As early as in 1940 landmark experiments by Hecht and colleagues showed that dark-adapted human subjects are capable of reporting light signals as low as a few photons (~5-7). However, as in classical light sources the distribution of the photon number follows Poissonian statistics and due to use of non-ideal psychophysical procedures, until now it remained unclear whether the visual system including the processing performed by the retina and brain is able to detect a single photon.
Representation of the experimental setup with the subject seated in the lightproof and soundproof box.
To answer this question we have built a quantum light source based on the process of spontaneous parametric down-conversion (SPDC). In SPDC which is often used in quantum optics and quantum information correlated pairs of photons (called signal and idler) are produced from a higher energetic pump photon in a non-linear crystal under energy and momentum conservation. We used a customized EMCCD to detect one of them, while the other was sent towards the observer’s eye.
Schematic of the setup for generating single photons via spontaneous parametric down-conversion (SPDC). Light stimuli are triggered (T) by subjects and coupled into a single-mode fiber entering the dark chamber. The light is directed and focused onto the pupil (Maxwellian view) at an angle of 23ᵒ temporal to a highly attenuated red fixation light presented at the fovea. ND, neutral density filter, L, lens, SPAD, single-photon avalanche detector. F, bandpass and spatial filter, HWP, half-wave-plate, PBS, polarizing beam-splitter, BBO, beta barium borate crystal, EMCCD, electron-multiplying charge-coupled device. A flip mirror (FM) allowed for the switching of the detection mechanism from the EMCCD to a SPAD.
Such a source can be tuned to feature a small ratio of multiple-to-single photon emissions. This allowed us to create an effective single-photon light source with a sub-Poissonian photon number distribution by identifying two and multiple photon events and rejecting these through post-selection. As a result, in the trials used for analysis, subjects’ responses were due to true single photon events only.
Probability of providing the correct response in 2AFC trials for all (brown) and high confidence responses (green). The horizontal dashed line indicates the upper theoretical limit of performance of an ideal detector operating at a physiological parameter of detection efficiency in the absence of additional noise.
We have performed over 30.000 trials using a rated two-alternative forced-choice (2-AFC) psychophysics procedure that improved both the sensitivity and the cross-trial reproducibility. We found that averaged across subjects and indicated confidence ratings by the subjects the probability of correct response was 0.516 ± 0.010 (p = 0.0545). As we have used a 2-AFC procedure this must be compared to the 0.5 baseline, which is the probability of random guessing. These results suggest that subjects could indeed detect a single photon with a probability above chance. In our 2-AFC we also asked the subjects to rate the confidence in all their responses. Analyzing the probability of correct response only for cases when subjects indicated a high-confidence answer yields even a higher probability of correct response and a more significant evidence for detection of single photons (0.60 ± 0.03 (p = 0.0010)). This result demonstrates that subjects can indeed detect a single photon impinging on their eye.
Probability of correct response as a function of the time to the preceding single-photon event, data averaged across subjects and ratings. 0.5 is the baseline and corresponds to random guessing. Solid line is a fit to our mathematical model.
Further we analyzed how the probability of correct response in single-photon events depends on the time to the previously detected photon. Surprisingly, we found a strong dependence on the temporal separation of the two events peaking at ~3.5 s, with a decay time on the order of seconds. We found that the probability of correctly reporting a single photon is highly enhanced by the presence of an earlier photon within ~5 s time interval. Given that this represents more than an order of magnitude of a disparity with the known integration time of the visual system suggests that a new physiological mechanism at extreme low light levels may be responsible for this phenomenon.
Finally, we developed a mathematical model based on Signal Detection Theory (SDT) that puts all our experimental observations, including the probability of single photon detection, the distribution of ratings and the above single-photon induced priming effect, within a single framework. We showed that our model can account for all our data and correctly predicted the probability of correct response at each rating.
Our results show that evolutionary pressure that have led to the optimization of a protein to the absolute physical limit could also be effectively exploited by an entire system that has co-evolved around it. In the future the use of light sources with sub-Poissonian photon number distributions might allow for a more direct access to the internal visual system’s noise and provide new avenues for probing yet undiscovered retinal pathways. Also, given the inherent quantum nature of light and the fact that single photons can be prepared in superposition states of space, time, energy and other degrees of freedom, our study opens up new, speculative possibilities to investigate to what extent such states may also bear unique physiological signatures as well as to test theoretical proposals that use human observers for experimental tests of quantum non-locality.
Relevant Publication:
Jonathan N. Tinsley, Maxim I. Molodtsov, Robert Prevedel, David Wartmann, Jofre Espigulé-Pons, Mattias Lauwers, and Alipasha Vaziri
Direct Detection of a Single Photon by Humans
Nature Communications 7, 12172 (2016).
