CRC Press eBooks

Linear quantum control of mechanical motion

Warwick P. Bowen

Published Nov 18, 2015• 0 citations

Abstract

Building on Chapters 3 and 4, this chapter introduces the concepts of measurement-based quantum control of mechanical systems in the linearised approximation for the optomechanical interaction, including techniques such as feedback cooling and back-action evading measurements using both stroboscopic optical driving and parametric mechanical driving. To model these techniques we introduce the stochastic master equation approach. We then discuss the application of squeezed light fields and ponderomotive optical squeezing to overcome the standard quantum limit introduced in Chapter 3. These methods are important both to improve the precision of quantum sensors and for quantum state tomography of mechanical systems.

DOI: 10.1201/b19379-9

Related papers

Optomechanics and Quantum Measurement

Aashish A. Clerk

After a quick review of the basic theory of quantum optomechanical systems, based largely on linearized Heisenberg–Langevin equations, this chapter focuses on selected topics related to quantum measurement and quantum optomechanics. Included are: a comprehensive discussion of the quantum limit on the added noise of a continuous position detector, following the quantum linear response approach; a detailed discussion of the role of noise correlations, and how these can be achieved in an optomechanical cavity (by using squeezed input light, or by modifying the choice of measured output quadrature); and a discussion of back-action evading measurements of a mechanical quadrature, discussing how this can be achieved in a two-tone driven cavity system. The chapter ends with a quick introduction to the theory of conditional continuous quantum measurement, and a discussion on how a back-action evading measurement can be used to produce conditional mechanical squeezed states.

Oxford University Press eBooksMar 5, 20205 citations

Linear quantum measurement of mechanical motion

Warwick P. Bowen

In this chapter we use the quantum theory of continuous measurement to describe the linearised interaction between light and a mechanical oscillator in a cavity optomechanical system, and quantify how the optical output field can be used to monitor the quantum state of the mechanics. We show that continuous measurement results in unavoidable quantum back-action that heats the mechanical oscillator and introduces a standard quantum limit to force and displacement sensing, and detail how important parameters in quantum optomechanics, including optomechanical coupling rate, cooperativity, and oscillator temperature, can be characterised by optical measurement.

CRC Press eBooksNov 18, 20151 citation

The quantum trajectory approach to quantum feedback control of an oscillator revisited

Andrew C. Doherty, Alex Szorkovszky, Glen I. Harris +1 more

We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesOct 22, 201238 citations

Hybrid Atomic-Optomechanical Systems -- Observing Quantum Effects in Macroscopic Oscillators

Swati Singh

This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.

Jan 1, 20120 citations

Towards optomechanical quantum state reconstruction of mechanical motion

Michael Ross Vanner, Igor Pikovski, M. S. Kim

Utilizing the tools of quantum optics to prepare and manipulate quantum states of motion of a mechanical resonator is currently one of the most promising routes to explore non‐classicality at a macroscopic scale. An important quantum optomechanical tool yet to be experimentally demonstrated is the ability to perform complete quantum state reconstruction. Here, after providing a brief introduction to quantum states in phase space, the current proposals for state reconstruction of mechanical motional states are reviewed and contrasted and experimental progress is discussed. Furthermore, it is shown that mechanical quadrature tomography using back‐action‐evading interactions gives an s‐parameterized Wigner function where the numerical parameter s is directly related to the optomechanical measurement strength. The effects of classical noise in the optical probe for both state reconstruction and state preparation by measurement are also discussed.

arXiv:1406.1013Annalen der PhysikAug 29, 201460 citations

Robust Control Design for Laser Cavity Squeezing in Quantum Optical Systems

Mohammad Salehizadeh

Quantum control theory is a rapidly evolving research field, which has developed over the last three decades. Quantum optics has practical importance in quantum technology and provides a promising means of implementing quantum information and computing device. \nIn quantum control, it is difficult to acquire information about quantum states without destroying them since microscopic quantum systems have many unique characteristics such as entanglement and coherence which do not occur in classical mechanical system. Therefore, \nthe Lyapunov-based control methodology is used to first construct an artificial closed-loop controller and then an open-loop law is derived by simulation of the artificial closed-loop system. \n \nThis work considers the stabilization of laser cavity as the main integral part of quantum optical systems through squeezing the output beam of the cavity. As a comprehensive example of this type of system, quantum optomechanical sensors are investigated. To this end, a nonlinear model \nof quantum optomechanical sensors is first extended incorporating various noises. Then, linear quadratic Gaussian (LQG) control method is used to tackle the problem of mode-squeezing in optomechanical sensors. \nCoherent feedback quantum control is synthesized by incorporating both shot noise and back-action noise to attenuate the output noise well below the shot noise level (Two waves are said to be coherent if they have a constant relative phase). In the second phase of this work, due to entanglement of the system with critical uncertainties and technical limitations such as laser noise and detector imprecision, robust H [infinity] method is employed for the robust stabilization and robust performance of the system in practice. In H [infinity] methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this. The effectiveness of the proposed control strategy in squeezing the cavity output beam is demonstrated by simulation.

Dec 20, 20110 citations