Simultaneous, Full Characterization of a Single-Photon State

As single-photon sources become more mature and are used more often in quantum information, communications, and measurement applications, their characterization becomes more important. Single-photon-like light is often characterized by its brightness, as well as two quantum properties: the suppression of multiphoton content and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we show that using two-photon ($n=2$) number-resolving detectors, one can completely characterize single-photon-like states in a single measurement, where previously two or more measurements were necessary. We simultaneously determine the brightness, the suppression of multiphoton states, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. We find $n\ge 3$ number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states and is particularly more efficient for statistical mixtures of photon states. Thus, using this $n=2$, number-resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.

Popular Summary

Light can behave as if it is made from discrete particles known as photons. Most light sources are made from vast numbers of photons. But some emerging technologies based on quantum information science and quantum optics require single photons. Moreover, these single photons should be bright, indistinguishable, and free of multiphoton content. Typically, two (or more) measurements are needed to verify these requirements. We demonstrate a new way to fully characterize single-photon states in a single measurement for the first time. The technique is based on the concept of photon-number-resolving detectors.

Our demonstration uses the bright single-photon light from a semiconductor quantum dot. Notably, we replace the typical single-photon detectors and instead emulate photon-number-resolving detectors that are capable of differentiating between one and two photons. Rarely in quantum optics does such a substitution fundamentally change the measurement by not only providing better accuracy but also enabling a simultaneous measurement of two different physical quantities.

We have shown that number-resolving detectors can advance the characterization of light and should also improve a diverse set of quantum optics experiments.

Figure 1

Second-order characterization of light with single, spatial-mode inputs. (a) The photon-state statistics can be measured to $n$th order using a single, appropriately fast, $n$-photon number-resolving detector. Such a detector does not exist. (b) Instead of using an $n=2$ number-resolving detector, correlation measurements to second order can be made with two single-photon (not number-resolving) detectors and a beam splitter. (c) An unbalanced interferometer can be used to interfere replicas of an input state to measure the indistinguishability from second-order correlations. If single-photon detectors are used, an additional measurement, for instance, like the one in (b), must be made for normalization.

Figure 2

Comparison of the efficiency of using number-resolving detectors vs single-photon detectors with a Fisher information analysis. Values higher than 1 mean that $n=2$ number-resolving detectors are more efficient. (a) Comparison of a single measurement made with $n=2$ number-resolving detectors with the traditional (trad) two-measurement scheme, using single-photon detectors ($\mathrm{Tr}{\mathcal{F}}_{\mathrm{trad}}^{-1}/\mathrm{Tr}{\mathcal{F}}_{\mathrm{n}=2}^{-1}$). It can be seen that for almost all combinations of $g_{\mathrm{HBT}}^{(2)}(0)$ and $C$, it is more efficient to use number-resolving detectors. Only for very low values of $g_{\mathrm{HBT}}^{(2)}(0)$ is the traditional method more efficient. (b) Comparison of a two-measurement scheme (composite) with $n=2$ number-resolving detectors and the traditional two-measurement scheme with single-photon detectors ($\mathrm{Tr}{\mathcal{F}}_{\mathrm{trad}}^{-1}/\mathrm{Tr}{\mathcal{F}}_{\text{composite}n=2}^{-1}$). Here, the measurement using number-resolving detectors is always more efficient.

Figure 3

(a) Measurement layout used to characterize the quantum light source. FBS is for fiber beam splitter, PC is for polarization control, HWP is the half-wave plate, BS is for beam splitter, and the detectors are A–D. The measurement arrangement consists of an unbalanced, unstabilized interferometer beginning at FBS, containing a delay line (delay) and ending at BS2. One portion is fiber (black lines), and the other portion is free space (red lines). The four detectors simulate two, two-photon, number-resolving detectors. The HWP is used in a comparison experiment (see text). (b) Equivalent optical circuit without the initial FBS and the associated unitary matrix $U$, where $r_j$ and $t_j$ are reflection and transmission coefficients for the three beam splitters.

Figure 4

Second-order characterization of quantum light—here, from a single QD source. Normalized conditional detector counts are plotted for the four detectors at $j=0$. Correlated detections on $AD,AC,BC$, and $BD$ (blue) represent cross-correlations. Correlations of the type $AB$ and $CD$ (red) are autocorrelations.

Figure 5

A comparison of the $g_{\mathrm{HBT}}^{(2)}$ measurements, uncorrected for spectral jitter. The $g_{\mathrm{HBT}}^{(2)}$ data for the number-resolving detector measurement (blue) are extracted from the data in Fig. 4 and compare well to the traditional HBT measurement (green). The two measurements are off-set laterally for clarity. The dip at $\pm 4$ pulses is due to the interferometer (and single-photon character of the source) (see text and Ref. [32] for details). Using Eq. (1), $g_{\mathrm{HBT}}^{(2)}[0]$ can be found.