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

Physical Review A

Amplitude-squeezed quantum states produced by the evolution of a quadrature-squeezed coherent state in a Kerr medium

Kasivishvanathan Sundar

Published Feb 1, 1996• 16 citations
Publisher

Abstract

The evolution of a quadrature-squeezed state through a Kerr medium is studied from the point of view of amplitude squeezing. We propose a Mach-Zehnder interferometer configuration, which incorporates a squeeze- state generator and a nonlinear Kerr medium, to generate and subsequently displace these states. The displaced states show amplitude squeezing for a proper choice of the initial quadrature squeezed state, and we study two such cases here in detail. In the limit where the evolution through a Kerr medium results in a macroscopic superposition, an initial phase-squeezed coherent state shows significant amplitude squeezing, and we have shown that the photon-number uncertainty 〈(\ensuremath{\Delta}n^${)}^{2}$〉 can be minimized to a value smaller than 〈n^${\mathrm{〉}}^{2/3}$. On the other hand, an initial quadrature-squeezed state, whose direction of squeezing is along the direction of excitation, upon evolving through a Kerr medium for a suitable small duration of time shows substantial amplitude squeezing for an appropriate displacement, and we show that the photon-number uncertainty in this case can be minimized to 〈n^${\mathrm{〉}}^{1/5}$, which is far below the previously achieved limits. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1096

Related papers

Highly Amplitude-Squeezed States of the Radiation Field

Kasivishwanathan Sundar

We propose here a quantum state obtained by evolving a quadrature-squeezed state through a Kerr medium. We give a Mach-Zhender interferometer configuration to generate and displace this state to an appropriate position in phase space. The displaced state is highly amplitude squeezed when the direction of squeezing of the initial quadrature squeezed state is along the direction of coherent excitation. We show that the photon number uncertainty $〈(\ensuremath{\Delta}\stackrel{^}{n}{)}^{2}〉<〈\stackrel{^}{n}{〉}^{1/5}$, which is far below the previously achieved limits in similar schemes.

Physical Review Letters•Sep 11, 1995•20 citations

Generation of amplitude squeezed states of light from phase squeezed coherent states

Kasivishvanathan Sundar

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.

Journal of Modern Optics•Apr 1, 1996•3 citations

Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer

Masahiro Kitagawa, Y. Yamamoto

The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^${〉}^{1/3}$, far below the limit 〈n^${〉}^{2/3}$ achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE

Physical Review A•Nov 1, 1986•404 citations

Statistical and phase properties of displaced Kerr states

A. D. Wilson‐Gordon, V. Buek, P. L. Knight

We study the statistical and phase properties of the output states of a Mach-Zehnder interferometer with a nonlinear Kerr medium in one of its arms. The combination of nonlinearity and displacement produced by the interferometer generates output states (displaced Kerr states) that, unlike those derived from a Kerr medium alone (Kerr states), do not necessarily retain the photon statistics of the initially coherent field. As the parameter characterizing the nonlinear medium is varied, the statistics of the output field vary from sub-Poissonian to super-Poissonian. The photon-number distributions of these states are rationalized by examining their quasiprobability distributions, which vary from banana-shaped for sub-Poissonian statistics to complicated interference structures for highly super-Poissonian statistics. The number-phase properties of the Kerr and displaced Kerr states are studied for the case of small photon numbers (relevant to cavity quantum electrodynamics) using a methodology based on the Pegg-Barnett formalism. In particular, we determine the range of parameters for which the states are minimum-uncertainty states and whether they are squeezed with respect to photon number and phase, drawing a distinction between a sub-Poissonian nature and number squeezing. Finally, we find that sub-Poissonian statistics can coexist with quadrature squeezing for a range of parameters.

