Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Review of Laser Engineering

Squeezing of light. Manipulation of quantum fluctuations.

Masahiro Kitagawa, Y. Yamamoto

Published Jan 1, 1987• 0 citations
Publisher

Abstract

The origin of quantum noise is addressed and it can be eliminated when the quantum state is optimally prepared for the single measured observable. Minimum uncertainty states are reviewed using Q (α) -representation, which include squeezed states and number-phase minimum uncertainty states. Squeezing is a concept of trading quantum uncertainties between two conjugate observables to optimize the state for the measurement. Need for optical nonlinearity to achieve squeezing is induced. Principles and experimental results for squeezing quadrature amplitude and photon number are delineated. Applications to optical communications and optical precision measurement are briefly stated.

DOI
10.2184/lsj.15.753

Related papers

Complement 5A: Squeezed states of light: the reduction of quantum fluctuations

G. Grynberg, Alain Aspect, Claude Fabre +1 more

We showed in Section 5.2 of the present chapter that according to quantum theory the value of the electric field of an electromagnetic wave could not be predicted to arbitrarily high precision, this being a consequence of the uncertainty relation satisfied by the two quadrature components of the field (Equation 5.32), which imposed a finite limit on the product of their variances. This limit is more than an abstract theoretical limit; it is often the overriding factor determining the resolution of high-precision optical measurements. In such situations measurements by photodetectors on the field exhibit uncontrollable fluctuations of quantum origin known as quantum noise . Fortunately, as we shall show in this complement, it is possible to overcome this by using non-classical states of the radiation field, namely the squeezed states , provided measurements are made of a single one of a pair of conjugate field variables. A field mode prepared in such a state exhibits reduced quantum noise in one of the variables at the expense of increased noise in the other, so that the uncertainty relation involving their variances is still satisfied. The potential of such states for increasing the obtainable precision of optical measurements is self-evident. However, the practical realization of the potential benefits requires delicate experimental techniques that we describe only briefly here.

Cambridge University Press eBooks•Sep 2, 2010•0 citations

Squeezed States of Light

Partha Pratim Mondal

Light exists in several distinct quantum states that include photon number and coherent states. But these are not the only states of light, and others that are known to display unusual properties raise hopes for a deeper understanding of the quantum behavior at the classical-quantum barrier. In the previous chapter, we learned about two important states of light: the coherent and number states. In this chapter, we will deal with a special state of light called the squeezed state. As the name suggests, conjugate quantities/variables (such as intensity and phase) can be squeezed beyond their short-noise limit, obeying Heisenberg’s uncertainty principle. These specialized states of light have the distinct ability to measure variables (e.g., intensity) below the short-noise limit. Of course, this comes at the cost of increased uncertainty in the associated conjugate variable. In this chapter, we will explore these possibilities and briefly discuss techniques to generate such light. These specialized light sources find applications in ultrahigh precision measurement (gravitational-wave detection) and sophisticated instrumentation.

•May 25, 2022•0 citations

Squeezing with fiber Sagnac loop and sub-shot-noise measurement

H. A. Haus, K. Bergman, Luc Boivin +2 more

Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>

Nonlinear Optics•Dec 17, 2002•0 citations

Optical squeezing and phase

David Thomas Pegg

A squeezed state of light is usually taken to mean a state in which the fluctuations of one of the quadratures are below the level associated with a coherent or vacuum state. These squeezed fluctuations are phase sensitive in the sense that they vary periodically as the field evolves, but the relationship between squeezing and phase fluctuations is not trivial. While squeezed states can exhibit an arbitrarily low level of phase fluctuations, the phase states, which are eigenstates of the Hermitian optical phase operator are not themselves quadrature squeezed. A phasesqueezed state is one with a lower level of phase fluctuations than a coherent state with the same mean photon number. Phase squeezing is fundamentally different from quadrature squeezing in much the same way that sub-Poissonian photon statistics is different. For this reason optimally squeezed states and states with minimum phase noise will be distinct. We derive the form of the states which minimum phase noise for a given intensity. These have an Airy function behavior for the photon number probability distribution. These phase squeezed states have a far better phase resolution than coherent states of similar intensity, but do not seem to offer a significant reduction of phase fluctuations compared with conventional squeezed states.

