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

Communications in Theoretical Physics

Laguerre Polynomial States and Phase States in k -Photon Sub-Fock Space

Fan Hong-Yi, Fan Yue

Published Dec 15, 1997• 1 citation
Publisher

Abstract

Using k -photon Brandt–Greenberg operators we introduce the concept of field intensity-dependent squeezing, and construct the minimum uncertainty states for this squeezing, which turns out to be a Laguerre polynomial state in sub-Fock space. The k -photon phase states is also derived, which turns out to be an SU(1,1) generalized coherent state.

DOI
10.1088/0253-6102/28/4/489

Related papers

Multiphoton Laguerre polynomial state as minimum uncertainty states of intensity-dependent squeezing

Qian-Fan Chen, Hong-Yi Fan

For a general multiphoton annihilation operator, F = f(N)ap, where N = a†a, we find the explicit form of an operator, G†, which satisfies [F, G†] = 1. Based on the nonlinear realization of the SU(1,1) Lie algebra whose generators are [Formula: see text], [Formula: see text], and R0 = [N/p] + 1/2. We introduce the concept of intensity-dependent multiphoton squeezing and find that the state Lm(–yR†)|j⟩, 0 ≤ j ≤ p, where Lm(x) is a Laguerre polynomial, is a minimum uncertainty state for intensity-dependent multiphoton squeezing. We also construct the phase states for multiphoton operator, which turn out to be SU(1,1) generalized coherent states. Additionally, we show that the photon-added coherent state |α, m⟩ (m is a non-negative integer), which can be interpreted as a nonlinear coherent state, can be expressed as [Formula: see text] in the whole Fock space.

Canadian Journal of Physics•Dec 19, 2013•0 citations

MINIMUM UNCERTAINTY SU(1,1) COHERENT STATES FOR NUMBER DIFFERENCE — TWO-MODE PHASE SQUEEZING

Hong-Yi Fan, Zhihu Sun

For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.

Modern Physics Letters B•Feb 28, 2000•5 citations

Exponential and Laguerre squeezed states for su(1,1) algebra and the Calogero-Sutherland model

Hong‐Chen Fu, Ryu Sasaki B

A class of squeezed states for the su(1,1) algebra is found and expressed by the exponential and Laguerre-polynomial operators acting on the vacuum states. As a special case it is proved that Perelomov's coherent state is a ladder-operator squeezed state and therefore a minimum uncertainty state. The theory is applied to the two-particle Calogero-Sutherland model. We find some squeezed states and compared them with the classical trajectories. The connection with some su(1,1) quantum optical systems (amplitude-squared realization, Holstein-Primakoff realization, the two-mode realization, and a four-mode realization) is also discussed. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9604004•Physical Review A•Jun 1, 1996•38 citations

Minimum uncertainty states for amplitude-squared squeezing: Hermite polynomial states

János A. Bergou, Mark S. Hillery, Daoqi Yu

The real and imaginary parts of the square of the field amplitude are the variables that describe amplitude-squared squeezing. These quantities obey an uncertainty relation. Here we find a particularly simple subset of the states that satisfy the uncertainty relation as an equality. These states are constructed by applying a squeeze operator to a state that consists of a Hermite polynomial, whose argument is the mode creation operator multiplied by a constant, acting on the vacuum. The squeezed vacuum is such a state. These states may or may not be squeezed in the normal sense, and may or may not have sub-Poissonian photon statistics.

Physical Review A•Jan 1, 1991•84 citations

INTELLIGENT STATES FOR AN INTERPOLATING ALGEBRA

Barnana Roy, Rajkumar Roychoudhury

Intelligent states in the sense of field intensity dependent squeezing for a closed and symmetric algebra which interpolates between the Heisenberg Weyl algebra W3 and su(1,1) algebra are constructed. The explicit expressions of these states in terms of Laguerre polynomials are derived and their quantum statistical properties are investigated.

International Journal of Modern Physics B•Oct 20, 2003•1 citation

Phase operators for SU(1,1): Application to the squeezed vacuum

Christopher C. Gerry

A phase-operator formalism is constructed for the Lie algebra of SU(1,1). Uncertainty relations, analogous to the usual number-phase relations, are also constructed. These relations are then evaluated for SU(1,1) coherent states, of which the squeezed-vacuum state of the electromagnetic field is an example. We argue that the new phase, in the case of single-mode fields, may be interpreted as the phase associated with the square of the field amplitude.

Physical Review A•Aug 1, 1988•18 citations
Using k -photon Brandt–Greenberg operators we introduce the concept of field intensity-dependent squeezing, and construct the minimum uncertainty states for this squeezing, which turns out to be a Laguerre polynomial state in sub-Fock space. The k -photon phase states is also derived, which turns out to be an SU(1,1) generalized coherent state.
For a general multiphoton annihilation operator, F = f(N)ap, where N = a†a, we find the explicit form of an operator, G†, which satisfies [F, G†] = 1. Based on the nonlinear realization of the SU(1,1) Lie algebra whose generators are [Formula: see text], [Formula: see text], and R0 = [N/p] + 1/2. We introduce the concept of intensity-dependent multiphoton squeezing and find that the state Lm(–yR†)|j⟩, 0 ≤ j ≤ p, where Lm(x) is a Laguerre polynomial, is a minimum uncertainty state for intensity-dependent multiphoton squeezing. We also construct the phase states for multiphoton operator, which turn out to be SU(1,1) generalized coherent states. Additionally, we show that the photon-added coherent state |α, m⟩ (m is a non-negative integer), which can be interpreted as a nonlinear coherent state, can be expressed as [Formula: see text] in the whole Fock space.
For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.
A class of squeezed states for the su(1,1) algebra is found and expressed by the exponential and Laguerre-polynomial operators acting on the vacuum states. As a special case it is proved that Perelomov's coherent state is a ladder-operator squeezed state and therefore a minimum uncertainty state. The theory is applied to the two-particle Calogero-Sutherland model. We find some squeezed states and compared them with the classical trajectories. The connection with some su(1,1) quantum optical systems (amplitude-squared realization, Holstein-Primakoff realization, the two-mode realization, and a four-mode realization) is also discussed. \textcopyright{} 1996 The American Physical Society.
The real and imaginary parts of the square of the field amplitude are the variables that describe amplitude-squared squeezing. These quantities obey an uncertainty relation. Here we find a particularly simple subset of the states that satisfy the uncertainty relation as an equality. These states are constructed by applying a squeeze operator to a state that consists of a Hermite polynomial, whose argument is the mode creation operator multiplied by a constant, acting on the vacuum. The squeezed vacuum is such a state. These states may or may not be squeezed in the normal sense, and may or may not have sub-Poissonian photon statistics.