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Quantum Electronics

Use of the squeezed (sub-Poisson) state of light in small-signal detection with preamplification upon four-wave mixing

A. V. Kozlovskiĭ

Published Jan 31, 2007• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qe2007v037n01abeh013344

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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 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.
We study statistical properties of quantum superposition states (Schr\"odinger-cat states) amplified by phase-sensitive (squeezed) amplifiers. We show that the phase-sensitive amplifier with a properly chosen phase can preserve quantum coherences and nonclassical behavior of the Schr\"odinger-cat-state input even for a gain factor G larger than 2. In particular, we show that for an even coherent state (CS) phase-sensitive amplifiers can preserve squeezing for G>2 but simultaneously in the process of amplification the noise added by the amplifier leads to a rapid increase of fluctuations in the photon number. Because of the finite maximum degree of squeezing obtainable for the even CS the maximum gain factor Gm{\mathit{G}}_{\mathit{m}}Gm​ for which squeezing can still be observed in the output state is finite. The phase-sensitive amplifier with a properly chosen phase can also reduce fluctuations in the photon number of the initial even CS. Nevertheless, one cannot amplify the initial even CS with super-Poissonian photon statistics into the state with sub-Poissonian photon statistics.
We analyze statistical properties of multicomponent superpositions of coherent states of light amplified by quantum-mechanical amplifiers with reduced quantum fluctuations. We show that sub-Poissonian (i.e., amplitude-squeezed) amplifiers can transform any initial superposition of coherent states of light into a nonclassical state with a high degree of sub-Poissonian photon statistics. Simultaneously the shape of the photon-number distribution of the initial state of light is preserved but shifted toward higher photon numbers. On the other hand, we show that phase-sensitive (i.e., quadrature-squeezed) amplifiers may preserve the initial reduction of quadrature fluctuations (quadrature squeezing). We show that by using amplifiers with reduced quantum noise one can, in principle, control the influence of the noise transferred from the amplifier to the system.
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 possibility of generating light in a squeezed quantum state during saturated light amplification in a semiconductor amplifier is theoretically analyzed. Due to four-wave mixing process during amplification, weak components of the spontaneous emission of the medium with symmetric frequency shifts relative to the strong amplified wave acquire the quantum properties of two-mode squeezed light. The squeezing of quadrature components occurs in the range of frequency shifts of several GHz (∼\sim∼ the inverse relaxation time of the charge carrier density) and can reach 10 dB or more under optimal conditions. The formation of a two-mode squeezing phase facilitates the observation of the squeezing effect, in which a strong wave, playing the role of a local wave, exhibits quadrature noise suppression without additional homodyne detection.
Quantum noise fundamentally limits the performance of fiber-optic systems beyond the standard quantum limit (SQL), restricting long-distance quantum key distribution, quantum communication, and precision quantum sensing. To overcome these limitations, quantum-squeezed states enable quadrature-dependent noise suppression, yet their benefits rapidly degrade under fiber attenuation, necessitating low-noise amplification. Since conventional phase-insensitive amplifiers (PIAs) impose a minimum 3 dB noise figure (NF) penalty and disrupt quantum correlations, phase-sensitive amplification (PSA) becomes essential. In this work, we propose a PSA based on dual-pump frequency-degenerate four-wave mixing (FWM) to amplify weak coherent squeezed states. Here, the PSA is seeded by an information-carrying single-mode squeezed state, where the information is encoded in the displacement degree of freedom, rather than in the squeezing itself. By optimizing the relative phases among the squeezed state, pump fields, and weak signal, the scheme maintains proper squeezing alignment and preserves the encoded quantum correlations during propagation. Under low-loss conditions, it is shown that the effective NF reaches −7.787 dB, demonstrating that the scheme enables quantum-limited amplification suitable for long-haul transmission and offering a viable path toward scalable fiber-based quantum technologies.