Quantum back-action evasion and filtering in optomechanical systems

authored by
Jakob Schweer
supervised by
Klemens Johannes Hammerer

The measurement precision of optomechanical sensors reached sensitivity levels such that they have to be described by quantum theory. In quantum mechanics, every measurement will introduce a back-action on the measured system itself. For optomechanical force sensors, a trade-off between back-action and measurement precision exists through the interplay of quantum shot noise and quantum radiation pressure noise. Finding the optimal power to balance these effects leads to the standard quantum limit (SQL), which bounds the sensitivity of force sensing. To overcome the SQL and reach the fundamental bound of parameter estimation, the quantum Cramér-Rao bound, techniques called quantum smoothing and quantum back-action evasion are required. The first part of this thesis explores quantum smoothing in the context of optomechanical force sensing. Quantum smoothing combines the concepts of prediction and retrodiction to estimate the parameters of a system in the past. To illustrate the intricacies of these estimations in the quantum setting, two filters, the Kalman and Wiener filters, are introduced. Their prediction and retrodiction estimates are given for a simple optomechanical setup, and resulting differences are analyzed concerning the available quantum smoothing theories in the literature. In the second part of this thesis, a back-action evasion technique called coherent quantum-noise cancellation (CQNC) is explored. In CQNC, an effective negative-mass oscillator is coupled to an optomechanical sensor to create destructive interference of quantum radiation pressure noise. An all-optical realization of such an effective negative-mass oscillator is introduced, and a comprehensive study of its performance in a cascaded CQNC scheme is given. We determine ideal CQNC conditions, analyze non-ideal noise cancellation and provide a case study. Under feasible parameters, the case study shows a possible reduction of radiation pressure noise of 20% and that the effective negative-mass oscillator as the first subsystem in the cascade is the preferable order.

Institute of Gravitation Physics
QUEST-Leibniz Research School
Doctoral thesis
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Electronic version(s)
https://doi.org/10.15488/13289 (Access: Open)

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