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

Optical homodyne measurements and entangled coherent states

Barry C. Sanders, K. S. Lee, M. S. Kim

Published Jul 1, 1995• 53 citations
Publisher

Abstract

We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.

DOI
10.1103/physreva.52.735

Related papers

Experimental generation of optical Schrödinger cats from photon number states

Alexei Ourjoumtsev, Hyunseok Jeong, Rosa Tualle-Brouri +1 more

A "Schrödinger cat" state of free-propagating light can be defined as a quantum superposition of well separated coherent states. 1, 2 We demonstrated, theoretically and experimentally, a protocol which allows to generate arbitrarily large squeezed Schrödinger cat states, using a homodyne detection and photon number states as resources. We implemented this protocol experimentally with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly presents several quantum phase-space interference fringes between the "dead" and "alive" components, and it is large enough to become useful for experimental tests of quantum theory and quantum information processing.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 9, 2007•0 citations

Optical homodyne detection in view of the joint probability distribution

Toru Kawakubo, Katsuji Yamamoto

Optical homodyne detection is examined in view of the joint probability distribution. The usual view is that the relative phase between independent laser fields is localized by photon-number measurements in interference experiments such as homodyne detection. This is why operationally coherent states for laser fields are used in the description of homodyne detection and optical quantum-state tomography. Here, we elucidate these situations by considering the joint probability distribution and the invariance of homodyne detection under the phase transformation of optical fields.

arXiv:1007.1596•Physical Review A•Sep 3, 2010•5 citations

Homodyne-like detection scheme based on photon-number-resolving detectors

Alessia Allevi, Matteo Bina, Stefano Olivares +1 more

Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.

International Journal of Quantum Information•Dec 1, 2017•13 citations

Superpositions of coherent states: Squeezing and dissipation

Vladimír Bužek, A. Vidiella-Barranco, P. L. Knight

In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.

Physical Review A•May 1, 1992•426 citations

Phase distributions of a two-mode squeezed coherent state

A. Lukš, Vlasta Peřinová

In experiments, pulses of two-mode squeezed light were generated by an optical parametric amplifier. For certain ranges of parameters the joint photon number distribution of two-mode squeezed coherent states exhibits nonclassical oscillations. The nonclassical features were explained using the interference-in-phase-space concept in four-dimensional phase space. We investigate joint phase distribution of two- mode squeezed coherent states for presence of peaks and attempt to relate the peaks to the manifest oscillations in the joint photon number distribution.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 1, 1998•0 citations

Coherent states on a circle and quantum interference

József Janszky, P. Domokos, Петер Адам

As a generalization of the optical Schr\"odinger cats, discrete sets of coherent states are considered on a circle in the \ensuremath{\alpha} plane. It is shown that simple superpositions of Schr\"odinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state.

Physical Review A•Sep 1, 1993•120 citations
We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.
A "Schrödinger cat" state of free-propagating light can be defined as a quantum superposition of well separated coherent states. 1, 2 We demonstrated, theoretically and experimentally, a protocol which allows to generate arbitrarily large squeezed Schrödinger cat states, using a homodyne detection and photon number states as resources. We implemented this protocol experimentally with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly presents several quantum phase-space interference fringes between the "dead" and "alive" components, and it is large enough to become useful for experimental tests of quantum theory and quantum information processing.
Optical homodyne detection is examined in view of the joint probability distribution. The usual view is that the relative phase between independent laser fields is localized by photon-number measurements in interference experiments such as homodyne detection. This is why operationally coherent states for laser fields are used in the description of homodyne detection and optical quantum-state tomography. Here, we elucidate these situations by considering the joint probability distribution and the invariance of homodyne detection under the phase transformation of optical fields.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
In experiments, pulses of two-mode squeezed light were generated by an optical parametric amplifier. For certain ranges of parameters the joint photon number distribution of two-mode squeezed coherent states exhibits nonclassical oscillations. The nonclassical features were explained using the interference-in-phase-space concept in four-dimensional phase space. We investigate joint phase distribution of two- mode squeezed coherent states for presence of peaks and attempt to relate the peaks to the manifest oscillations in the joint photon number distribution.
As a generalization of the optical Schr\"odinger cats, discrete sets of coherent states are considered on a circle in the \ensuremath{\alpha} plane. It is shown that simple superpositions of Schr\"odinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state.