Physical Review A•Dec 1, 1991•66 citations

Quantum metrology with a squeezed Kerr oscillator

Jiajie Guo, Qiongyi He, Matteo Fadel

We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.

arXiv:2406.11789•Physical Review A•May 6, 2024•13 citations

Generation of number-phase squeezed states

Matthew J. Collett

A number-phase interaction is suggested that is analogous to the usual quadrature squeezing Hamiltonian for a mode of the electromagnetic field. Applied to an initial coherent state, it produces number-phase squeezed states. For moderate squeezing in either direction the result is close to a minimum uncertainty state. Two different ${\mathrm{\ensuremath{\chi}}}^{(3)}$ approximations to the ideal interaction are found, appropriate for the different directions of squeezing. Even with the approximate interaction, the fluctuations in photon number can be reduced to less than half a photon for an arbitrarily intense field.

Physical Review Letters•May 31, 1993•21 citations
The evolution of a quadrature-squeezed state through a Kerr medium is studied from the point of view of amplitude squeezing. We propose a Mach-Zehnder interferometer configuration, which incorporates a squeeze- state generator and a nonlinear Kerr medium, to generate and subsequently displace these states. The displaced states show amplitude squeezing for a proper choice of the initial quadrature squeezed state, and we study two such cases here in detail. In the limit where the evolution through a Kerr medium results in a macroscopic superposition, an initial phase-squeezed coherent state shows significant amplitude squeezing, and we have shown that the photon-number uncertainty 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉 can be minimized to a value smaller than 〈n^〉2/3{\mathrm{〉}}^{2/3}〉2/3. On the other hand, an initial quadrature-squeezed state, whose direction of squeezing is along the direction of excitation, upon evolving through a Kerr medium for a suitable small duration of time shows substantial amplitude squeezing for an appropriate displacement, and we show that the photon-number uncertainty in this case can be minimized to 〈n^〉1/5{\mathrm{〉}}^{1/5}〉1/5, which is far below the previously achieved limits. \textcopyright{} 1996 The American Physical Society.
We propose here a quantum state obtained by evolving a quadrature-squeezed state through a Kerr medium. We give a Mach-Zhender interferometer configuration to generate and displace this state to an appropriate position in phase space. The displaced state is highly amplitude squeezed when the direction of squeezing of the initial quadrature squeezed state is along the direction of coherent excitation. We show that the photon number uncertainty $〈(\ensuremath{\Delta}\stackrel{^}{n}{)}^{2}〉<〈\stackrel{^}{n}{〉}^{1/5}$, which is far below the previously achieved limits in similar schemes.
We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.
The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^〉1/3{〉}^{1/3}〉1/3, far below the limit 〈n^〉2/3{〉}^{2/3}〉2/3 achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE
We study the statistical and phase properties of the output states of a Mach-Zehnder interferometer with a nonlinear Kerr medium in one of its arms. The combination of nonlinearity and displacement produced by the interferometer generates output states (displaced Kerr states) that, unlike those derived from a Kerr medium alone (Kerr states), do not necessarily retain the photon statistics of the initially coherent field. As the parameter characterizing the nonlinear medium is varied, the statistics of the output field vary from sub-Poissonian to super-Poissonian. The photon-number distributions of these states are rationalized by examining their quasiprobability distributions, which vary from banana-shaped for sub-Poissonian statistics to complicated interference structures for highly super-Poissonian statistics. The number-phase properties of the Kerr and displaced Kerr states are studied for the case of small photon numbers (relevant to cavity quantum electrodynamics) using a methodology based on the Pegg-Barnett formalism. In particular, we determine the range of parameters for which the states are minimum-uncertainty states and whether they are squeezed with respect to photon number and phase, drawing a distinction between a sub-Poissonian nature and number squeezing. Finally, we find that sub-Poissonian statistics can coexist with quadrature squeezing for a range of parameters.
We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.
A number-phase interaction is suggested that is analogous to the usual quadrature squeezing Hamiltonian for a mode of the electromagnetic field. Applied to an initial coherent state, it produces number-phase squeezed states. For moderate squeezing in either direction the result is close to a minimum uncertainty state. Two different ${\mathrm{\ensuremath{\chi}}}^{(3)}$ approximations to the ideal interaction are found, appropriate for the different directions of squeezing. Even with the approximate interaction, the fluctuations in photon number can be reduced to less than half a photon for an arbitrarily intense field.