

Conclusions:

• The study successfully characterized higher-order mechanical motion correlations in an optical tweezer phonon laser.
• Theoretical models provide a good description of the system's behavior, particularly near the lasing threshold.
• Discrepancies with Ginzburg-Landau theory suggest limitations of the analytical model for this specific system.