1. INTRODUCTION

Advances in photonic quantum science [1–5] occur with increased complexity of the available sources of non-classical light. The main technologies to date for producing single-, and multi-photon states are based on either frequency-conversion in nonlinear media [6–8], or atomic transitions of quantum emitters [9–11]. The former produces heralded single- and entangled-photon statistics or squeezed states of light, and the latter primarily results in deterministic single-photon emission at high efficiencies and rates. The most advanced multi-photon experiments thus far involved the interference of up to 14 particles using single-photon sources [12,13] or the detection of hundreds of photons using squeezed light sources [14,15].

Temporal-to-spatial demultiplexing has played a key role in enabling these levels of complexity. This technique allowed the preparation of the multi-photon sources in the cases of space-encoded interference [13] and enabled the measurement of up to 16 consecutive temporal modes from time-bin interferometers [15]. This protocol deals with routing subsequent events, or time bins, from one spatial mode toward different locations, and it has been widely used to allow multi-photon experiments using quantum emitters [13,16–20]. Indeed, creating multiple indistinguishable photons from a single demultiplexed source is still technically more viable than fabricating many quantum emitters that produce indistinguishable photons, where the state-of-the-art remains in the demonstration of photon indistinguishability from two remote sources [21].

The standard approach for building a temporal-to-spatial demultiplexer starts by using an active element, e.g., an electro-optic modulator (EOM), for producing orthogonal polarizations in two subsequent photons, later following different trajectories after traversing a polarization selective element, such as a polarizing beam splitter (PBS). By repeating this process for each new output, any number $N$ of consecutive time bins can be demultiplexed; however, it is at the increasing cost of using $N{-}1$ active elements. At the outputs of the demultiplexer, photons originally separated in units of a temporal distance $\tau$ are appropriately delayed such that they all propagate simultaneously and can interfere. Most implementations to date have employed this method [16–19], with the current record of using $19$ high-voltage bulk EOMs for obtaining 20 photons [13], each occupying one spatial mode. Evidently, this approach becomes resource expensive and costly.

Here, we demonstrate a temporal-to-spatial demultiplexer that uses only one active element to produce, in principle, an arbitrary number of outputs. We combine our device with a highly efficient single-photon source from a quantum dot, and demonstrate the generation of an eight-photon state, where each indistinguishable photon is propagating in a separate spatial mode. One interesting feature of our approach is that the demultiplexed time bins can be as close as a few nanoseconds apart, which is beneficial for maintaining high indistinguishability from quantum emitters [22,23]. Our implementation underlines the feasibility of our scheme that can enable near future practical multi-photon sources at larger scale.

2. SOURCE

A sample containing semiconductor quantum dots (QDs) in micropillar cavities is placed inside a cryostat at $\sim$4K, see Fig. 1(a). A QD is resonantly driven with laser pulses of 80-MHz repetition rate, and it is spectrally tailored to match the QD cavity wavelength of 922.2 nm, and linewidth at FWHM of $120$ pm. We use a $97{:}3$ beam splitter (BS) to guide a fraction of the laser pump toward the sample while maintaining high transmission for the emitted single photons. The pump pulse is then focused on the sample by an aspheric lens placed inside the cryostat. We use a cross-polarized configuration for optical excitation and collection. In the excitation path, we control the power of the laser light and initialize its polarization with a quarter- and a half-wave plate, $Q_1,H_1$, respectively, to one of the linear-polarization cavity modes. In the collection path, we place another set of wave plates, $Q_2,H_2$, and a Glan–Taylor (GT) polarizer to suppress the laser by more than seven orders-of-magnitude. Thus, only single photons are coupled into the fiber of the collection setup.

 

Fig. 1. Single-photon source. (a) Schematic figure of the excitation and collection setup with crossed-polarized configuration to separate pump light from single-photon emission. (b) Rabi oscillations: detected single-photon count rate versus pump pulse area. (c) Second-order auto-correlation measurement at $\pi$-pulse excitation. The value at zero time delay is $g^{(2)}(0){=}{1.57(2)}{{\% }}$. (d) Hong–Ou–Mandel interference at $\pi$-pulse, resulting in photon indistinguishability $\mathcal {I}{=}{95.35(3)}{{\% }}$. Both values in panels (c) and (d) are obtained by integrating peak areas in a 3-ns window. Measurement uncertainties are estimated following Poissonian counting statistics.

