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

Quantum Electronics

Non-Poisson photon statistics in an n-level (n = 2–4) laser above the threshold

A. V. Kozlovskiĭ, Anatolii N Oraevsky

Published Mar 31, 1994• 2 citations
Publisher

Abstract

A quantitative analysis is made of quantum fluctuations in the number of photons in the resonator of a single-mode laser considered in a quasi-linear approximation. An expression is obtained for a general four-level system, which is exact above the lasing threshold, but can also be used to calculate the fluctuations in the case of three- and two-level lasers. Above the threshold when certain relationships between the spontaneous decay constants are satisfied, the photon statistics are of the sub-Poisson type in four- and three-level systems. However, for other relationships between the decay constants, pumping rate, and average number of photons, fluctuations in the resonator obey both the Poisson and super-Poisson statistics with variances much greater than the average number of photons. Both Poisson and super-Poisson statistics with large values of the variance are found for a two-level system. The results of calculations indicate that, in general, there is no coherent Glauber state of the field in a laser resonator when the threshold is significantly exceeded.

DOI
10.1070/qe1994v024n03abeh000066

Related papers

Super-poissonian fluctuations of number of photons in the radiation of a single-mode laser operating near active particles number threshold

A. V. Kozlovskiĭ

It is shown that considerably exceeding the threshold pump power for laser oscillation is not sufficient for attaining Poissonian statistics of laser-emitted photons. The necessary and sufficient condition for achieving the Poissonian level of fluctuations of the number of photons in a laser mode consists in simultaneously considerably exceeding the threshold level with respect to the pumping rate and the threshold with respect to the number of active particles of the laser medium. In the case of arbitrarily large pump-power excess over the threshold, but close to the threshold with respect to the number of active particles, fluctuations of the number of photons are substantially higher than the shot noise level (super-Poissonian statistics of photons) and can reach the level of fluctuations of thermal (chaotic) light.

Optics and Spectroscopy•Jan 1, 2014•4 citations

Statistics of nonclassical lasers generated via pump-noise suppression

Chang Jun Zhu

We calculate intracavity photon-number and extracavity photocount distributions for a pump-noise-suppressed laser, using both the Lamb-Scully laser model in the number-state representation and the Haken-Risken laser model in the coherent representation. When pump fluctuations and spontaneous decay are suppressed, a pump-noise-suppressed laser has intracavity photon-number fluctuations squeezed by a factor up to 1/2. The extracavity photocount fluctuations are at the Poisson level for counting times much shorter than the cavity lifetime, whereas the variance for photocounts can be reduced to the mean of the intracavity photon number, which is markedly sub-Poissonian, under ideal conditions when the counting time is much longer than the cavity lifetime.

Physical Review A•Nov 1, 1993•16 citations

Interaction of Two-Level Atoms with a Single-Mode Quantized Radiation Field

M. Molla Gessesse

We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.

Ukrainian Journal of Physics•Aug 4, 2021•1 citation

Photon statistics of a single atom laser

Bobby D. Jones, Shohini Ghose, James Clemens +2 more

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.

Physical Review A•Oct 1, 1999•57 citations

Behavior of a Single-Atom Laser in the Sub-Poissonian Regime

Ларионов Николай Владимирович

In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is derived. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pumping tends to zero.

arXiv:2009.04563•International Conference on Electrical Engineering and Photonics (EExPolytech)•Oct 15, 2020•2 citations

Photocount statistics for pump-noise-suppressed lasers

Chang Jun Zhu, Carlton M. Caves

A laser with a Poissonian random pump, operated far above threshold, has Poissonian statistics both for the intracavity photon number and for extracavity photocounts. We analyze a pump-noise-suppressed laser using the positive P representation. When the pump noise is suppressed below a critical level, the intracavity photon-number distribution becomes sub-Poissonian.1,2 When the spontaneous decay of the upper lasing level is also eliminated, intracavity photon-number fluctuations can be diminished by a factor up to half. For counting times much shorter than the cavity decay time, the extracavity photocount statistics are essentially Poissonian, since cavity decay dominates. For counting times comparable with or larger than the cavity lifetime, the extracavity photocount statistics become sub-Poissonian. In the limit that intracavity photon-number fluctuations are diminished by one half, the extracavity photocount noise can be completely suppressed for counting times much longer than the cavity lifetime. The cavity mode occupies an incoherent superposition of two states 180° out of phase, both of which diffuse in phase. In the microlaser regime, quantum diffusion between these two states can result in 180° phase jumps, which are in addition to ordinary phase diffusion.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
A quantitative analysis is made of quantum fluctuations in the number of photons in the resonator of a single-mode laser considered in a quasi-linear approximation. An expression is obtained for a general four-level system, which is exact above the lasing threshold, but can also be used to calculate the fluctuations in the case of three- and two-level lasers. Above the threshold when certain relationships between the spontaneous decay constants are satisfied, the photon statistics are of the sub-Poisson type in four- and three-level systems. However, for other relationships between the decay constants, pumping rate, and average number of photons, fluctuations in the resonator obey both the Poisson and super-Poisson statistics with variances much greater than the average number of photons. Both Poisson and super-Poisson statistics with large values of the variance are found for a two-level system. The results of calculations indicate that, in general, there is no coherent Glauber state of the field in a laser resonator when the threshold is significantly exceeded.
It is shown that considerably exceeding the threshold pump power for laser oscillation is not sufficient for attaining Poissonian statistics of laser-emitted photons. The necessary and sufficient condition for achieving the Poissonian level of fluctuations of the number of photons in a laser mode consists in simultaneously considerably exceeding the threshold level with respect to the pumping rate and the threshold with respect to the number of active particles of the laser medium. In the case of arbitrarily large pump-power excess over the threshold, but close to the threshold with respect to the number of active particles, fluctuations of the number of photons are substantially higher than the shot noise level (super-Poissonian statistics of photons) and can reach the level of fluctuations of thermal (chaotic) light.
We calculate intracavity photon-number and extracavity photocount distributions for a pump-noise-suppressed laser, using both the Lamb-Scully laser model in the number-state representation and the Haken-Risken laser model in the coherent representation. When pump fluctuations and spontaneous decay are suppressed, a pump-noise-suppressed laser has intracavity photon-number fluctuations squeezed by a factor up to 1/2. The extracavity photocount fluctuations are at the Poisson level for counting times much shorter than the cavity lifetime, whereas the variance for photocounts can be reduced to the mean of the intracavity photon number, which is markedly sub-Poissonian, under ideal conditions when the counting time is much longer than the cavity lifetime.
We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.
In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is derived. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pumping tends to zero.
A laser with a Poissonian random pump, operated far above threshold, has Poissonian statistics both for the intracavity photon number and for extracavity photocounts. We analyze a pump-noise-suppressed laser using the positive P representation. When the pump noise is suppressed below a critical level, the intracavity photon-number distribution becomes sub-Poissonian.1,2 When the spontaneous decay of the upper lasing level is also eliminated, intracavity photon-number fluctuations can be diminished by a factor up to half. For counting times much shorter than the cavity decay time, the extracavity photocount statistics are essentially Poissonian, since cavity decay dominates. For counting times comparable with or larger than the cavity lifetime, the extracavity photocount statistics become sub-Poissonian. In the limit that intracavity photon-number fluctuations are diminished by one half, the extracavity photocount noise can be completely suppressed for counting times much longer than the cavity lifetime. The cavity mode occupies an incoherent superposition of two states 180° out of phase, both of which diffuse in phase. In the microlaser regime, quantum diffusion between these two states can result in 180° phase jumps, which are in addition to ordinary phase diffusion.