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/9912023 · Physical Review A

Input-output relations in optical cavities: A simple point of view

Andrea Aiello

Published Nov 15, 2000• 14 citations
arXivHTMLPDF

Abstract

In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.

DOI
10.1103/physreva.62.063813

Related papers

Quantum-state input–output relations for absorbing cavities

M Khanbekyan, D-G Welsch, A A Semenov +1 more

The quantized electromagnetic field inside and outside an absorbing high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schrödinger cat-like state is discussed.

arXiv:quant-ph/0512184•Journal of Optics B Quantum and Semiclassical Optics•Nov 22, 2005•3 citations

Quantum-state input-output relations for absorbing cavities

M. Khanbekyan, D.‐G. Welsch, А. А. Семенов +1 more

The quantized electromagnetic field inside and outside an absorbing high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schr\\"{o}dinger cat-like state is discussed.

•Dec 21, 2005•1 citation

Quantum theory of a one-dimensional optical cavity with output coupling. Field quantization

Kikuo Ujihara

The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.

Physical Review A•Jul 1, 1975•55 citations

Space-time descriptions of quantum fields interacting with optical cavities

Julio R. Gea-Banacloche

The purpose of this paper is to compare two unitary, deterministic approaches to the study of the interaction of quantized fields with atomic systems in optical cavities. In particular it is shown that the ``modes of the universe'' approach, in which each mode has both an intracavity and an outside part, is formally equivalent, in an appropriate limit, to the better known ``input-output'' formalism in its unitary (i.e., Hermitian-Hamiltonian based) form; the latter may be called a ``quasimode'' theory, since it treats the field inside the cavity as a separate degree of freedom. Differences that arise between the two approaches for numerical calculations involving a finite set of discrete modes are also pointed out. The formalism is illustrated with an in-depth discussion of the explicit solution for a single-photon pulse, of arbitrary shape and detuning, incident on a cavity containing a two-level atom.

Physical Review A•Feb 22, 2013•20 citations

Generating non-classical light inside an optical cavity by depositing photons

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, Francisco Soto +1 more

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.

Journal of Modern Optics•Jul 16, 2017•5 citations

QED of lossy cavities: Operator and quantum-state input-output relations

M. Khanbekyan, L. Knöll, D.‐G. Welsch +2 more

Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the $s$-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.

arXiv:quant-ph/0505117•Physical Review A•Nov 18, 2005•28 citations
In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.
The quantized electromagnetic field inside and outside an absorbing high-QQQ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schrödinger cat-like state is discussed.
The quantized electromagnetic field inside and outside an absorbing high-QQQ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schr\\"{o}dinger cat-like state is discussed.
The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.
The purpose of this paper is to compare two unitary, deterministic approaches to the study of the interaction of quantized fields with atomic systems in optical cavities. In particular it is shown that the ``modes of the universe'' approach, in which each mode has both an intracavity and an outside part, is formally equivalent, in an appropriate limit, to the better known ``input-output'' formalism in its unitary (i.e., Hermitian-Hamiltonian based) form; the latter may be called a ``quasimode'' theory, since it treats the field inside the cavity as a separate degree of freedom. Differences that arise between the two approaches for numerical calculations involving a finite set of discrete modes are also pointed out. The formalism is illustrated with an in-depth discussion of the explicit solution for a single-photon pulse, of arbitrary shape and detuning, incident on a cavity containing a two-level atom.
The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.
Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-QQQ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the sss-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.