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We use this setup to characterize our source. Figure 1(b) displays Rabi oscillations as a signature of the coherent driving of the system. At $\pi$-pulse excitation, we measure a maximum single-photon count rate of $17.1$ MHz that corresponds to an end-to-end source efficiency of $\eta _{\mathrm {s}} = 21.4{{\% }}$ recorded with a superconducting nanowire single-photon detector of $85{{\% }}$ system efficiency. We now characterize the single-photon purity by measuring the second-order auto-correlation function $g^{(2)}(\Delta t)$ using a standard Hanbury Brown and Twiss setup. At $\pi$-pulse excitation, we retrieve a value at zero time delay of $g^{(2)}(0){=}{1.57(2)}{{\% }}$, as shown in Fig. 1(c). At these same conditions, a two-photon Hong–Ou–Mandel (HOM) interference experiment [24] reveals a photon indistinguishability [25] $\mathcal {I}{=}95.35(3){{\% }}$ [see Fig. 1(d)]. Moreover, lifetime measurements reveal a single-photon decay rate of $207.4(5)$ ps, as shown in Supplement 1. For the demultiplexer implementation, the input rate of the single-photon source is effectively doubled by increasing the laser excitation rate to 160 MHz.

3. SINGLE-ACTIVE-ELEMENT DEMULTIPLEXER

The second and main part of our experiment consists of the temporal-to-spatial demultiplexer. It employs a single broadband EOM placed at the center of a near-recurrent geometry, as shown in Fig. 2. The temporal sequence of single photons emitted by the QD is guided to the demultiplexing setup via single-mode fibers; here the photons’ polarization is set to horizontal. The scheme consists of two phases, a loading phase and a release phase. During the loading part, the EOM is off, maintaining horizontal polarization. Here, photons follow trajectories slightly displaced from the center of a telescope of unity magnification made of two converging lenses, with the EOM placed in its center. The two lenses have an effective focal length of $300$ mm, such that the beams pass through the EOM with small angles. After the PBS transmits the horizontal modes, the single photons follow a free-space delay line, matched to the separation between the input photons, and reenter the setup on a new parallel trajectory. This process is repeated several times, until a mirror $M_r$ back-reflects the photons’ trajectories, doubling the number of photons that pass through the EOM. For the release phase, with all modes loaded into the setup, we turn on the EOM, switching the photons’ polarization to vertical. Now the PBSs reflect the photons simultaneously into distinct spatial output modes, where the photons are coupled separately into single-mode fibers. The geometry of the setup can, in principle, be extended to more optical output paths as long as the optical elements’ clear apertures allow. In practice, both the channel efficiency and the initial source efficiency are limiting factors for large multi-photon sources, as these determine exponentially decreasing multi-photon rates. In this work, our efficiencies enable us to demultiplex up to eight single photons.

 

Fig. 2. Demultiplexer setup. A stream of single photons emitted by the QD enters the demultiplexer with horizontal polarization. During the loading phase, polarization is maintained and photons follow the gray-colored trajectory. The temporal delay introduced by the free-space path matches the temporal separation of the single photons. For the release phase, the EOM switches the photons’ polarization to vertical, such that they are reflected at the PBSs. The input stream that initially contained $N$ single photons in the same spatial mode and in consecutive time bins is transformed into $N$ distinct trajectories containing a single photon each, in the same time bin.

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We now operate and characterize our demultiplexer with the input single-photon source of Fig. 1. First, we insert photons separated by a shorter delay of $\tau {=}{6.25}$ ns [see Fig. 3(a)] for which we passively increase the repetition rate of our laser [26] to $f_{\mathrm {L}}{=}\tau ^{-1}{=}{160}$ MHz. We use this reduced temporal distance to allow for a shorter free-space delay. We drive the EOM with a frequency of $f_{\mathrm {EOM}}{=}{8}$ MHz phase-locked to the laser, a switching rise time of $\sim$5 ns, and an on-state duration of $25$ ns [see Fig. 3(b)]. Note that although EOMs with faster repetition rates exist to date, reducing the modulation rise time is favored in the present architecture.

