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

Physical Review A

Intrinsic phase coherence of laser light

David Thomas Pegg

Published May 19, 2009• 6 citations
Publisher

Abstract

We examine the phase relationships between different packets of a beam of light emitted from a cavity through a partially transmitting mirror. We find that the beam has a pronounced phase coherence even when the intracavity field has a completely indeterminate phase such as, for example, when it is in a pure photon number state. In this case, the phase coherence can be directly attributed to entanglement caused by the partially transmitting mirror and, even though the external light has phase coherence, it has no identifiable phase. Consequently there is no phase diffusion but there is diffusion of the phase difference between a packet and the intracavity field. Remarkably, we find that the phase coherence of the beam is almost independent of the intracavity state, provided this has a reasonably narrow number-state distribution about a large mean value.

DOI
10.1103/physreva.79.053837

Related papers

Quantum properties of correlated emission laser with dephasing and phase fluctuation

Desalegn Ayehu

We consider a two-photon laser in a cascade configuration coupled to an ordinary vacuum reservoir via a partially transmitting mirror. The impacts of the dephasing and the phase fluctuation on the entanglement, two-mode squeezing, and the intensity of the intracavity radiation are studied at steady-state. It so happens that the initial atomic coherence is the cause for the quantum properties of the cavity radiation even in the presence of the decoherence. We show that the dephasing rates and the phase fluctuations hurt the amount of squeezing and entanglement of the intracavity radiation. However, the dephasing rate leads to an increase in the intensity of the cavity radiation. Moreover, the phase fluctuation degrades the intensity of the intracavity radiation near to the initial maximum atomic coherence and it enhances otherwise.

Results in Physics•Jul 24, 2021•8 citations

Entropy Flow of a Laser Beam

Howard M. Wiseman

A laser beam is often modelled by a pure coherent state. In fact its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate $\ell$, equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of $\dot{S} = \kB\sqrt{\dot{N}\ell}$, where $\dot{N}$ is the number flow. We give an intuitive explanation for this remarkably simple result, and compare it to the entropy flow of a unidirectional thermal beam.

quant-pharXiv:2512.01230•Dec 2, 2025

Statistical Properties of Randomly Modulated Laser Beams

B. Picinbono

Results were recently reported on statistical properties of phase-modulated laser light. A detailed analysis is presented here of random-phase modulation. In particular it is shown that there are two kinds of such modulation: modulation by phase fluctuations, in which the instantaneous phase is a stationary stochastic process, and modulation by phase diffusion in which the phase is a diffusion process with an always increasing variance. In the case of a Gaussian modulation we show that the optical fields in the two preceding cases are very different, and we calculate their coherence functions. This difference can be detected by an interference experiment, but more easily by photon coincidence or intensity-correlation experiments on a beat between a reference beam and the modulated beams. We present a theoretical analysis of such experiments in the two cases of modulation.

Physical Review A•Dec 1, 1971•9 citations

Quantum Theory of Interference Effects Produced by Independent Light Beams

L. Mandeļ

The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.

Physical Review•Apr 6, 1964•54 citations

Decoherence as phase diffusion

P. Milman, Yvan Castin, L. Davidovich

We show that the decoherence of a superposition of two coherent states of the electromagnetic field in a cavity may be interpreted as a phase-diffusion process.Received 5 October 1999DOI:https://doi.org/10.1103/PhysRevA.61.063803©2000 American Physical Society

Physical Review A•May 8, 2000•3 citations

Interference of light from independent sources

David Thomas Pegg

We extend and generalize previous work on the interference of light from independent cavities that began with the suggestion of Pfleegor and Mandel [Phys. Rev. 159, 1084 (1967)] that their observed interference of laser beams should not be associated too closely with particular states of the beams but more with the detection process itself. In particular we examine how the detection of interference induces a nonrandom-phase difference between internal cavity states with initial random phases for a much broader range of such states than has previously been considered. We find that a subsequent interference measurement should give results consistent with the induced phase difference. The inclusion of more cavities in the interference measurements enables the construction in principle of a laboratory in the sense used by Aharonov and Susskind, made up of cavity fields that can serve as frames of phase reference. We also show reasonably simply how intrinsic phase coherence of a beam of light leaking from a single cavity arises for any internal cavity state, even a photon number state. Although the work presented here may have some implications for the current controversy over whether or not a typical laboratory laser produces a coherent state, it is not the purpose of this paper to enter this controversy; rather it is to examine the interesting quantum physics that arises for cavities with more general internal states.

