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

Laser with thresholdless intensity fluctuations

N. J. van Druten, Yngve Lien, Carles Serrat, Sumant S. R. Oemrawsingh, Martin P. van Exter, J. P. Woerdman

Published Oct 17, 2000• 46 citations
Publisher

Abstract

We have studied the quantum-noise properties of a small slow-inversion laser experimentally and theoretically. As a function of pump rate, the average output intensity shows a sharp threshold, but the intensity fluctuations do not. Under quite generic conditions the intensity fluctuations of a sufficiently small slow-inversion laser show highly super-Poissonian statistics (even two times above threshold), due to the very weak damping of the spontaneous-emission-driven relaxation oscillation.

DOI
10.1103/physreva.62.053808

Related papers

Nonlinear features of quantum fluctuations in a slow-inversion laser

E G Lariontsev

We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\ensuremath{\omega}}_{r}$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\ensuremath{\omega}}_{c}$ appear two lines at frequencies ${\ensuremath{\omega}}_{c}+{\ensuremath{\omega}}_{r}$ and ${\ensuremath{\omega}}_{c}\ensuremath{-}{\ensuremath{\omega}}_{r}$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\ensuremath{\omega}}_{r}$ and the decay rates of the field correlation function.

Physical Review A•Jun 6, 2011•6 citations

Photon Statistics of a Laser with Slow Inversion

Yngve Lien, S. M. de Vries, N. J. van Druten +2 more

We have measured the photon number probability distribution of a laser in which the inversion is not slaved to the field. For the experiments, we have used a Nd(3+):YVO(4) laser which has a sufficiently slow inversion to allow measurement of the photon fluctuations at a time scale much shorter than that of the relaxation oscillations. The photon distribution function becomes highly nonstandard (i.e., non-Poissonian) in such a laser; this is consistent with available theoretical work. We point out the relevance of our results for the case of the semiconductor microlaser.

Physical Review Letters•Mar 26, 2001•21 citations

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

Amplitude noise reduction in atomic and semiconductor lasers

T. A. B. Kennedy, Daniel F. Walls

The quantum noise properties of atomic and semiconductor lasers are compared. The intensity fluctuation spectrum of the output field is calculated for the case of regularly, i.e., sub-Poissonian, pumped lasers. The effects of spontaneous emission on the output amplitude fluctuations may be suppressed in regularly pumped atomic lasers by requiring the lifetime of the lower lasing level to be short in comparison with that of the upper laser level. The output amplitude fluctuations then tend to zero at the laser frequency. In regularly pumped semiconductor lasers, net stimulated emission of photons dominates over spontaneous emission because of the combination of pumping and rapid intraband thermalization due to Coulomb scattering.

Physical Review A•Dec 1, 1989•37 citations

4A3 - Intensity fluctuations in the output of laser oscillators

D. E. McCumber

Using population rate equations, we have calculated the intrinsic intensity fluctuations expected in the output of 3-level and 4-level CW laser oscillators. Such fluctuations stem from the quantum shot noise implicit in a restriction of the atomic and photon population-operator eigenvalues to discrete integral values (in the manner of Shimoda, Takahasi, and Townes). The intrinsic fluctuations below threshold are typical of a Gaussian distribution ofe-mfield amplitudes (Bose-Einstein distribution of photons) and above threshold of an amplitude-stabilizede-mfield (Poisson distribution of photons). The noise properties of 3-level and 4-level lasers are qualitatively similar, although for a given output power the intensity fluctuations of 3-level oscillators are greater than (or equal to) those in 4-level oscillators, principally as a consequence of the increased spontaneous emission associated with the larger upper-state occupation necessary to achieve a net gain in 3-level systems.

IEEE Journal of Quantum Electronics•Aug 1, 1966•6 citations

Stochastic quantum dynamics of a continuously monitored laser

Howard M. Wiseman

The stochastic dynamics of the quantum state of a laser conditioned on continuous intensity and phase-sensitive measurements on its output are examined. We first develop the essential model for a Poissonian laser, and then generalize it for regularly pumped lasers. We show that the rate of phase diffusion (which gives the laser linewidth) is not affected by the regularity of the pump. In both cases, heterodyne detection causes the phase variance in the conditioned laser state to become very small, yet remain significantly above (at least three times) that of a coherent state. The phase diffusion is manifest by a random walk undertaken by the mean phase, with the stochasticity arising from the local-oscillator shot noise. In contrast, intensity measurements have no effect on a Poissonian laser. For a perfectly regularly pumped laser, coarse-grained intensity measurements (for which an approximate theory is developed here) collapse the state to one with an arbitrarily small photon-number variance-to-mean ratio.

Physical Review A•Jun 1, 1993•42 citations
We have studied the quantum-noise properties of a small slow-inversion laser experimentally and theoretically. As a function of pump rate, the average output intensity shows a sharp threshold, but the intensity fluctuations do not. Under quite generic conditions the intensity fluctuations of a sufficiently small slow-inversion laser show highly super-Poissonian statistics (even two times above threshold), due to the very weak damping of the spontaneous-emission-driven relaxation oscillation.
We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\ensuremath{\omega}}_{r}$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\ensuremath{\omega}}_{c}$ appear two lines at frequencies ${\ensuremath{\omega}}_{c}+{\ensuremath{\omega}}_{r}$ and ${\ensuremath{\omega}}_{c}\ensuremath{-}{\ensuremath{\omega}}_{r}$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\ensuremath{\omega}}_{r}$ and the decay rates of the field correlation function.
We have measured the photon number probability distribution of a laser in which the inversion is not slaved to the field. For the experiments, we have used a Nd(3+):YVO(4) laser which has a sufficiently slow inversion to allow measurement of the photon fluctuations at a time scale much shorter than that of the relaxation oscillations. The photon distribution function becomes highly nonstandard (i.e., non-Poissonian) in such a laser; this is consistent with available theoretical work. We point out the relevance of our results for the case of the semiconductor microlaser.
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.
The quantum noise properties of atomic and semiconductor lasers are compared. The intensity fluctuation spectrum of the output field is calculated for the case of regularly, i.e., sub-Poissonian, pumped lasers. The effects of spontaneous emission on the output amplitude fluctuations may be suppressed in regularly pumped atomic lasers by requiring the lifetime of the lower lasing level to be short in comparison with that of the upper laser level. The output amplitude fluctuations then tend to zero at the laser frequency. In regularly pumped semiconductor lasers, net stimulated emission of photons dominates over spontaneous emission because of the combination of pumping and rapid intraband thermalization due to Coulomb scattering.
Using population rate equations, we have calculated the intrinsic intensity fluctuations expected in the output of 3-level and 4-level CW laser oscillators. Such fluctuations stem from the quantum shot noise implicit in a restriction of the atomic and photon population-operator eigenvalues to discrete integral values (in the manner of Shimoda, Takahasi, and Townes). The intrinsic fluctuations below threshold are typical of a Gaussian distribution ofe-mfield amplitudes (Bose-Einstein distribution of photons) and above threshold of an amplitude-stabilizede-mfield (Poisson distribution of photons). The noise properties of 3-level and 4-level lasers are qualitatively similar, although for a given output power the intensity fluctuations of 3-level oscillators are greater than (or equal to) those in 4-level oscillators, principally as a consequence of the increased spontaneous emission associated with the larger upper-state occupation necessary to achieve a net gain in 3-level systems.
The stochastic dynamics of the quantum state of a laser conditioned on continuous intensity and phase-sensitive measurements on its output are examined. We first develop the essential model for a Poissonian laser, and then generalize it for regularly pumped lasers. We show that the rate of phase diffusion (which gives the laser linewidth) is not affected by the regularity of the pump. In both cases, heterodyne detection causes the phase variance in the conditioned laser state to become very small, yet remain significantly above (at least three times) that of a coherent state. The phase diffusion is manifest by a random walk undertaken by the mean phase, with the stochasticity arising from the local-oscillator shot noise. In contrast, intensity measurements have no effect on a Poissonian laser. For a perfectly regularly pumped laser, coarse-grained intensity measurements (for which an approximate theory is developed here) collapse the state to one with an arbitrarily small photon-number variance-to-mean ratio.