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arXiv:1602.02335 · The Astrophysical Journal

Photon Flux and Bunching Noise from Measurement of the Shot Noise Variance

Richard Lieu, Michael Stefszky, Chun-Hui Shi

Published Jul 20, 2018• 3 citations
arXivHTMLPDF

Abstract

Abstract We report the experimental observation of photon-bunching noise through shot noise measurements made on a pseudo-thermal state of light using balanced detection. A full theory describing the measurement is developed, and, in agreement with the theory, it is found that the shot noise variance in the balanced signal reproduces the time series of the flux of the primary incoherent beam. Moreover, when the average power of the pseudo-thermal light is varied, the balanced detection is seen to track this change. A comparison of direct detection and balanced detection of the thermal field shows that the balanced detection performs at least as well as the direct detection and under some conditions appears to outperform the direct detection. There is not necessarily a contradiction with quantum field theory, which predicts that at best the performance of the balanced detection should be equal to the direct detection because the direct detection process is subject to nonlinearity that has not been excluded by measurements (even though any tests we performed suggest that such effects are small). This is the first time that the bunching noise effect of high occupation number chaotic light via the shot noise of the field has successfully been measured, to the point of using it to infer the flux of the field. The findings may be relevant to radio receiver design, specifically from the viewpoint of sensitivity improvement.

DOI
10.3847/1538-4357/aac330

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arXiv:1205.3229•Classical and Quantum Gravity•Jun 25, 2012•127 citations
Abstract We report the experimental observation of photon-bunching noise through shot noise measurements made on a pseudo-thermal state of light using balanced detection. A full theory describing the measurement is developed, and, in agreement with the theory, it is found that the shot noise variance in the balanced signal reproduces the time series of the flux of the primary incoherent beam. Moreover, when the average power of the pseudo-thermal light is varied, the balanced detection is seen to track this change. A comparison of direct detection and balanced detection of the thermal field shows that the balanced detection performs at least as well as the direct detection and under some conditions appears to outperform the direct detection. There is not necessarily a contradiction with quantum field theory, which predicts that at best the performance of the balanced detection should be equal to the direct detection because the direct detection process is subject to nonlinearity that has not been excluded by measurements (even though any tests we performed suggest that such effects are small). This is the first time that the bunching noise effect of high occupation number chaotic light via the shot noise of the field has successfully been measured, to the point of using it to infer the flux of the field. The findings may be relevant to radio receiver design, specifically from the viewpoint of sensitivity improvement.
A hierarchy of statistics of increasing sophistication and accuracy is proposed, to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level, with the help of high precision computers, to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this method of flux measurement is limited by the timing resolution of the detector, the precision of the computer in manipulating numbers, and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is sensitivity enhancement of radio astronomical observations.
Lieu et al. (2015) have recently claimed that it is possible to substantially improve the sensitivity of radio astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival rate. Lieu et al. (2015) provide a detailed quantum-mechanical calculation of a proposed measurement scheme that uses two detectors and conclude that this scheme avoids the sensitivity degradation that is associated with photon bunching. If correct, this result could have a profound impact on radio astronomy. Here I present a detailed analysis of the sensitivity attainable using shot-noise measurement schemes that use either one or two detectors, and demonstrate that neither scheme can avoid the photon bunching penalty. I perform both semiclassical and fully quantum calculations of the sensitivity, obtaining consistent results, and provide a formal proof of the equivalence of these two approaches. These direct calculations are furthermore shown to be consistent with an indirect argument based on a correlation method that establishes an independent limit to the sensitivity of shot-noise measurement schemes. Collectively, these results conclusively demonstrate that the photon bunching sensitivity penalty applies to shot noise measurement schemes just as it does to ordinary photon counting, in contradiction to the fundamental claim made by Lieu et al. (2015). The source of this contradiction is traced to a logical fallacy in their argument.
An analysis is presented which shows that photon-bunching effects in a spatially coherent noise field can be enhanced by the superposition of a monochromatic coherent ``signal'' and/or by shaping the spectrum of the incident noise. For a Lorentz spectral shape, the addition of ``signal'' to noise is shown to increase bunching effects by a factor no greater than 4. By changing the noise spectrum from a Lorentz to a rectangular shape, bunching effects are shown to increase by a factor of 2 despite the fact that total incident noise power decreases. In all cases, the ratio of bunching noise to shot noise is proportional to the average number of detected noise photons per cycle of noise bandwidth. For the specific problem analyzed, the maximum value of the ratio of bunching noise to shot noise is determined. In the absence of ``signal,'' the results are found to agree with the exact distribution of Bèdard.
The shot noise which occurs in photoelectric detection is calculated utilizing fully quantum mechanical procedures. The results which are obtained in this paper include the effects of photon bunching and they differ considerably from classical results which are obtained on the assumption of Poisson statistics. In some cases the Poisson-based classical results lead to shot-noise powers that are in error by as much as an order of magnitude. The results reveal the existence of a relative minimum in the plot of shot noise vs input signal to noise ratio. This suggests the possibility of optimum input signal to noise ratios within certain restricted ranges of the input signal to noise ratio. A plot of the shot noise which is in excess of that predicted by Poisson-based statistics vs input signal to noise ratio reveals a maximum at an input signal to noise ratio of approximately 1.5. This suggests that the enhancement of the Hanbury-Brown and Twiss effect that is obtained when coherent radiation is superposed upon chaotic radiation will be maximized at a coherent-to-chaotic ratio of approximately 1.5.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.