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Europhysics Letters (EPL)

Feedback-measurement–induced anticorrelation between in-loop photocurrent fluctuation and amplifier dark noise

Jianping Yin, Weijian Gao, Yuzhu Wang, Yifu Zhu, Yiqiu Wang

Published Feb 1, 2000• 2 citations
Publisher

Abstract

Suppression of in-loop photocurrent fluctuation below the amplifier dark noise was observed in both a negative-feedback light-emitting diode (LED) and a laser diode (LD). We use a new semiclassical model to analyze the squeezed mechanism of the in-loop photocurrent noise mentioned above and find that there is a feedback-measurement–induced anticorrelation effect between the measured photocurrent fluctuation and the amplifier dark noise, which results in the suppression of the in-loop photocurrent fluctuation below the amplifier dark noise. Our theoretical analysis gives the correlation coefficient between the photocurrent fluctuation and amplifier noise, and also yields the squeezed spectrum of the in-loop intensity fluctuation according to our experimental results.

DOI
10.1209/epl/i2000-00150-y

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Suppression of in-loop photocurrent fluctuation below the amplifier dark noise was observed in both a negative-feedback light-emitting diode (LED) and a laser diode (LD). We use a new semiclassical model to analyze the squeezed mechanism of the in-loop photocurrent noise mentioned above and find that there is a feedback-measurement–induced anticorrelation effect between the measured photocurrent fluctuation and the amplifier dark noise, which results in the suppression of the in-loop photocurrent fluctuation below the amplifier dark noise. Our theoretical analysis gives the correlation coefficient between the photocurrent fluctuation and amplifier noise, and also yields the squeezed spectrum of the in-loop intensity fluctuation according to our experimental results.
Suppression of the closed-loop photocurrent fluctuation below the amplifier dark noise was observed in both a negative-feedback light-emitting diode and a laser diode. We apply the concept of an anticorrelation light state proposed by Masalov et al to analyze the anticorrelation effect between the measured photocurrent fluctuation and the amplifier dark noise, which successfully explains our experimental observations. Our theoretical analysis also yields the squeezed spectrum of the light intensity fluctuation in the loop and the correlation coefficient between the photocurrent and the amplifier noise.
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.
A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^)2{)}^{2})2〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.
We examine the quantum-limited behavior of an electro-optical intensity feedback loop and present a simple theory and experimental data showing excellent agreement. We show that, although the light incident upon the in-loop detector may be sub-Poissonian, this light has unique properties different from those of a freely propagating beam of intensity squeezed light. We support this by presenting the results of homodyne measurements of the phase noise of light extracted from the loop. The utility of the in-loop field is discussed, and it is shown that in all cases in which linear optical components are used, no advantage in signal-to-noise ratio is gained by taking measurements by using this light rather than a coherent source. We also discuss effects seen in the extracted or out-of-loop light. We demonstrate the existence of, and derive an expression for, an optimum gain for suppressing low-level classical noise. Conversely, in the high-gain limit, we demonstrate that the extra noise seen in the out-of-loop photocurrent that is due to the feedback process is expressible purely in terms of the mean photocurrents involved. Lastly, we introduce the novel concept of using an intensity feedback loop in conjunction with a squeezed source and show that the feedback loop has the capability of electronically transferring squeezing from one light beam to another.
We have produced amplitude-squeezed light whose noise is reduced by ~10 dB below the quantum noise limit in four different feedback systems. In our experimental method we have directly compared the noise power spectrum of the laser diode with the quantum noise limit in the low-frequency region, where the classical noise is stronger than the quantum noise. In addition to the well-known methods for extracting the out-loop beams from the feedback system by use of a 50:50 beam splitter, a polarizing beam splitter, or the leakage light from the rear side of a laser diode, we also have tried to use the spatial coherence of the laser light. We also have examined the vacuum fluctuations that prohibited the out-loop beam from being amplitude squeezed. In all these systems we have verified that the noise power spectrum for the in-loop beam is reduced below the quantum noise limit but not that for the out-loop beam; the difference arises mainly because vacuum fluctuations enter each system differently.
Summary form only given.Laser diodes with pump noise suppression are reliable sources for the generation of amplitude-squeezed light. Recently, it was shown that this amplitude squeezing is not always a single mode effect but can result from a cancellation among anticorrelated fluctuations between the main mode and competing side modes. To obtain more details on this correlation effect, we performed spectrally resolved intensity noise measurements with a pump noise suppressed SDL 5410-C (810 nm) diode laser in different configurations: free-running, injection-locked, and with an external Littrow grating feedback.