Physical Review A•Dec 14, 2006•4 citations
We examine the phase relationships between different packets of a beam of light emitted from a cavity through a partially transmitting mirror. We find that the beam has a pronounced phase coherence even when the intracavity field has a completely indeterminate phase such as, for example, when it is in a pure photon number state. In this case, the phase coherence can be directly attributed to entanglement caused by the partially transmitting mirror and, even though the external light has phase coherence, it has no identifiable phase. Consequently there is no phase diffusion but there is diffusion of the phase difference between a packet and the intracavity field. Remarkably, we find that the phase coherence of the beam is almost independent of the intracavity state, provided this has a reasonably narrow number-state distribution about a large mean value.
We consider a two-photon laser in a cascade configuration coupled to an ordinary vacuum reservoir via a partially transmitting mirror. The impacts of the dephasing and the phase fluctuation on the entanglement, two-mode squeezing, and the intensity of the intracavity radiation are studied at steady-state. It so happens that the initial atomic coherence is the cause for the quantum properties of the cavity radiation even in the presence of the decoherence. We show that the dephasing rates and the phase fluctuations hurt the amount of squeezing and entanglement of the intracavity radiation. However, the dephasing rate leads to an increase in the intensity of the cavity radiation. Moreover, the phase fluctuation degrades the intensity of the intracavity radiation near to the initial maximum atomic coherence and it enhances otherwise.
A laser beam is often modelled by a pure coherent state. In fact its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate ℓ\ellℓ, equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of $\dot{S} = \kB\sqrt{\dot{N}\ell}$, where N˙\dot{N}N˙ is the number flow. We give an intuitive explanation for this remarkably simple result, and compare it to the entropy flow of a unidirectional thermal beam.
Results were recently reported on statistical properties of phase-modulated laser light. A detailed analysis is presented here of random-phase modulation. In particular it is shown that there are two kinds of such modulation: modulation by phase fluctuations, in which the instantaneous phase is a stationary stochastic process, and modulation by phase diffusion in which the phase is a diffusion process with an always increasing variance. In the case of a Gaussian modulation we show that the optical fields in the two preceding cases are very different, and we calculate their coherence functions. This difference can be detected by an interference experiment, but more easily by photon coincidence or intensity-correlation experiments on a beat between a reference beam and the modulated beams. We present a theoretical analysis of such experiments in the two cases of modulation.
The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.
We extend and generalize previous work on the interference of light from independent cavities that began with the suggestion of Pfleegor and Mandel [Phys. Rev. 159, 1084 (1967)] that their observed interference of laser beams should not be associated too closely with particular states of the beams but more with the detection process itself. In particular we examine how the detection of interference induces a nonrandom-phase difference between internal cavity states with initial random phases for a much broader range of such states than has previously been considered. We find that a subsequent interference measurement should give results consistent with the induced phase difference. The inclusion of more cavities in the interference measurements enables the construction in principle of a laboratory in the sense used by Aharonov and Susskind, made up of cavity fields that can serve as frames of phase reference. We also show reasonably simply how intrinsic phase coherence of a beam of light leaking from a single cavity arises for any internal cavity state, even a photon number state. Although the work presented here may have some implications for the current controversy over whether or not a typical laboratory laser produces a coherent state, it is not the purpose of this paper to enter this controversy; rather it is to examine the interesting quantum physics that arises for cavities with more general internal states.