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 Letters

Photon Antibunching and Squeezing for a Single Atom in a Resonant Cavity

H. J. Carmichael

Published Dec 16, 1985• 190 citations
Publisher

Abstract

The transmitted light from an optical cavity containing a single two-level atom may show photon antibunching and squeezing. The two effects are closely related and simply understood in terms of the theory of single-atom resonance fluorescence. It follows that corresponding nonclassical effects in optical bistability do not originate in atomic collectivity.

DOI
10.1103/physrevlett.55.2790

Related papers

Single-atom cavity-enhanced absorption with injected squeezed vacuum: photon statistics

Perry R. Rice, L. M. Pedrotti, J. Walden

We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Photon antibunching in the single-atom limit of absorptive bistability

H. J. Carmichael

Photon antibunching has been predicted at weak intensities along the lower branch in optical bistability. Existing theories assume large atomic numbers to justify their linearized analysis. From such a theory photon antibunching in absorptive bistability is given for weak intensities by where C is the bistability parameter, μ is the ratio of atomic and cavity decay times, and N is the number of atoms. Clearly this result becomes invalid as the system size is reduced to the limit of a single atom; then g(2) (0) is negative for moderate values of C. I calculate g(2) (0) for the transmitted light from an optical cavity containing a single atom, where the injected field, the atom, and the cavity are all resonant.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Squeezing and quantum effects in optics

M. D. Reid

In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.

•Jan 1, 1984•0 citations

Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit

Perry R. Rice, H. J. Carmichael

The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>

IEEE Journal of Quantum Electronics•Jul 1, 1988•130 citations

Weak-field transmitted and fluorescent spectra for an atom in a resonant cavity

Perry R. Rice, H. J. Carmichael

There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Photon antibunching and squeezing in resonance fluorescence of two interacting atoms

Z. Ficek, R. Tanaś, S. Kielich

The equal-time intensity correlation function and variances of the in-phase and out-of-phase components of the electric field radiated by a system of two interacting atoms in the process of resonance fluorescence are calculated analytically for arbitrary values of the field strength, interatomic interaction, and detuning and are illustrated graphically. It is shown that not only photon antibuching but also squeezing can occur in two-atom resonance fluorescence. The influence of dipole-dipole interaction between the atoms on both nonclassical effects is discussed. It is shown that a considerable amount of photon antibunching and squeezing can be obtained for finite detuning of the laser frequency from atomic resonance, especially when the detuning and dipole-dipole interaction parameters cancel out mutually. The maximum value of squeezing for interacting atoms is shown to be less, however, than that for noninteracting atoms. Very strong dipole-dipole interaction reduces the squeezing effect to zero.

Physical Review A•Apr 1, 1984•56 citations
The transmitted light from an optical cavity containing a single two-level atom may show photon antibunching and squeezing. The two effects are closely related and simply understood in terms of the theory of single-atom resonance fluorescence. It follows that corresponding nonclassical effects in optical bistability do not originate in atomic collectivity.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
Photon antibunching has been predicted at weak intensities along the lower branch in optical bistability. Existing theories assume large atomic numbers to justify their linearized analysis. From such a theory photon antibunching in absorptive bistability is given for weak intensities by where C is the bistability parameter, μ is the ratio of atomic and cavity decay times, and N is the number of atoms. Clearly this result becomes invalid as the system size is reduced to the limit of a single atom; then g(2) (0) is negative for moderate values of C. I calculate g(2) (0) for the transmitted light from an optical cavity containing a single atom, where the injected field, the atom, and the cavity are all resonant.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.
The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.
The equal-time intensity correlation function and variances of the in-phase and out-of-phase components of the electric field radiated by a system of two interacting atoms in the process of resonance fluorescence are calculated analytically for arbitrary values of the field strength, interatomic interaction, and detuning and are illustrated graphically. It is shown that not only photon antibuching but also squeezing can occur in two-atom resonance fluorescence. The influence of dipole-dipole interaction between the atoms on both nonclassical effects is discussed. It is shown that a considerable amount of photon antibunching and squeezing can be obtained for finite detuning of the laser frequency from atomic resonance, especially when the detuning and dipole-dipole interaction parameters cancel out mutually. The maximum value of squeezing for interacting atoms is shown to be less, however, than that for noninteracting atoms. Very strong dipole-dipole interaction reduces the squeezing effect to zero.