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

Journal of Modern Optics

Multiphoton Coherent States and the Linear Superposition Principle

Igor Jex, Vladimír Bužek

Published May 1, 1993• 37 citations
Publisher

Abstract

We show that multiphoton coherent states can be expressed as linear quantum superpositions of a finite number of generalized coherent states. Quantum interferences between component states lead to appearance of non-classical effects such as oscillations in the photon number distribution, quadrature squeezing, SU(1, 1) squeezing and others.

DOI
10.1080/09500349314550811

Related papers

Macroscopic superposition states of light via two-photon resonant interaction of atoms with cavity field

Vladimír Bužek

Recently considerable attention has been devoted to description of macroscopic superpositions of coherent states of lightl. This interest in part arises due to the fact that quantum interference be- tween component states leads to various nonclassical effects such as quadrature squeezing, higher order squeezing, sub-Poissonian photon statistics and oscillations in the photon number distribution.

16th Congress of the International Commission for Optics: Optics as a Key to High Technology•Jul 26, 1993•1 citation

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

Jaynes-Cummings model with intensity-dependent coupling and Schrbdinger cat state

王晓光

Linear superposition principle is a basic characteristic of quantum mechanics. The quantum interference of matter wave results from this principle. Recently, considerable effort has been devoted to the study of the properties of superpositions of two or more coherent states, i.e. the Schr(?)dinger cat states.It is shown that the superpositions of coherent states have properties different from those of the coherent state, such as the higher-order squeezing, sub-Poissonian distribution, oscillatory photon statistics and antibunching effect, because of the quantum interference between the components of the cat states. The emergence of these non-classical effects makes the study of the Schr(?)dinger

中国科学通报：英文版•Jan 1, 1996•0 citations

Role of quantum interference in producing non-classical states

P. Domokos, József Janszky, Петер Адам +1 more

Approximating a continuous superposition by a discrete one leads to an understanding of the role of quantum interference in generating squeezed coherent states, and in its quantum properties. It was shown that discrete superposition with a large enough number of coherent states with appropriate coefficients can have practically the same features as the squeezed coherent state. Dependent on the parameters W, r and 8, different numbers of coherent states are required for the interference fringe to form a Wigner function resembling that of the squeezed vacuum state and to reduce the deviation below a certain value. For the case of rotating the direction of squeezing, about 20 states were required to lower the deviation to 0.05%, while 640 states would be necessary when a unit displacement along the imaginary axis is included. When only a few coherent states are superimposed, the resulting state changes chaotically. In the case when the approximated squeezed coherent state was displaced along the imaginary axis an interesting Schrodinger cat-like state was found with about 20 coherent states on the real axis. At this point a significant peak occurs in the variances of the quadratures. It turned out that non-classical states can be effectively produced by a discrete superposition of coherent states with the coefficients derived from the one-dimensional representation of the given state.

Quantum Optics Journal of the European Optical Society Part B•Jun 1, 1994•14 citations

The origin of non-classical effects in a one-dimensional superposition of coherent states

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

We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the 1-D superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.

•Feb 1, 1992•3 citations

Superposition of two squeezed vacuum states and interference effects

Barry C. Sanders

The superposition of two squeezed vacuum states is analyzed by studying the photon-number probability distribution and the quadrature-phase-eigenstate marginal distributions. Interference fringes in the distributions are observed for some superposition states. The nonlinear oscillator generates a particular superposition of two squeezed vacuum states and the properties of this superposition state are discussed and contrasted with the other superposition states.

Physical Review A•Apr 1, 1989•73 citations
We show that multiphoton coherent states can be expressed as linear quantum superpositions of a finite number of generalized coherent states. Quantum interferences between component states lead to appearance of non-classical effects such as oscillations in the photon number distribution, quadrature squeezing, SU(1, 1) squeezing and others.
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.
Linear superposition principle is a basic characteristic of quantum mechanics. The quantum interference of matter wave results from this principle. Recently, considerable effort has been devoted to the study of the properties of superpositions of two or more coherent states, i.e. the Schr(?)dinger cat states.It is shown that the superpositions of coherent states have properties different from those of the coherent state, such as the higher-order squeezing, sub-Poissonian distribution, oscillatory photon statistics and antibunching effect, because of the quantum interference between the components of the cat states. The emergence of these non-classical effects makes the study of the Schr(?)dinger
Approximating a continuous superposition by a discrete one leads to an understanding of the role of quantum interference in generating squeezed coherent states, and in its quantum properties. It was shown that discrete superposition with a large enough number of coherent states with appropriate coefficients can have practically the same features as the squeezed coherent state. Dependent on the parameters W, r and 8, different numbers of coherent states are required for the interference fringe to form a Wigner function resembling that of the squeezed vacuum state and to reduce the deviation below a certain value. For the case of rotating the direction of squeezing, about 20 states were required to lower the deviation to 0.05%, while 640 states would be necessary when a unit displacement along the imaginary axis is included. When only a few coherent states are superimposed, the resulting state changes chaotically. In the case when the approximated squeezed coherent state was displaced along the imaginary axis an interesting Schrodinger cat-like state was found with about 20 coherent states on the real axis. At this point a significant peak occurs in the variances of the quadratures. It turned out that non-classical states can be effectively produced by a discrete superposition of coherent states with the coefficients derived from the one-dimensional representation of the given state.