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

Higher-Order Squeezing of Quantum Field and the Generalized Uncertainty Relations in Non-Degenerate Four-Wave Mixing

Xi-Zeng Li, Bao-Xia Su

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.

Related papers

Higher-order squeezing of quantum field and higher-order uncertainty relations in non-degenerate four-wave mixing

Xi-Zeng Li, Su Bao-Xia, Chai Lu

It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.

Chinese Physics•Aug 25, 2005•1 citation

Generation of higher-order squeezing of quantum electromagnetic fields by degenerate four-wave mixing

Xi-Zeng Li, Shan Ying

It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The degree of squeezing increases with the order N, and the higher-order squeeze parameter ${q}_{N}$ may approach -1.

Physical Review A•Dec 1, 1989•10 citations

High-order squeezing of the quantum electromagnetic field and the generalized uncertainty relations in two-mode squeezed states

Xi-Zeng Li, Bao-Xia Su

It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.

•May 1, 1994•0 citations

Phase Conjugation of Squeezed Light

Shiqun Li, Ling-An Wu

Phase conjugation in degenerate four-wave mixing with a squeezed input beam is investigated. We show that the phase conjugate mode is always super-Poissonian and never squeezed, but the combination mode may be squeezed to an extent even greater than the input probe wave.

Chinese Physics Letters•Apr 1, 1993•0 citations

Quantum phase fluctuations and squeezing in degenerate four-wave mixing

Gerard J Milburn, Daniel F. Walls, M. D. Levenson

We consider the generation of squeezed states in degenerate four-wave mixing, retaining all significant phase-matched terms in the third-order polarization. It is shown that, for output modes combined with appropriate phase shifts, ideal squeezed states are produced when the pump field is treated classically. An approximation scheme is used to investigate the effect of pump-field quantization. We show that for reasonable crystal lengths, the effect of pump-field quantization is insignificant in the region of significant squeezing.

Journal of the Optical Society of America B•Jun 1, 1984•40 citations

Higher-order squeezing in three- and four-wave mixing processes with loss

Jiaxin Gong, P. K. Aravind

An investigation is carried out of higher-order squeezing in a class of three- and four-wave mixing processes that can be modeled by a master equation. In (2N)th-order squeezing, as defined by Hong and Mandel, the Nth-power of the variance of a field quadrature falls below the value it would have for a coherent state. Higher-order squeezing is of interest because (i) it occurs in many processes in which ordinary (or second-order) squeezing occurs, and (ii) it allows a much larger fractional noise reduction to be achieved than ordinary squeezing. The master equation we use models a degenerate three- or four-wave process and takes into account the losses in the signal mode. We convert the master equation into a Fokker-Planck equation for the Wigner distribution function and solve it for a wide range of initial signal states (including thermal, coherent, Fock states, and mixtures of these). Results are presented for the enhancement of fourth- and sixth-order squeezing over second-order squeezing. Differences in the character of higher-order squeezing for different input states are pointed out. The role of losses in limiting the amount of achievable squeezing in all orders is especially investigated.

Physical Review A•Aug 1, 1992•38 citations
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The degree of squeezing increases with the order N, and the higher-order squeeze parameter qN{q}_{N}qN​ may approach -1.
It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
We consider the generation of squeezed states in degenerate four-wave mixing, retaining all significant phase-matched terms in the third-order polarization. It is shown that, for output modes combined with appropriate phase shifts, ideal squeezed states are produced when the pump field is treated classically. An approximation scheme is used to investigate the effect of pump-field quantization. We show that for reasonable crystal lengths, the effect of pump-field quantization is insignificant in the region of significant squeezing.
An investigation is carried out of higher-order squeezing in a class of three- and four-wave mixing processes that can be modeled by a master equation. In (2N)th-order squeezing, as defined by Hong and Mandel, the Nth-power of the variance of a field quadrature falls below the value it would have for a coherent state. Higher-order squeezing is of interest because (i) it occurs in many processes in which ordinary (or second-order) squeezing occurs, and (ii) it allows a much larger fractional noise reduction to be achieved than ordinary squeezing. The master equation we use models a degenerate three- or four-wave process and takes into account the losses in the signal mode. We convert the master equation into a Fokker-Planck equation for the Wigner distribution function and solve it for a wide range of initial signal states (including thermal, coherent, Fock states, and mixtures of these). Results are presented for the enhancement of fourth- and sixth-order squeezing over second-order squeezing. Differences in the character of higher-order squeezing for different input states are pointed out. The role of losses in limiting the amount of achievable squeezing in all orders is especially investigated.