Digest on Nonlinear Optics: Materials, Phenomena and Devices•Jan 1, 1990•0 citations

Quantum stochastic communication with photon-number squeezed light

Joshua Paramanandam

Squeezed states of light have found importance in quantum cryptography due to the no-cloning theorem which prevents two states from being identical to each other. The quantum state with quadrature operators X1 and X2 can be visualized as a point in phase space with the center being l angle X1 r angle, l angle X2 r angle surrounded by an error region which satisfies the minimum uncertainty product l angle Delta X [1 over 2] r angle l angle Delta X [2 over2] r angle=1/16. These states are intrinsically secure since one needs to know which quadrature the measurement is to be made and any attempt to measure the wrong quadratures with arbitrary accuracy would disturb the message. Of course, the eavesdropper cannot simultaneously measure both quadratures with infinite precision for each. This thesis describes a method that not only encodes information in the amplitudes of the quadratures alone but also in the uncertainty of those states. One example of squeezed light is the number-phase squeezed state which satisfying the uncertainity relation l angle Delta n [superscript] 2 r angle l angle Delta phi [superscript] 2 r angle=1/4. An implementation is demonstrated where the information is encoded only in the photon number uncertainity and the phase variable is ignored.The barrier regulation mechanisms such as macroscopic coulomb blockade in semiconductor junction diodes are responsible for generating photon fluxes with penetration below the standard quantum limit(shot noise level). The thesis describes a comprehensive quantum mechanical Langevin model which details the various mechanisms responsible for producing photon number squeezing from the thermionic emission to the diffusion current limits. Quantities such as the pump fluctuations and cross correlation spectral densities are studied under constant current and constant voltage conditions. The research investigates the generation of photon number squeezed light from high efficiency light emitting diodes. A measurement setup for subshot noise is constructed and each stage is properly calibrated. Experiments were performed to determine the squeezing spectra and Fanofactors for the L2656 and the L9337 high efficiency LEDs. The L9337 produces a squeezing of 1.5dB below the shot noise level over a bandwidth of 25Mhz, the largest known penetration at room temperature. The quantum stochastic communicator is also demonstrated. The research shows that the switching elements used in the modulation of the electrical bias which in turn affect the regulation mechanisms do not affect the statistics of the emitted light under certain conditions. The decoding of the time varying variances is achieved by using time frequency analysis with the aid of the spectrum analyzer.

•Jan 1, 2007•0 citations

Quantum fluctuations and applications of squeezed light

Harry J. Kimble, G-L Oppo

This chapter is a short summary of recent developments concerning quantum noise. A quantum state is said to be squeezed when the fluctuations of one observable have been reduced below that of the vacuum state, that is, the ‘shot-noise’ level of the coherent state. Squeezed states are detected using the technique known as balanced homodyne detection. The chapter reviews the reductions in phase and amplitude fluctuations of a squeezed state and discusses their use in interferometry and spectroscopy. The phase-dependent nature of the squeezed field results in line-narrowing of the incoherent spectrum for particular phase choices while other choices of phase result in line-broadening. Interferometry with squeezed light as well as quantum non-demolition measurements are attempting to assess quantum measurement limits in order to further extend the experimental manipulation of light.

