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

arXiv:1110.4200

Geometric Phases for Coherent States

Da-Bao Yang, Jing‐Ling Chen, Chunfeng Wu, Changhun Oh

Published Oct 19, 2011• 0 citations
arXivHTMLPDF

Abstract

We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled coherent states, several interesting results followed by considering different cases for the parameters. The effects of entanglement and harmonic potential on the geometric phase are discussed.

DOI
10.48550/arxiv.1110.4200

Related papers

Geometric phases for nonlinear coherent and squeezed states

Da-Bao Yang, Ying Chen, Fu-Lin Zhang +1 more

The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞ , the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

arXiv:1011.0501•Journal of Physics B Atomic Molecular and Optical Physics•Mar 16, 2011•12 citations

Geometric Phase for degenerate states of spin-1 and spin-1/2 pair

Zhu, G Q

The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and the entanglement or mixedness of the initial state is considered.

•Mar 14, 2007•0 citations

Geometric phases of nonlinear coherent and squeezed states: a new approach

S.AL. Modares Vamegh, Mohammad Kazem Tavassoly

Recently, geometric phases of nonlinear coherent and squeezed states have been investigated by Yang et al (2011 J. Phys. B: At. Mol. Opt. Phys. 44 075502). In this paper, after a modification of Yang et al's derivation procedure, we deduced the non-cyclic and non-unitary geometric phases of nonlinear coherent and nonlinear squeezed states with a new approach which is consistent with the nonlinear coherent states theory. Indeed, the most important distinguishable feature of our presentation lies in the fact that we employed the (nonlinear) Hamiltonian which appropriately generates the time evolution of nonlinear coherent and squeezed states. It is established that this modification directly affects the resultant geometric phases of the states under consideration. As a physical realization, we applied our formalism to a particular nonlinear physical system corresponding to the centre-of-mass motion of a trapped ion coherent state. Then, the variation of the geometric phases of the considered nonlinear states in terms of time, intensity of radiation field, squeezing and Lamb–Dicke parameters are investigated. Finally, we discuss our numerical results.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 18, 2012•0 citations

COHERENT STATES AND GEOMETRIC PHASES IN THE CALOGERO–SUTHERLAND MODEL

Dae-Yup Song, JeongHyeong Park

Exact coherent states in the Calogero–Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the AN-1 Calogero–Sutherland model, the phase is calculated for a general coherent state. The phases for other models are also considered.

arXiv:quant-ph/0109108•International Journal of Modern Physics A•Jan 20, 2002•4 citations

Geometric phases for two-mode squeezed state

Da-Bao Yang, Ji-Xuan Hou

Although the geometric phase for one-mode squeezed state had been studied in detail, the counterpart for two-mode squeezed state is vacant. It is be evaluated explicitly in this paper. Furthermore, the total phase factor is in an elegent form, which is just identical to one term of product of two squeezed operators. In addition, when this system undergoes cyclic evolutions, the corresponding geometric phase is obtained, which is just the sum of the counterparts of two isolated one-mode squeezed state. Finally, the relationship between the cyclic geomtric phase and entanglement of two-mode squeezed state is established.

arXiv:1510.00770•Oct 3, 2015•0 citations

Geometric Phase in Two-state System and in Coherent State of Forced Oscillator

Suqing Chen

The formula for deriving the geometric phase in two-state system is dicussed, emphasizing on the property of Bargmann invariant. A comparison with the coherent state of forced oscillator is also made.

Fudan xuebao. Ziran Kexue ban•Jan 1, 2000•0 citations
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled coherent states, several interesting results followed by considering different cases for the parameters. The effects of entanglement and harmonic potential on the geometric phase are discussed.
The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞ , the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.
Recently, geometric phases of nonlinear coherent and squeezed states have been investigated by Yang et al (2011 J. Phys. B: At. Mol. Opt. Phys. 44 075502). In this paper, after a modification of Yang et al's derivation procedure, we deduced the non-cyclic and non-unitary geometric phases of nonlinear coherent and nonlinear squeezed states with a new approach which is consistent with the nonlinear coherent states theory. Indeed, the most important distinguishable feature of our presentation lies in the fact that we employed the (nonlinear) Hamiltonian which appropriately generates the time evolution of nonlinear coherent and squeezed states. It is established that this modification directly affects the resultant geometric phases of the states under consideration. As a physical realization, we applied our formalism to a particular nonlinear physical system corresponding to the centre-of-mass motion of a trapped ion coherent state. Then, the variation of the geometric phases of the considered nonlinear states in terms of time, intensity of radiation field, squeezing and Lamb–Dicke parameters are investigated. Finally, we discuss our numerical results.
Exact coherent states in the Calogero–Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the AN-1 Calogero–Sutherland model, the phase is calculated for a general coherent state. The phases for other models are also considered.
Although the geometric phase for one-mode squeezed state had been studied in detail, the counterpart for two-mode squeezed state is vacant. It is be evaluated explicitly in this paper. Furthermore, the total phase factor is in an elegent form, which is just identical to one term of product of two squeezed operators. In addition, when this system undergoes cyclic evolutions, the corresponding geometric phase is obtained, which is just the sum of the counterparts of two isolated one-mode squeezed state. Finally, the relationship between the cyclic geomtric phase and entanglement of two-mode squeezed state is established.