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Physical Review A

Reduction in laser-intensity fluctuations by a feedback-controlled output mirror

Howard M. Wiseman, Gerard J Milburn

Published Sep 1, 1992• 19 citations
Publisher

Abstract

We present the theory of a laser in which the transmittivity of one output mirror is controlled by a current derived from a photodetector illuminated by the output light from that end of the cavity. That is, one output port of the laser is controlled by a feedback loop. We calculate the photon statistics inside the cavity. We also calculate the spectrum of intensity fluctuations for the light leaving the cavity through the output mirror not controlled by feedback. We show that intensity fluctuations inside the cavity may be reduced to 50% below the Poissonian limit while outside the cavity the reduction is at best 25% of the shot-noise limit. These optimum results, however, are not achieved under the same operating conditions.

DOI
10.1103/physreva.46.2853

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We present the theory of a laser in which the transmittivity of one output mirror is controlled by a current derived from a photodetector illuminated by the output light from that end of the cavity. That is, one output port of the laser is controlled by a feedback loop. We calculate the photon statistics inside the cavity. We also calculate the spectrum of intensity fluctuations for the light leaving the cavity through the output mirror not controlled by feedback. We show that intensity fluctuations inside the cavity may be reduced to 50% below the Poissonian limit while outside the cavity the reduction is at best 25% of the shot-noise limit. These optimum results, however, are not achieved under the same operating conditions.
We present an exact nonlinear derivation of the spectrum of fluctuations in the difference of output intensities for the signal and idler beams generated by intracavity two-photon gain, when the cavity decay rates are the same for the two modes, and taking into account the atomic fluctuations. For the field inside the cavity, we show that the variance in the difference of intensities may be up to 50% below the shot-noise value. We also consider the case of different decay rates, and show that the noise in the output-intensity difference vanishes at zero frequency, for single-ported cavities, and as long as the only source of field decay is the transmission through the mirror. Within this general approach, we show that for the two-photon laser there is a strong correlation between signal and idler output beams when the relay-level detuning is larger than the power broadening. We calculate, in lowest order, the correction to the noise spectrum of the difference of intensities due to the population of the relay level.
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 present theoretical results that demonstrate a new technique that can be used to improve the sensitivity of thermal noise measurements: intracavity intensity stabilization. It is demonstrated that electro-optic feedback can be used to reduce intracavity intensity fluctuations, and the consequent radiation pressure fluctuations, by a factor of 2 below the quantum-noise limit. We show that this reduction is achievable in the presence of large classic intensity fluctuations in the incident laser beam. The benefits of this scheme are a consequence of the sub-Poissonian intensity statistics of the field inside a feedback loop and the quantum nondemolition nature of radiation pressure noise as a readout system for the intracavity intensity fluctuations.
We detected a portion of the output from a semi-conductor diode laser and used the detected signal as a source of negative feedback to the laser drive current. At frequencies below the characteristic frequency of the feedback loop, the power spectral density of the detected photocurrent was as much as 15 dB below the shot noise limit. This reduction can be described by a semiclassical theory of the effects of feedback on an injected shot noise current. Physically, this corresponds to a process whereby the laser output is changed in response to changes in the noise current.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.