Quantum-limited estimation of continuous spontaneous localization

Abstract

We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homodyne and heterodyne measurements. We also compare the performances of such strategies with those of a spin-assisted optomechanical system, where the estimation of the CSL parameter is performed through time-gated spin-like measurements.Understanding the nature of the quantum-to-classical (QtC) transition is a long-sought problem that attracts an evergrowing attention [1][2][3][4][5][6]. While quantum mechanics has undergone exhaustive and extremely successful testings in the microscopic realm, the apparent absence of quantum manifestations at the macroscopic scale cries for a deeper understanding. In particular, this lack of evidence reinforces the need of assessing the causes for the emergence of classical mechanics from fundamental quantum evolution. The most widely accepted theory behind such process is quantum decoherence [6]: The environment surrounding any quantum system monitors its state continuously, practically collapsing the system's wavefunction and curtailing any quantum behaviour. Such process is conjectured to occur more quickly with the growing size of the system at hand. Under this regime, macroscopic superpositions would be possible in macroscopic systems perfectly isolated from their environment, a condition that is, for all practical purposes, not realisable.However, a set of theories, usually referred to as collapse models (CMs), suggests an alternative route to the explanation of the QtC transition by putting forward fundamental underlying mechanisms responsible for the collapse of the wavefunction [7]. The strength of this effect should increase with the size (mass) of the system, leaving microscopic (macroscopic) systems fully within the quantum (classical) realm. The key difference between CMs and standard quantum mechanics is that in the framework entailed by the former, perfectly isolated macroscopic objects would continue to act classically.Among the proposals put forward so far to test (or rule out) some of the currently formulated CMs [8][9][10], those based on the experimental platform of cavity optomechanics offer features of undemanding scalability of the mass of the system to be probed and high-sensitivity of measurement. Most remarkably, at variance with standardly pursued approaches [11], they bypass the need for the construction and quantum-limited management of large interferometers [12,13]. notwithstanding such promising features, the investigation of CMs still poses considerable experim...

Trends in Quantum Nanophotonics

“…[ 151 ] This problem reduces to the precise estimation of key parameters of the collapse model, and the quantum limits on these estimates have themselves been studied. [ 152 ] One can extend such proposals to the possibility of rotational optomechanics experiments [ 153 ] and different types of collapse models. [ 154 ] Not surprisingly, the detection requirements are very demanding; a careful analysis of a variety of electrical and optical detection techniques has recently been undertaken.…”

Time-local optimal control for parameter estimation in the Gaussian regime

“…Several extensions of the ideas we have proposed here can be envisioned, most notably dropping the assumption of fast parameter encoding. This means that, instead of only delaying the demise of the QFI of an initial state, we should consider the situation where the parameter is encoded simultaneously to the open dynamics, e.g., by adding an Hamiltonian term in the Lindblad master equation or estimating parameters of the non-unitary part of the Gaussian dynamics, see, e.g., [83][84][85][86][87][88][89]. In such scenarios time-local control would be used to increase the rate at which information about the parameter is acquired during the dynamics.…”

Force Tracking in Cavity Optomechanics with a Two-Level Quantum System by Kalman Filtering

“…sian equation under quantum nondemolition measurements [22][23][24]. Inspired by the applications of Kalman filter in quantum sensors, e.g., estimating the phase of a light beam [25], estimating the waveform in a paradigmatic atomic sensor [26], and estimating the quantum state of an optomechanical oscillator in real time [27,28], it is natural to apply the filtering theory on linear Gaussian systems to obtain an estimator of timevarying force.…”