Experimental and theoretical studies in quantum metrology with optomechanical and multi-parameter-estimation applications
<p>This thesis explores the field of optomechanics and the theory of multi-parameter estimation for quantum metrology applications.</p> <p>An optomechanical state inside a microresonator-taper system is studied experimentally, where the optical and mechanical modes interact by mean...
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2018
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| Summary: | <p>This thesis explores the field of optomechanics and the theory of multi-parameter estimation for quantum metrology applications.</p> <p>An optomechanical state inside a microresonator-taper system is studied experimentally, where the optical and mechanical modes interact by means of Brillouin anti-Stokes scattering. The scattering leads to sideband cooling of the mechanical (acoustic) mode and the underlying optomechanical coupling takes the form of a beam-splitter interaction Hamiltonian. The mechanical mode is further cooled by continuously monitoring the optical anti-Stokes mode by a heterodyne detector. The resulting time-domain data is input offline to a stochastic master equation model for Gaussian states to optimally estimate the mechanical phase space trajectories and subsequently reduce the observer’s uncertainty associated with the phase space coordinates. It is shown that more information about the mechanical mode can be obtained by heterodyne monitoring than by the commonly used in optomechanics homodyne detection for the beam-splitter type interaction Hamiltonians.</p> <p>The second part of this thesis theoretically considers the problem of simultaneous estimation of phase and phase diffusion using fixed-particle number states in the framework of quantum Cramér-Rao bound. Quantum Fisher information matrices are derived analytically in the limits of large and small diffusive noise to quantify the maximum amount of information available in the individual estimation of the parameters. The former is for a general fixed-particle number state and the latter for Holland-Burnett states for which quantum-enhanced estimation of phase as well as diffusion can be obtained. The precision limits given by quantum Fisher information may not be achievable in the joint estimation of the parameters due to the possible non-commutativity of the optimal measurements and this can be quantified in terms of a trade-off relation. This trade-off relation can reach the maximum of 2 in the large diffusion regime, whereas in the small diffusion regime a numerical evidence is shown that the optimal trade-off relation approaches 1 for Holland-Burnett states. These numerical results are valid in the small particle number regime. Finally, numerical results showing behaviour of the trade-off for a general value of phase diffusion when using Holland-Burnett states are provided.</p> |
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