Farid Ya. Khalili

Quantum Measurement Theory in Gravitational-Wave Detectors

The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.

Preparing a mechanical oscillator in non-Gaussian quantum states

We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.

Noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization

It is shown that photon shot noise and radiation-pressure back-action noise are the sole forms of quantum noise in interferometric gravitational wave detectors that operate near or below the standard quantum limit, if one filters the interferometer output appropriately. No additional noise arises from the test masses initial quantum state or from reduction of the test-mass state due to measurement of the interferometer output or from the uncertainty principle associated with the test-mass state. Two features of interferometers are central to these conclusions: (i) The interferometer output [the photon number flux [script N]-hat(t) entering the final photodetector] commutes with itself at different times in the Heisenberg picture, [[script N]-hat(t),[script N]-hat(t[prime])] = 0 and thus can be regarded as classical. (ii) This number flux is linear to high accuracy in the test-mass initial position and momentum operators x-hato and p-hato, and those operators influence the measured photon flux [script N]-hat(t) in manners that can easily be removed by filtering. For example, in most interferometers x-hato and p-hato appear in [script N]-hat(t) only at the test masses ~1 Hz pendular swinging frequency and their influence is removed when the output data are high-pass filtered to get rid of noise below ~10 Hz. The test-mass operators x-hato and p-hato contained in the unfiltered output [script N]-hat(t) make a nonzero contribution to the commutator [[script N]-hat(t),[script N]-hat(t[prime])]. That contribution is precisely canceled by a nonzero commutation of the photon shot noise and radiation-pressure noise, which also are contained in [script N]-hat(t). This cancellation of commutators is responsible for the fact that it is possible to derive an interferometers standard quantum limit from test-mass considerations, and independently from photon-noise considerations, and get identically the same result. These conclusions are all true for a far wider class of measurements than just gravitational-wave interferometers. To elucidate them, this paper presents a series of idealized thought experiments that are free from the complexities of real measuring systems.

A Squeezed state source using radiation pressure induced rigidity

We propose an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noises. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of 5 dB, with a frequency-independent squeeze angle for frequencies below 1 kHz. This squeeze source is well suited for injection into a gravitational-wave interferometer, leading to improved sensitivity from reduction in the quantum noise. Furthermore, this design provides an experimental test of quantum-limited radiation pressure effects, which have not previously been tested.

Observation of Generalized Optomechanical Coupling and Cooling on Cavity Resonance

Optomechanical coupling between a light field and the motion of a cavity mirror via radiation pressure plays an important role for the exploration of macroscopic quantum physics and for the detection of gravitational waves (GWs). It has been used to cool mechanical oscillators into their quantum ground states and has been considered to boost the sensitivity of GW detectors, e.g., via the optical spring effect. Here, we present the experimental characterization of generalized, that is, dispersive and dissipative, optomechanical coupling, with a macroscopic (1.5u2009u2009mm)2-size silicon nitride membrane in a cavity-enhanced Michelson-type interferometer. We report for the first time strong optomechanical cooling based on dissipative coupling, even on cavity resonance, in excellent agreement with theory. Our result will allow for new experimental regimes in macroscopic quantum physics and GW detection.

Quantum back-action in measurements of zero-point mechanical oscillations

Measurement-induced back-action, a direct consequence of the Heisenberg uncertainty principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Lett. 108 033602 (2012)], and show that the results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise—through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the standard quantum limit.

Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors

We consider enhancing the sensitivity of future gravitational-wave detectors by using double optical spring. When the power, detuning and bandwidth of the two carriers are chosen appropriately, the effect of the double optical spring can be described as a “negative inertia,” which cancels the positive inertia of the test masses and thus increases their response to gravitational waves. This allows us to surpass the free-mass standard quantum limit (SQL) over a broad frequency band, through signal amplification, rather than noise cancellation, which has been the case for all broadband SQL-beating schemes so far considered for gravitational-wave detectors. The merit of such signal amplification schemes lies in the fact that they are less susceptible to optical losses than noise-cancellation schemes. We show that it is feasible to demonstrate such an effect with the Gingin High Optical Power Test Facility, and it can eventually be implemented in future advanced GW detectors.

QND measurements for future gravitational-wave detectors

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit (SQL), a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the SQL significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.

Energetic Quantum Limit in Large-Scale Interferometers

For each optical topology of an interferometric gravitational wave detector, quantum mechanics dictates a minimum optical power (the energetic quantum limit) to achieve a given sensitivity. For standard topologies, when one seeks to beat the standard quantum limit by a substantial factor, the energetic quantum limit becomes impossibly large. Intracavity readout schemes may do so with manageable optical powers.

Universal Decoherence under Gravity: A Perspective through the Equivalence Principle

Pikovski etxa0al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einsteins equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski etxa0al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie waves dispersion relation. We provide an alternative view to the situation considered by Pikovski etxa0al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is violated.