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Physics World

Atoms used to detect non-classical light

Richard Claude Thompson

Published Dec 1, 1990• 0 citations
Publisher

Abstract

It is a well known fact that photons behave like particles in many ways. One consequence of this is that any measurements of the intensity of a light beam made by counting photons (e.g. with a photomultiplier tube) in fixed time intervals will show statistical fluctuations. In most cases these fluctuations are characterised by Poissonian statistics, which means that if the mean count is n, the fluctuations are of order n½.

DOI
10.1088/2058-7058/3/12/16

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It is a well known fact that photons behave like particles in many ways. One consequence of this is that any measurements of the intensity of a light beam made by counting photons (e.g. with a photomultiplier tube) in fixed time intervals will show statistical fluctuations. In most cases these fluctuations are characterised by Poissonian statistics, which means that if the mean count is n, the fluctuations are of order n½.
If a beam of light is coherent, then the photons constituting the beam arrive at random moments in time. Consequently, the photon counting statistics in a given time interval below the coherence time, should in theory follow a Poissonian distribution. When the measurement interval exceeds the coherence time, the distribution should broaden and become a super-Poissonian distribution. The aim of this study is to experimentally demonstrate the Poissonian nature of light, as well as quantifying the transition to a super-Poissonian distribution. In the experiment, a low-intensity laser beam was measured with single-photon detectors, able to capture individual photons. The arrival time of the photons was detected with an oscilloscope, and the data further analysed with our own Python code. The probability distribution of the arrival time of photons was constructed and fitted with a Poissonian distribution for different time intervals. The results showed a clear Poissonian distribution for all intervals from 0.2 μs up to 2000 μs. We did however, observe tendencies of randomness for the longest measured intervals. A Poissonian distribution is defined by the variance being equal to the mean, whilst for a super-Poissonian distribution the variance is higher. The biggest measured ratio between the variance and the mean in our experiment was 1.06 for interval time 2000 μs, which is too small to infer super-Poissonian. Due to limited data memory, our dataset was restricted in length and resolution. Therefore, longer intervals could not be studied without statistical uncertainty. To cross-check the result we also calculated the probability distribution for the arrival time itself. The result perfectly fitted an exponential distribution which was in accordance with the theory of coherent light. Hence, within the given measurement accuracy and statistical uncertainty, it is safe to conclude that the laser beam is coherent for all tested time intervals. However, this does not allow us to conclude that it is a single-mode laser.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.
ABSTRACT We demonstrate the use of a commercial mode-locked and Q-switched Nd:YAG laser in photon-noisereduction experiments. There are many frequency bands wherein the photodetection of such a laser isshot-noise limited. By appropriately filtering the photocurrent produced in direct detection of light froman optical parametric amplifier that is pumped with this laser, we have successfully generated twin-beam states of light. We demonstrate that such twin beams can be used to make measurements below the shot-noise limit. 2. INTRODUCTION The fundamental noise in optical measurements using lasers results from the fact that photons of light are detected at random. In a lossless system, one can ascribe the random detection of photons to the random emission of photons by the laser itself. It can be shown from the detailed laser theory' that anideal laser emits photons in a Poissonian fashion2 as shown in Fig. 1. This fact implies that there willalways be fluctuation in the number of photons that are counted in a given time interval. If = ii photonsare counted by the detector in an observation time T, then the variance in the photon count will be givenby the Poisson formula Var(N) = ii. This fluctuation in the detected photon number leads to the followingmaximum signal-to-noise ratio (SNR) that can be obtained using laser light: