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Journal of Experimental and Theoretical Physics

Possibility of suppressing quantum light fluctuations when excess photon fluctuations occur inside a cavity

Yu. M. Golubev, I. V. Sokolov, Mikhail I. Kolobov

Published May 1, 1997• 2 citations
Publisher

Abstract

Using the optical excitation of a high-Q cavity as an example, it is shown that when light is observed at the output of this cavity, effective suppression of the photocurrent shot noise below the quantum limit is in general independent of the parameters of the stationary state of the field oscillator (in particular, it is independent of the rms photon fluctuations) inside the cavity and can occur not only at any allowed negative value but even at a positive value of the Mandel parameter. It was assumed in solving the problem that the cavity is optically excited by superimposing the radiation of a sub-Poisson laser and a laser with excess photon noise. A formal solution was obtained in terms of the kinetic equation for the density matrix of the actual fields (inside the laser cavities and the empty cavity), which is derived here on the basis of the Heisenberg-Langevin quantum equations, taking into account directed propagation of the field from the laser cavities inside the empty cavity. The resulting kinetic equation can also be used to solve other physical problems, since it is applicable to optical systems that contain, in principle, an arbitrary number of coupled cavities and interference mixers.

DOI
10.1134/1.558224

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Using the optical excitation of a high-Q cavity as an example, it is shown that when light is observed at the output of this cavity, effective suppression of the photocurrent shot noise below the quantum limit is in general independent of the parameters of the stationary state of the field oscillator (in particular, it is independent of the rms photon fluctuations) inside the cavity and can occur not only at any allowed negative value but even at a positive value of the Mandel parameter. It was assumed in solving the problem that the cavity is optically excited by superimposing the radiation of a sub-Poisson laser and a laser with excess photon noise. A formal solution was obtained in terms of the kinetic equation for the density matrix of the actual fields (inside the laser cavities and the empty cavity), which is derived here on the basis of the Heisenberg-Langevin quantum equations, taking into account directed propagation of the field from the laser cavities inside the empty cavity. The resulting kinetic equation can also be used to solve other physical problems, since it is applicable to optical systems that contain, in principle, an arbitrary number of coupled cavities and interference mixers.
Photocurrent shot-noise suppression is observed in closed optoelectronic loop below the limit (1 − η) of standard shot-noise level (SNL) imposed by conventional theory of photodetector with quantum efficiency η. Experimental results on photocurrent noise are presented for different values of feedback strength and quantum efficiency η of in-loop photodiode. It is shown that at fixed feedback strength the suppression factor does not depend on η. Minimum noise spectral density is observed below the SNL by a factor 17·8 (− 12·5 dB). Such large suppression cannot be explained in terms of an ordinary sub-Poissonian light state in the loop. We suggest the concept of an anticorrelation light state, where the light in the loop is described as a non-stationary state with Poissonian quantum fluctuations, and superimposed anticorrelated classical fluctuations. While the degree of noise reduction in the photocurrent can be arbitrary large, the degree of anticorrelation between the classical and quantum fluctuations in the light beam remains limited by the quantum efficiency of the feedback photodiode. Calculations based on this concept are in a good agreement with experimental data on super-shot-noise power, obtained for the beam extracted from the loop by a beam splitter.
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.
The general expression of the output-light Mandel parameter(xi) out is obtained in case of purely absorptive bistability, for arbitrary value of (xi) in of incident light. Calculations are based on stochastic rate equations. No adiabatic elimination of atomic variables is made; the coherent nature of 'incoming' of incident photon is into a cavity is correctly taken into account. On condition of bistability, although the strongly sub-Poisson input-photon statistics generally reduces the output noise as compared to the case of coherent input, the inequality (xi) out > 0 still near the switching points.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
We consider here the problem of quantum noise in light produced by an optical parametric oscillator operating below threshold inside a singlesided cavity. By employing the correct boundary conditions on quantum fields at the output mirror, a procedure that is valid for arbitrary mirror transmission, we derive exact expressions for quantum noise reduction for arbitrary pump phase and mirror out-coupling. We find that for a given out-coupling, squeezing of quantum noise in the intracavity field increases to a final value of 50%, as the pump intensity is increased and the oscillation threshold is approached. The output field on the other hand exhibits perfect squeezing of noise in one quadrature of its central Fourier component at threshold regardless of the mirror out-coupling. The present approach, which is based on boundary conditions, is quite general and applicable to any matter-field interaction problem inside a cavity. In fact, we have previously employed this approach in the calculation of the intrinsic linewidth of a laser with arbitrary out-coupling.1
We demonstrate that the intensity fluctuations of a laser with a Raman gain medium, described by a large number of independent 3-level atoms, can drop well below the shot noise level. In the limit of a good cavity, where one can adiabatically eliminate the atoms, we find an optimum Mandel Q parameter of Q ≈ −1/2 over a large range of parameters, when the laser is operated well above threshold. This leads to a strong suppression of the low-frequency quantum fluctuations in the laser output. In addition we find that due to suppression of spontaneous emission into the lasing mode, the spectral linewidth of the emitted light can be reduced below the Schawlow-Townes limit by more than one order of magnitude.