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Annual Meeting Optical Society of America

Photocount statistics for pump-noise-suppressed lasers

Chang Jun Zhu, Carlton M. Caves

Published Jan 1, 1991• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1991.mo3

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Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
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.
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.
A method on how to take into account pump statistics and spontaneous atomic decays when calculating the photon-number distribution of lasers in photon-number representation is presented. The intracavity phonon-number and extracavity photocount distributions with binomial pump and spontaneous atomic decays are calculated. In two limit cases, the results of calculations transit respectively to the photon-number distributions of systems with common Poissonian pump and regular pump, and both with the spontaneous atomic decays being suppressed.
It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.
We solve the problem of a laser with variable pumping statistics for any relative magnitude of the atomic- and cavity-decay constants, and obtain a different regime of sub-Poissonian light generation. We show that, even for Poissonian pumping, the noise in the amplitude quadrature outside the cavity can be reduced up to 50% below the shot-noise level when the polarization but not the populations can be adiabatically eliminated. Maximum noise reduction in this case is obtained when the lower level decays much faster than the upper one and occurs at a frequency given by the geometrical mean of the decay rates of the field and the lower-level population. Furthermore, the full consideration of atomic memory effects leads to a generalization of previous results on regularly pumped lasers. We find that, for regular pumping, maximum amplitude-noise reduction (up to complete quieting) still occurs at zero frequency in all cases. However, a long-living polarizaton leads to an increase in amplitude noise and may even eliminate the dip at zero frequency, at the same time leading to a significant quenching of the laser linewidth in the bad-cavity limit.
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.
We present new results for the quantum noise reduction owing to the mth harmonic generation (m = ½, 2, 3) in a laser. Study of such a source of light with noise beyond the quantum limit is now in progress.1,2 We consider this problem for both the laser with conventional random pumping and the laser with reduced pump noise, i.e., the sub-Poissonian laser. In the case of the laser with a conventional pump, the noise in the mth harmonic can be suppressed by m times as compared to the shot noise limit. For the sub-Poissonian laser, perfect noise reduction can be achieved in any harmonic mode. Cross correlations between the fundamental mode and the harmonic mode lead to the quantum noise interference effect, which manifests itself in the noise of the total photon flux from the laser. The system with two nonlinear crystals inside the laser cavity can serve as a source of two perfectly squeezed modes with divisible frequencies. The first crystal is driven by the external field of frequency 2ω. This field is downconverted in the crystal to the frequency ω, which is the frequency of lasing. In the second crystal the lasing field is again downconverted to the frequency ω/2. The lasing mode m and the subharmonic mode ω/2 from such a laser can be perfectly squeezed; that means complete quantumnoise reduction of these two modes if mixing with local oscillators of phase shifts π/2 is used.