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Annual Meeting Optical Society of America

Direct detection of Gaussian state light

Jeffrey H. Shapiro, Ke-Xun Sun

Published Jan 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1992.fjj3

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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.
The detection of squeezed optical fields generated by intracavity nonlinear-optical interactions is described. The relationship between quantum-statistical properties of the cavity mode and those of the field at a detector placed outside the cavity discussed. The detected field is composed of a source field from the cavity plus a free external field. The free field couples weakly to the cavity so that it is correlated with the source field. The photocurrent spectrum in optical homodyne detection is calculated, and the spectrum of squeezing is defined. This spectrum can be calculated entirely in terms of intracavity fields without requiring knowledge of the correlations between source and free-field contributions in the cavity output. This follows from an explicitly normally ordered, time-ordered treatment of the photodetection problem. Contrasting earlier treatments of photodetection for squeezed fields, in a normally ordered approach, shot noise arises naturally from the self-correlation of photocurrent for pulses. The derived spectrum is converted into nonnormally ordered, non-time-ordered form to recover the results of these earlier treatments and their interpretation of shot noise in terms of local-oscillator quantum noise, signal and quantum noise, and detector-efficiency quantum noise.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.
We present an algorithmic approach to calculate the quantum-noise spectral density of photocurrents generated by optical fields with arbitrary discrete classical spectrum in coherent or squeezed states. The measurement scheme may include an arbitrary number of demodulations of the photocurrent. Thereby, our method is applicable to the general heterodyne detection scheme, which is implemented in many experiments. For some of these experiments, e.g., in laser-interferometric gravitational-wave detectors, a reliable prediction of the quantum noise of fields in coherent and squeezed states plays a decisive role in the design phase and detector characterization. Still, our investigation is limited in two ways. First, we consider only coherent and squeezed states of the field, and second, we demand that the photocurrent depends linearly on the field's vacuum amplitudes, which means that at least one of the classical components is comparatively strong.
We have discussed the possibilities of correlation spectroscopy (light beating spectroscopy) technique if squeezed light is used as a probe radiation for medium monitoring. The dispersion of the fluctuation of photocurrent spectrum measured in this method is expressed in terms of fourth order photocurrent correlation function. This correlation function is considered and evaluated in assumptions of photodetection theory developed by Glauber in first nonvanishing orders in interaction of probe light with the atoms of a photodetector. We show that fourth order correlation function is determined by all field TN-ordered amplitude correlation functions up to the fourth order. In case of heterodyne detection, when the light incident on photodetector surface is the mix of strong coherent modes of local oscillator wave and weak non-coherent (squeezed) modes, the observable (photocurrent spectrum) as well as its fluctuation (noise of photocurrent spectrum) is expressed in terms of spectrum-dependent Mandel parameter. We have discussed possible improvement of sensitivity limit for correlation spectroscopy in this case.
Gaussian quantum states hold special importance in the continuous variable regime. In quantum information science, the understanding and characterization of central resources such as entanglement may strongly rely on the knowledge of the Gaussian or non-Gaussian character of the quantum state. However, the quantum measurement associated with the spectral photocurrent of light modes consists of a mixture of quadrature observables. Within the framework of two recent papers [Phys. Rev. A 88, 052113 (2013) and Phys. Rev. Lett. 111, 200402 (2013)], we address here how the statistics of the spectral photocurrent relates to the character of the Wigner function describing those modes. We show that a Gaussian state can be misidentified as non-Gaussian and vice versa, a conclusion that forces the adoption of tacit a priori assumptions to perform quantum state reconstruction. We experimentally analyze the light beams generated by the optical parametric oscillator operating above threshold to show that the data strongly supports the generation of Gaussian states of the field, validating the use of necessary and sufficient criteria to characterize entanglement in this system.