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Quantum Optics Journal of the European Optical Society Part B

Quantum noise reduction in lasers with nonlinear absorbers

Helmut Ritsch

Published Apr 1, 1990• 25 citations
Publisher

Abstract

The author uses an extension of the Scully-Lamb laser theory to show that, by the help of nonlinear absorbers in the cavity, laser light with nonclassical sub-Poissonian photon statistics can be generated. For an N-photon absorber the variance of the photon number distribution can be reduced by a factor of ( 1 / 2 +1/N) compared to the usual laser. Using a modified version of such nonlinear absorbers, like a nonlinear feedback or a Raman-type nonlinear transition, the noise can be reduced even further and approach the ideal limit, characterised by a Mandel Q parameter of Q approximately=-1. Furthermore he investigates how this noise reduction via nonlinearities can be combined with a regular pump mechanism and show that in certain configurations the effect of both methods of generating sub-Poissonian light can be combined.

DOI
10.1088/0954-8998/2/2/007

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Acta Physica Sinica•Jan 1, 1998•0 citations
The author uses an extension of the Scully-Lamb laser theory to show that, by the help of nonlinear absorbers in the cavity, laser light with nonclassical sub-Poissonian photon statistics can be generated. For an N-photon absorber the variance of the photon number distribution can be reduced by a factor of ( 1 / 2 +1/N) compared to the usual laser. Using a modified version of such nonlinear absorbers, like a nonlinear feedback or a Raman-type nonlinear transition, the noise can be reduced even further and approach the ideal limit, characterised by a Mandel Q parameter of Q approximately=-1. Furthermore he investigates how this noise reduction via nonlinearities can be combined with a regular pump mechanism and show that in certain configurations the effect of both methods of generating sub-Poissonian light can be combined.
Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.
We show that the injection of an external field in a laser helps to improve amplitude squeezing and sub-Poissonian light generation close to threshold, but spoils quantum noise reduction for very high pumping rates. A general nonlinear theory is developed for the resonant case (no detunings), without any assumption on the relative magnitudes of field and atomic decay constants, thus encompassing a large class of lasers. Several possible pumping schemes are accommodated, ranging from regular to Poissonian. We carry out a detailed stability analysis of the general equations of motion, relating it to the noise-reduction problem. Both the photon-number variance inside the cavity and the homodyne spectra of the output are discussed.
The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
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 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.
It is shown that the Λ quantum beat system, into which a new atomic coherence is introduced, can produce bright two-mode sub-Poissonian light. The Mandel Q parameter is calculated using Scully-Lamb theory. On one hand, when quantum noises of the relative amplitude and relative phase drop to vaccum noise levels, the average mode exhibits sub-Poissonian photon distribution; when quantum noises of the average amplitude and average phase drop to vaccum noise levels, the relative mode exhibits sub-Poissonian photon statistics; the optimum Mandel Q parameter is -0.5. On the other hand, in the above two cases, each of the correlated spontaneous emission laser modes exhibits sub-Poissonian photon statistics with optimum Mandel Q parameter of -0.25.