Indirect measurement of three-photon correlation in nonclassical light sources

Byoung-moo Ann, Younghoon Song, Junki Kim, Daeho Yang, and Kyungwon An

Phys. Rev. A 93, 063816 – Published 9 June 2016

Abstract

We observe the three-photon correlation in nonclassical light sources by using an indirect measurement scheme based on the dead-time effect of photon-counting detectors. We first develop a general theory which enables us to extract the three-photon correlation from the two-photon correlation of an arbitrary light source measured with detectors with finite dead times. We then confirm the validity of our measurement scheme in experiments done with a cavity-QED microlaser operating with a large intracavity mean photon number exhibiting both sub- and super-Poissonian photon statistics. The experimental results are in good agreement with the theoretical expectation. Our measurement scheme provides an alternative approach for $N$ -photon correlation measurement employing $(N - 1)$ detectors and thus a reduced measurement time for a given signal-to-noise ratio, compared to the usual scheme requiring $N$ detectors.

Received 27 March 2016

DOI:https://doi.org/10.1103/PhysRevA.93.063816

Physics Subject Headings (PhySH)

Photon statistics Quantum measurements Quantum optics

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Byoung-moo Ann, Younghoon Song, Junki Kim, Daeho Yang, and Kyungwon An^*

Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea

^*kwan@phya.snu.ac.kr

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Issue

Vol. 93, Iss. 6 — June 2016

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Images

Figure 1
Illustration of photodetection events and dead-time effect in a two-detector configuration. Black circles represent the observed photodetection events, whereas gray circles indicate the missed events caused by detector dead time, whose duration is shown by blue arrows. The correlation between the observed photodetection events (black circles in the first and third rows) corresponds to $g^{' (2)} (t)$ . The second and fourth rows are copies of the first and third rows, respectively, without distinction between observed and missed photodetection events.
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Figure 2
(a) Illustration of the missed coincidence photodetection when only the stop detector has a dead time indicated by the blue arrow. For a photodetection scenario like a, b, and c, we miss a coincidence event. (b) A third row, a duplicate of the second row, has been added to show that the correlation among a, b, and c in (a) is the same as that in (b). Therefore, the correlation among these three events is given by $g^{' (3)} (t, 0; ϕ_{sp}, ϕ_{st}, ϕ_{sp}; τ_{sp}, 0, 0)$ .
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Figure 3
Photon statistics of the cavity-QED microlaser operating in the large-photon-number region (black dots), well away from the regions where quantum jumps occur, compared to the Poissonian distributions (red dots) that have the same mean photon number. Here, $N_{a}$ refers to the mean atom number. The photon statistics of the cavity-QED microlaser shows a near-symmetric single-peak distribution in both (a) super-Poissonian and (b–d) sub-Poissonian regions when the mean photon number is sufficiently large. Skewness values of the cavity-QED microlaser are similar to or less than the $γ_{poi}$ of the Poissonian distributions. The coupling constant and interaction time between the cavity mode and the impinging atoms assumed in the calculation were $2 π \times 190$ kHz and $0.1 μ s$ , respectively, while the cavity line width was assumed to be 138 kHz. These operating parameters are basically the same as in Ref. [22].
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Figure 4
(a) Relation between $g^{' (2)} (0)$ and dead time, observed by experiment and by prolonged dead times. Red squares indicate experimentally observed results in the cavity-QED microlaser. Observed photodetection fluxes at each detector were 2.6 and 3.3 Mcps, respectively. We simulated the prolonged dead-time results (black circles) by deleting photodetection events from the actual data. The resulting $g^{' (2)} (0)$ is almost linearly increasing up to 128 ns dead time. The solid blue line indicates the least-chi-square fit curve when the data points up to the 14th participate in the fitting process. (b) Values of $g^{(3)} (0, 0)$ (filled circles) and $g^{(2)} (0)$ (open circles) obtained by performing second-order polynomial fitting over the data points in (a) and by using Eq. (11). Here, the horizontal coordinate indicates the number of data points participating in the fitting process. (c) Ratio of $g^{(3)} (0, 0) - 1$ to $g^{(2)} (0) - 1$ based on the results in (b). The higher the number of data points used in the fitting, the more reliable the results will become. Eventually the ratio converges to the theoretical expectation (dashed red line). The mean photon number in the cavity was roughly 600.
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Figure 5
(a) Relation between $g^{' (2)} (0)$ and the dead time, observed in the super-Poissonian regime of the cavity-QED microlaser (black circles). (b) Values of $g^{(3)} (0, 0)$ (open circles) and $g^{(2)} (0)$ (filled circles) obtained by performing second-order polynomial fitting over the data points in (a) and by using Eq. (11). Fitting errors for individual black circles are less than $1 %$ of $g^{' (2)} (0) - 1$ . Here, the horizontal coordinate indicates the number of data points participating in the fitting process. The solid blue line in (a) is the second-order polynomial fitting curve when all the presented data points are involved in the fitting process. (c) Ratio of $g^{(3)} (0, 0) - 1$ to $g^{(2)} (0) - 1$ . The obtained values of $| 1 - g^{(3)} (0, 0) | / | 1 - g^{(2)} (0) |$ from the fitting with all data points is $3.00 \pm 0.03$ .
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