Spectrum analysis with quantum dynamical systems

Abstract

Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous optical phase estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.Comment: 12 pages, 4 figure

Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

“…While several strategies based on time-continuous measurements and feedback have been proposed for quantum state engineering, in particular with the main goal of generating steady-state squeezing and entanglement [5,[7][8][9][10][11][12][13][14][15] or to study and exploit trajectories of superconducting qubits [16,17], less attention has been devoted to parameter estimation. Notable exceptions are the estimation of a magnetic field via a continuously monitored atomic ensemble [18], the tracking of a varying phase [19][20][21], the estimation of Hamiltonian and environmental parameters [22][23][24][25][26][27][28][29], and optimal state estimation for a cavity optomechanical system [30].…”

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

“…which approaches the quantum limit given by equation (6.9) for q  0. The argument can be made more precise if the form of ( ) x F 0 is known, as the extended convexity of the quantum Fisher information can be used to obtain a tighter upper bound [70,72], while the ( ) q O 4 term in equation (6.14) can be computed to obtain an explicit lower bound for any θ.…”

Unravelling the noise: the discrimination of wave function collapse models under time-continuous measurements

“…In the optomechanical paradigm, one could also take into account the coupled light field: the extension of the present study to the full, two-mode optomechanical system, and the identification of associated optimal global detection strategies, will be an interesting development of this line of enquiry. Moreover one can also investigate how to exploit the information obtained through the time- continuous monitoring in order to improve the estimation of the parameters of interest, as, for example described in [40], where the time-continuous estimation of a classical stochastic process coupled to a dynamical system is studied in detail. Regardless of such issues, which are common to all investigations into fundamental decoherence, it is crucial to remark that the schemes we described have the power to falsify wave function collapse theories, in the sense that they can rule out regions in the noise parameters space by setting upper bounds to the diffusion rates, which hold even in the presence of unknown additional noise.…”