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Journal of the Optical Society of America B

Pictorial interpretation of quantum-enhanced measurements with wave functions

Yuki Sano, Yasuyuki Ozeki

Published Nov 23, 2021• 4 citations
Publisher

Abstract

Quantum-enhanced measurements using squeezed states of light provide sensitivities beyond the shot noise limit. Although the mechanism of quantum enhancement is well described by quantum mechanics, it is difficult to intuitively understand how squeezed states are exploited. In this paper, we present a pictorial interpretation of quantum-enhanced measurements using wave functions, which provides intuitive pictures of squeezed states in various experimental systems.

DOI
10.1364/josab.439556

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Quantum-enhanced measurements using squeezed states of light provide sensitivities beyond the shot noise limit. Although the mechanism of quantum enhancement is well described by quantum mechanics, it is difficult to intuitively understand how squeezed states are exploited. In this paper, we present a pictorial interpretation of quantum-enhanced measurements using wave functions, which provides intuitive pictures of squeezed states in various experimental systems.
Squeezed light, a prominent non-classical state of light, exhibits reduced quantum noise in one quadrature component below the standard quantum limit (SQL). The property enables quantum-enhanced precision measurements, surpassing the SQL in quantum sensing applications. This review comprehensively introduces the fundamental concepts, classifications, and experimental generation techniques of squeezed light. It further explores its pivotal role and recent advances in diverse quantum sensing domains, including interferometry, gravitational wave detection, magnetometry, force sensing, biomedical sensing, and quantum radar. The review covers theoretical foundations of squeezed states (including quadrature operators and classification schemes, experimental generation techniques in atomic ensembles, nonlinear crystals, and fibers), fundamentals of quantum sensing with squeezed light (from quantum noise theory to quantum-enhanced metrology), and quantum-enhanced sensing applications across the aforementioned domains. Finally, future challenges and opportunities in the field are discussed.
Quantum enhanced optical measurement protocols aim at reducing the uncertainty in the estimation of some physical quantities of a system below the shot-noise limit, classically unavoidable. In particular when small number of photons is used the shot noise can be the main source of uncertainty, in these cases the use of quantum light is of great interest. Note that there are several situations where the number of photons in the probe can not be increased arbitrarily, as when fragile biological samples are under investigation. Two different imaging protocols are discussed in the following.
An experimental scheme is proposed for squeezing-enhanced simultaneous measurement of the polarization angle and ellipticity of laser beam beyond the shot noise limit. In the scheme, a two-mode squeezed light is exploited to enhance the sensitivity of the measurement of polarization rotation angle, and a single-mode squeezed light is used to improve the sensitivity of ellipticity measurement. Noise analysis is performed to show that the signal-to-noise ratios in both the measurements of polarization angle and ellipticity can exceed the shot noise limit. This work is expected to be of considerable interest for experiments such as the observation of vacuum magnetic birefringence, gravitational wave detection, spin–orbital interaction, material characterization, polarization microscopy, atomic magnetometer, or biomedical optics.
Quantum metrology enables us to estimate optical phase shifts beyond the shot noise limit. Applications include quantum-enhanced biological measurement [1], microscopy [2] and gravitational wave detection[3]. For two-mode N-photon system, the NOON state can achieve the highest possible phase sensitivity where multi-photon coherence between two states significantly contributes to improving the phase sensitivity. Another alternative approach to improve the phase sensitivity by use of squeezed states. Squeezing is usually characterized by reducing the quantum noise of desired observable at the expense of increasing the quantum noise for its non-commute partner. Because shot-noise limits the phase sensitivity of any classical states, the reduced quantum noise can be used for improving the phase sensitivity. Here we experimentally study the phase sensitivity of an optical spin-squeezed state by using linear optics. We generated the optical spin-squeezed state using one photon subtraction from a down converted photon source. To implement the sub-shot noise measurement, we used multiplexed photon number resolving detectors so that we can reconstruct the photon number statistics of the state. In the talk, we will analyse the generated state in terms of both squeezing and phase sensitivity by using Fisher information.
Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.