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Physical Review A

Photon noise reduction by passive optical bistable systems

Serge Reynaud, Claude Fabre, E. Giacobino, A. Heidmann

Published Aug 1, 1989• 72 citations
Publisher

Abstract

We show that when a coherent light beam is sent through a passive bistable device, the output beam may exhibit a substantial reduction of photon noise below the shot-noise level, within some frequency range of the noise spectrum. This effect is not limited to the case of a high-finesse cavity and is observable as soon as a bistability turning point is approached. Linear losses have the unexpected consequence of improving the noise-reduction factor at low frequencies.

DOI
10.1103/physreva.40.1440

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We show that when a coherent light beam is sent through a passive bistable device, the output beam may exhibit a substantial reduction of photon noise below the shot-noise level, within some frequency range of the noise spectrum. This effect is not limited to the case of a high-finesse cavity and is observable as soon as a bistability turning point is approached. Linear losses have the unexpected consequence of improving the noise-reduction factor at low frequencies.
Abstract The intensity noise spectrum is investigated quantum‐mechanically for incident coherent light passing through a resonator which is filled with a k‐photon‐absorber. For k⩽ 2 the noise of the outgoing light is reduced below the shot noise level the reduction being maximal for frequencies that are small in comparison to the cavity bandwidth. It turns out that the highest possible value of this low‐frequency noise reduction is obtained when the resonator losses due to transmission through the outcoupling mirror are 2k – 1 times as large as the k‐photon absorption losses. In this case the noise at zero frequency is reduced with respect to the shot noise level by a factor of k/(2k – 1).
We present two experiment that demonstrate intensity noise reduction in light below the standard quantum noise level. A first experiment establishes a reduction of 86 % in the intensity difference noise spectrum of twin beams generated by an Optical Parametric Oscillator. The second experiment exploits this intensity correlation between the twin beams and uses one beam to electro-optically control the other, generating a single beam whose intensity noise is reduced 24 % below the shot noise level. General theories are presented for both processes using a semi-classical input-output formalism. Control configurations are examined where the noise reduction is effected directly from one beam to the other (feedforward), or indirectly through the pump beam (feedback). We determine the maximum amount of noise reduction that may be obtained from active control and detail for these configurations the limitations imposed by constraints of causality and stability. Finally, we demonstrate the equivalence of the semi-classical model with a "corpuscular" photon model in the small fluctuation limit, which we substantiate using Monte-Carlo simulation.
We perform a systematic comparison between the spectrum of the intensity fluctuations and the spectrum of squeezing optimized with respect to the phase of the local oscillator, for the case of a one-photon single-mode optical bistability. In the bad-cavity limit the quantum noise reduction in the intensity fluctuations becomes comparable to the optimum level of squeezing. We consider also the case of a one-photon, single-mode laser with injected signal and show that under appropriate conditions the system can exhibit a meaningful level of squeezing.
Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom–field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (−1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting.