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Quantum Electronics

Photodetection of a weak light signal in various quantum states by using an optical amplifier

A. V. Kozlovskiĭ

Published Mar 31, 2006• 3 citations
Publisher

Abstract

The photodetection of weak light signals preliminary amplified in optical light amplifiers is analysed quantum-mechanically. A linear amplifier and a four-wave-mixing amplifier are considered. The parameters of the signal-to-noise ratio are calculated and analysed for light sources with various quantum-statistical properties. The signal-to-noise ratio for the detector photocurrent is studied as a function of the quantum-statistical properties of the signal and idler waves involved in amplification by using the four-wave-mixing scheme. The four-wave-mixing scheme with the idler wave in the coherent or Fock (squeezed, sub-Poisson) state has a higher signal-to-noise ratio compared to the linear preamplification regime.

DOI
10.1070/qe2006v036n03abeh013135

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The photodetection of weak light signals preliminary amplified in optical light amplifiers is analysed quantum-mechanically. A linear amplifier and a four-wave-mixing amplifier are considered. The parameters of the signal-to-noise ratio are calculated and analysed for light sources with various quantum-statistical properties. The signal-to-noise ratio for the detector photocurrent is studied as a function of the quantum-statistical properties of the signal and idler waves involved in amplification by using the four-wave-mixing scheme. The four-wave-mixing scheme with the idler wave in the coherent or Fock (squeezed, sub-Poisson) state has a higher signal-to-noise ratio compared to the linear preamplification regime.
Detection of weak and extremely weak light signals amplified by linear and four-wave mixing laser amplifiers is analyzed. Photoelectron distributions are found for different input photon statistics over a wide range of gain. Signal-to-noise ratios are calculated and analyzed for preamplification schemes using linear and four-wave mixing amplifiers. Calculations show that the high signal-to-noise ratio (much higher than unity), ensuring reliable detection of weak input signals, can be attained only with a four-wave mixing preamplification scheme. Qualitative dependence of the signal-to-noise ratio on the quantum statistical properties of both signal and idler waves is demonstrated.
The scheme of an active interferometer for amplification of small optical signals for their subsequent photodetection is proposed. The scheme provides a considerable amplification of signals by preserving their quantum-statistical properties (ideal amplification) and also can improve these properties under certain conditions. The two-mode squeezed state of light produced upon four-wave mixing, which is used for signal amplification, can be transformed to the non-classical state of the output field squeezed in the number of photons. The scheme is phase-sensitive upon amplification of the input coherent signal. It is shown that in the case of the incoherent input signal with the average number of photons ⟨ n s ⟩∼1, the amplification process introduces no additional quantum noise at signal amplification as large as is wished. A scheme is also proposed for the cascade small-signal amplification (⟨ n s ⟩∼1) in the coherent state producing the amplified signal in the squeezed sub-Poisson state, which can be used for the high-resolution detection of weak and ultraweak optical signals.
The principal problem of light amplifiers is to find a means to amplify a coherent amplitude without decreasing the SNR. Consider a signal with amplitude squeezed quantum fluctuations, that is, less noise in the amplitude quadrature than the phase quadrature. The objective is to find a phase sensitive amplifier, which, while amplifying the coherent amplitude, adds quantum noise preferentially to the phase quadrature. We take as a concrete model for the amplifier an intracavity parametric amplifier. We go beyond the usual linear analysis and include the nonlinear regime where pump depletion is important. We find that in the linear region the quantum noise added by the amplification process may be reduced by squeezing the idler mode, while in the nonlinear regime the quantum fluctuations from the pump become more important. These results are of direct application to practical light amplifiers.
The quantum theory of photodetection is applied to the direct detection of multi-mode Gaussian-state light, with particular attention to the mean photocurrent and the photocurrent noise spectrum. Gaussian-state light comprises squeezed-state light plus additional classical Gaussian noise. By extending the familiar Gaussian moment-factoring formula of classical statistics to the antinormally ordered characteristic function of Gaussian-state light, the first and second moment photocurrent statistics for such illumination are shown to be completely characterized by knowledge of the mean function, the phase-sensitive correlation function, and the normally ordered correlation of the input light. The theory delineates the condition under which the strong-mean-field approximation is applicable to direct detection of such beams, i.e., it tells us when a direct detector yields the same noise spectrum as that of an in-phase homodyne detector. Numerical results are presented for the noise spectra of a squeezed amplifier, i.e., an optical parametric amplifier with signal-injection-induced gain saturation.
Quantum fluctuations in optical amplification are investigated with a nondegenerate optical parametric amplifier whose internal idler mode is coupled to a squeezed vacuum. Reductions of the inherent quantum noise of the amplifier are observed with a minimum noise level 0.7 dB below the usual noise level of the amplifier with its internal idler mode in a vacuum state. With a small coherent field as the signal input, the amplified output exhibits an improvement in signal-to-noise ratio of 0.5 dB for the case of a squeezed-vacuum as compared to a vacuum state for the amplifier's internal mode.
The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.