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:quant-ph/0102026 · Physical Review A

Comprehensive theory of the relative phase in atom-field interactions

J. Delgado, E. C. Yustas, Luis Lorenzo Sánchez-Soto, A. B. Klimov

Published May 4, 2001• 8 citations
arXivHTMLPDF

Abstract

We explore the role played by the quantum relative phase in a well-known model of atom-field interaction, namely, the Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties, as we demonstrate by studying the positive operator-valued measure derived from it. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.

DOI
10.1103/physreva.63.063801

Related papers

Exploring the role of the relative phase in atom-field interactions

Luis Lorenzo Sánchez-Soto, J. Delgado, E. C. Yustas +1 more

We explore the role played by the quantum relative phase in the well-known Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 3, 2002•0 citations

Quantum dynamics of the relative phase in second-harmonic generation

J Delgado, Alfredo Luis, Luis Lorenzo Sánchez-Soto +1 more

We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.

Journal of Optics B Quantum and Semiclassical Optics•Jan 19, 2000•8 citations

Relative phase for a quantum field interacting with a two-level system

Alfredo Luis, Luis Lorenzo Sánchez-Soto

Several quantum descriptions of the relative phase between an atomic dipole and a one-mode electromagnetic field are examined. Positive-operator measures for this variable are derived from dipole and field-phase formalisms. They are analyzed and compared with an operator defined by a polar decomposition. Some examples of time evolution are discussed.

Physical Review A•Jul 1, 1997•19 citations

Description of entanglement in terms of quantum phase

Luis Lorenzo Sánchez-Soto, Julián Delgado, A. B. Klimov +1 more

We explore the role played by the phase in an accurate description of the entanglement of bipartite systems. We first present an appropriate polar decomposition that leads to a truly Hermitian operator for the phase of a single qubit. We also examine the positive operator-valued measures that can describe the qubit phase properties. When dealing with two qubits, the relative phase seems to be a natural variable to understand entanglement. In this spirit, we propose a measure of entanglement based on this variable.

arXiv:quant-ph/0202100•Physical Review A•Oct 21, 2002•12 citations

Phase states for a three-level atom interacting with quantum fields

A. B. Klimov, Luis Lorenzo Sánchez-Soto, J. Delgado +1 more

We introduce phase operators associated with the algebra su(3), which is the appropriate tool to describe three-level systems. The rather unusual properties of this phase are caused by the small dimension of the system and are explored in detail. When a three-level atom interacts with a quantum field in a cavity, a polynomial deformation of this algebra emerges in a natural way. We also introduce a polar decomposition of the atom-field relative amplitudes that leads to a Hermitian relative-phase operator, whose eigenstates correctly describe the corresponding phase properties. We claim that this is the natural variable to deal with quantum interference effects in atom-field interactions. We find the probability distribution for this variable and study its time evolution in some special cases.

arXiv:quant-ph/0212012•Physical Review A•Jan 10, 2003•3 citations

Phase Properties of a Quantized Field Interacting With an Atom

周鹏

The study of the quantized field phase dates back to Diracs definition of the phase operator which came from a polar decomposition of the annihilation operator following a simple analogy with the phase of a classical harmonic oscillator, according to the usual procedure of quantization. Unfortunately, this approach causes inconsistency. Some people attempted to investigate the phase properties from various angles after Dirac.

中国科学通报：英文版•Jan 1, 1993•0 citations
We explore the role played by the quantum relative phase in a well-known model of atom-field interaction, namely, the Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties, as we demonstrate by studying the positive operator-valued measure derived from it. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.
We present a comprehensive and self-consistent theory of the relative phase between fundamental and harmonic modes in the nonlinear process of second-harmonic generation. We introduce an adequate polar decomposition of the field amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties of the fields. We find the probability distribution for the relative phase and, by using a numerical diagonalization of the interaction Hamiltonian, we study its time evolution. This evolution shows quite different asymptotic behaviours for long times depending on the total number of quanta.
We explore the role played by the phase in an accurate description of the entanglement of bipartite systems. We first present an appropriate polar decomposition that leads to a truly Hermitian operator for the phase of a single qubit. We also examine the positive operator-valued measures that can describe the qubit phase properties. When dealing with two qubits, the relative phase seems to be a natural variable to understand entanglement. In this spirit, we propose a measure of entanglement based on this variable.
We introduce phase operators associated with the algebra su(3), which is the appropriate tool to describe three-level systems. The rather unusual properties of this phase are caused by the small dimension of the system and are explored in detail. When a three-level atom interacts with a quantum field in a cavity, a polynomial deformation of this algebra emerges in a natural way. We also introduce a polar decomposition of the atom-field relative amplitudes that leads to a Hermitian relative-phase operator, whose eigenstates correctly describe the corresponding phase properties. We claim that this is the natural variable to deal with quantum interference effects in atom-field interactions. We find the probability distribution for this variable and study its time evolution in some special cases.