CRC Press eBooks•Dec 12, 2020•0 citations
The origin of quantum noise is addressed and it can be eliminated when the quantum state is optimally prepared for the single measured observable. Minimum uncertainty states are reviewed using Q (α) -representation, which include squeezed states and number-phase minimum uncertainty states. Squeezing is a concept of trading quantum uncertainties between two conjugate observables to optimize the state for the measurement. Need for optical nonlinearity to achieve squeezing is induced. Principles and experimental results for squeezing quadrature amplitude and photon number are delineated. Applications to optical communications and optical precision measurement are briefly stated.
We showed in Section 5.2 of the present chapter that according to quantum theory the value of the electric field of an electromagnetic wave could not be predicted to arbitrarily high precision, this being a consequence of the uncertainty relation satisfied by the two quadrature components of the field (Equation 5.32), which imposed a finite limit on the product of their variances. This limit is more than an abstract theoretical limit; it is often the overriding factor determining the resolution of high-precision optical measurements. In such situations measurements by photodetectors on the field exhibit uncontrollable fluctuations of quantum origin known as quantum noise . Fortunately, as we shall show in this complement, it is possible to overcome this by using non-classical states of the radiation field, namely the squeezed states , provided measurements are made of a single one of a pair of conjugate field variables. A field mode prepared in such a state exhibits reduced quantum noise in one of the variables at the expense of increased noise in the other, so that the uncertainty relation involving their variances is still satisfied. The potential of such states for increasing the obtainable precision of optical measurements is self-evident. However, the practical realization of the potential benefits requires delicate experimental techniques that we describe only briefly here.
Light exists in several distinct quantum states that include photon number and coherent states. But these are not the only states of light, and others that are known to display unusual properties raise hopes for a deeper understanding of the quantum behavior at the classical-quantum barrier. In the previous chapter, we learned about two important states of light: the coherent and number states. In this chapter, we will deal with a special state of light called the squeezed state. As the name suggests, conjugate quantities/variables (such as intensity and phase) can be squeezed beyond their short-noise limit, obeying Heisenberg’s uncertainty principle. These specialized states of light have the distinct ability to measure variables (e.g., intensity) below the short-noise limit. Of course, this comes at the cost of increased uncertainty in the associated conjugate variable. In this chapter, we will explore these possibilities and briefly discuss techniques to generate such light. These specialized light sources find applications in ultrahigh precision measurement (gravitational-wave detection) and sophisticated instrumentation.
Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>
A squeezed state of light is usually taken to mean a state in which the fluctuations of one of the quadratures are below the level associated with a coherent or vacuum state. These squeezed fluctuations are phase sensitive in the sense that they vary periodically as the field evolves, but the relationship between squeezing and phase fluctuations is not trivial. While squeezed states can exhibit an arbitrarily low level of phase fluctuations, the phase states, which are eigenstates of the Hermitian optical phase operator are not themselves quadrature squeezed. A phasesqueezed state is one with a lower level of phase fluctuations than a coherent state with the same mean photon number. Phase squeezing is fundamentally different from quadrature squeezing in much the same way that sub-Poissonian photon statistics is different. For this reason optimally squeezed states and states with minimum phase noise will be distinct. We derive the form of the states which minimum phase noise for a given intensity. These have an Airy function behavior for the photon number probability distribution. These phase squeezed states have a far better phase resolution than coherent states of similar intensity, but do not seem to offer a significant reduction of phase fluctuations compared with conventional squeezed states.
Squeezed states of light have found importance in quantum cryptography due to the no-cloning theorem which prevents two states from being identical to each other. The quantum state with quadrature operators X1 and X2 can be visualized as a point in phase space with the center being l angle X1 r angle, l angle X2 r angle surrounded by an error region which satisfies the minimum uncertainty product l angle Delta X [1 over 2] r angle l angle Delta X [2 over2] r angle=1/16. These states are intrinsically secure since one needs to know which quadrature the measurement is to be made and any attempt to measure the wrong quadratures with arbitrary accuracy would disturb the message. Of course, the eavesdropper cannot simultaneously measure both quadratures with infinite precision for each. This thesis describes a method that not only encodes information in the amplitudes of the quadratures alone but also in the uncertainty of those states. One example of squeezed light is the number-phase squeezed state which satisfying the uncertainity relation l angle Delta n [superscript] 2 r angle l angle Delta phi [superscript] 2 r angle=1/4. An implementation is demonstrated where the information is encoded only in the photon number uncertainity and the phase variable is ignored.The barrier regulation mechanisms such as macroscopic coulomb blockade in semiconductor junction diodes are responsible for generating photon fluxes with penetration below the standard quantum limit(shot noise level). The thesis describes a comprehensive quantum mechanical Langevin model which details the various mechanisms responsible for producing photon number squeezing from the thermionic emission to the diffusion current limits. Quantities such as the pump fluctuations and cross correlation spectral densities are studied under constant current and constant voltage conditions. The research investigates the generation of photon number squeezed light from high efficiency light emitting diodes. A measurement setup for subshot noise is constructed and each stage is properly calibrated. Experiments were performed to determine the squeezing spectra and Fanofactors for the L2656 and the L9337 high efficiency LEDs. The L9337 produces a squeezing of 1.5dB below the shot noise level over a bandwidth of 25Mhz, the largest known penetration at room temperature. The quantum stochastic communicator is also demonstrated. The research shows that the switching elements used in the modulation of the electrical bias which in turn affect the regulation mechanisms do not affect the statistics of the emitted light under certain conditions. The decoding of the time varying variances is achieved by using time frequency analysis with the aid of the spectrum analyzer.
This chapter is a short summary of recent developments concerning quantum noise. A quantum state is said to be squeezed when the fluctuations of one observable have been reduced below that of the vacuum state, that is, the ‘shot-noise’ level of the coherent state. Squeezed states are detected using the technique known as balanced homodyne detection. The chapter reviews the reductions in phase and amplitude fluctuations of a squeezed state and discusses their use in interferometry and spectroscopy. The phase-dependent nature of the squeezed field results in line-narrowing of the incoherent spectrum for particular phase choices while other choices of phase result in line-broadening. Interferometry with squeezed light as well as quantum non-demolition measurements are attempting to assess quantum measurement limits in order to further extend the experimental manipulation of light.