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

Wigner Functions for Coherent and Squeezed States with Thermal Noise

Bai-Gen Wang, Jian‐Xin Zhu

Published Oct 1, 1993• 1 citation
Publisher

Abstract

A generalized Wigner function W T(α, ) including the thermal degrees of freedom is presented to calculate the ‘reduced’ Wigner functions for all kinds of coherent and squeezed states with thermal noise by the formalism of thermofield dynamics. The results show that the different definitions of coherent and squeezed state with the same corresponding density matrix give rise to the same reduced Wigner function. By our method, the reduced Wigner function can be calculated for an arbitrary vector in the thermal Fock space, of which the density matrix is too complicated to use.

DOI
10.1080/09500349314551941

Related papers

Thermalized Displaced Squeezed Thermal States

Lu, W F

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have diffenent correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.

•Jan 1, 2000•1 citation

Thermalized displaced squeezed thermal states

Wen-Fa Lu

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeezing and coherence components. Moreover, different from the properties of the position, the average value and variance of the particle number operator as well as the second-order correlation function are time independent.

arXiv:quant-ph/9905073•Journal of Physics A Mathematical and General•Jan 7, 2000•2 citations

NEW APPLICATION OF THERMO FIELD DYNAMICS IN SIMPLIFYING THE CALCULATION OF WIGNER FUNCTIONS

Hong-Yi Fan

We find that the Thermo Field Dynamics, invented by Takahashi and Umezawa, can simplify calculations of Wigner functions for density matrices ρ. Using the coherent thermal state representation (Phys. Lett.A246, 242 (1998)), we show that the Wigner function W = Tr (Δρ) (an ensemble average of the Wigner operator Δ) can be expressed as a matrix element of ρ in the pure coherent thermal states. Wigner functions for some complicated density matrices are derived in this way.

Modern Physics Letters A•Apr 10, 2003•9 citations

Higher-order squeezing properties of two-mode squeezed states

Jiaxin Gong, P. K. Aravind

We have investigated the properties of two-mode squeezed states of various kinds: squeezed coherent states, squeezed number states, squeezed thermal states, and squeezed number-thermal states. The properties studied include characteristic functions, photon number distributions, and high-order moments. We show that a two-mode squeezed coherent state appears in either of its modes as a Glauber-Lachs superposition of a coherent signal with thermal noise; this generalizes the well-known thermofield result that a two-mode squeezed vacuum state behaves like a pure thermal state in either of its modes. We investigate the higher-order squeezing (in the sense of Hong and Mandel) of squeezed coherent-thermal and squeezed number-thermal states. Although the squeezing is found to increase with order in both cases, there are nevertheless interesting differences that can be traced to the fact that the Wigner function has a Gaussian form for the former but not for the latter.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Lie algebras and generalized thermal coherent states

Sérgio Floquet, Marco A. S. Trindade, J. David M. Vianna

In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a thermofield dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on SU(2) and SU(1,[Formula: see text]1) symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.

arXiv:1507.00372•International Journal of Modern Physics A•Jan 25, 2017•4 citations

Wigner function and density operator of the photon-subtracted squeezed thermal state

Liyun Hu, Fan Hong‐Yi

By using the technique of integration within an ordered product of operators, the normal ordered density operator of the photon-subtracted squeezed thermal state (PSSTS) is derived. Then the corresponding Wigner function is presented by using the coherent state representation of the Wigner operator. The nonclassical properties of the PSSTS are discussed based on the negativity of the Wigner function.

Chinese Physics B•Nov 1, 2009•30 citations
A generalized Wigner function W T(α, ) including the thermal degrees of freedom is presented to calculate the ‘reduced’ Wigner functions for all kinds of coherent and squeezed states with thermal noise by the formalism of thermofield dynamics. The results show that the different definitions of coherent and squeezed state with the same corresponding density matrix give rise to the same reduced Wigner function. By our method, the reduced Wigner function can be calculated for an arbitrary vector in the thermal Fock space, of which the density matrix is too complicated to use.
In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have diffenent correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.
In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeezing and coherence components. Moreover, different from the properties of the position, the average value and variance of the particle number operator as well as the second-order correlation function are time independent.
We have investigated the properties of two-mode squeezed states of various kinds: squeezed coherent states, squeezed number states, squeezed thermal states, and squeezed number-thermal states. The properties studied include characteristic functions, photon number distributions, and high-order moments. We show that a two-mode squeezed coherent state appears in either of its modes as a Glauber-Lachs superposition of a coherent signal with thermal noise; this generalizes the well-known thermofield result that a two-mode squeezed vacuum state behaves like a pure thermal state in either of its modes. We investigate the higher-order squeezing (in the sense of Hong and Mandel) of squeezed coherent-thermal and squeezed number-thermal states. Although the squeezing is found to increase with order in both cases, there are nevertheless interesting differences that can be traced to the fact that the Wigner function has a Gaussian form for the former but not for the latter.