 

Fig. 3. Time traces. (a) Single-photon stream generated at 160 MHz. The red colored area indicates the on state of the EOM. The numbering denotes the demultiplexer channel at which the single-photon modes exit. (b) Time modulation of the EOM. The loading phase has a duration of approximately 40 ns and a switching time (light-red colored area) of $\sim$5 ns to the release phase. Approximately 25 ns pass before the EOM returns to the off state. (c) Time trace of all demultiplexer outputs. Eight single photons (red peaks) are demultiplexed into different spatial modes in the same time bin. The intensity of the correctly routed peak of a given channel is decreased by the sum of incorrectly routed peaks appearing in the loading phase among all previous channels.

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The loading phase of the demultiplexer is conducted for as long as the EOM is off. In this time interval, ideally no signal should be observed at any demultiplexer output. Thereon, as a result of the synchronized modulation on the input single-photon stream, every time the EOM reaches its on state (every 125 ns), a number of accumulated single photons is released, ideally one photon at every demultiplexer output. Figure 3(c) displays such time traces for eight outputs.

In an ideal implementation, we expect peaks only appearing in the targeted spatial-temporal outputs, and repeated every 125 ns, while no signal should be observed at all other times. In practice, we find additional peaks in other time bins. Here, we distinguish between three cases native to our architecture. In the first case, additional prominent peaks appear in the first output channel. They exist because the modulation pulse width is longer than the separation between time bins. Thus, single photons that continue entering the setup after the start of the release phase are directly switched and reflected by the second PBS into the first output channel. However, these events have no impact in the resulting $N$-photon rates and, if necessary, they can be suppressed prior to entering the demultiplexer. In a second case, incorrect routing of events occurs during the loading process, showing that the horizontal polarization of every path is not optimally maintained, such that photons reflect with a small probability when passing through the PBSs. This occurs because the trajectories followed by the photons are slightly misaligned from normal incidence toward the EOM central axis. This second case is a main reason for performance degradation in this scheme. Albeit small, the probability of incorrectly releasing a photon at any time bin of the loading phase accumulates, and thus it increases with higher number of outputs. In the third and final case, the EOM imperfectly switches the photons’ polarization during the release phase, i.e., the maximum probability of reflecting is smaller than unity. Thus, some photons continue on the delay path and are likely to be released at the next output channel in the following time bin.

To assess the performance of the single-active-element demultiplexer, we now estimate the channel efficiency $\eta _{k}$ of every output $k$. This denotes the probability of a given input time bin—labeled from 1 to 8 in Fig. 3(a)—to be released in the targeted output—red-colored peaks in Fig. 3(c). We obtain efficiencies ranging from $\eta _{1}{=}0.74$ for the first channel to $\eta _{8}{=}0.14$ for the eighth channel. These values are estimated as the ratio of the integrated counts of the main peak $S_k$ in a given output channel to the counts of the corresponding input time bin, see Supplement 1. Note that this efficiency parameter is affected by any reason that leads to a reduced performance, for instance, losses of the optical elements, fiber-coupling losses, losses in connecting and mating fibers, as well as incorrect active switching of the EOM, which is the main contributing factor.

The main figure-of-merit of our demultiplexing scheme is the multi-fold coincidence rate $R_N$ that describes the simultaneous detection of $N$ photons in distinct output modes. We expect rates that follow $R_N = f_{\mathrm {EOM}} \times \eta _{\mathrm {s}}^{N} \times \prod _{k=1}^{N} \eta _k$ (see Supplement 1), scaling with the source efficiency $\eta _{\mathrm {s}}$ depending on the total number of channels $N$ as well as the efficiency of the contributing channels $\eta _{k}$. The results we measure with our implementation are shown in Fig. 4. Here, the four-photon coincidence rate allows a direct comparison of our results to previous works. In our case, we detect a four-photon rate of ${\sim }$1.4 kHz, a minimum of three orders-of-magnitude higher than almost all previous implementations, with the exception of Ref. [13], where our work compares similarly in the same count rate scale. The values $R_N$ depend and decrease exponentially with the source efficiency, as well as channel efficiencies. In our work, the high levels of efficiencies enable us to measure up to eight photons at a coincidence rate of ${\sim }6$ mHz. Our implementation, therefore, is at the state-of-the-art of active spatial-to-temporal demultiplexing schemes, but notably by using only a single active element.

 

Fig. 4. Multi-photon rates. Measured multi-fold coincidence rates $R_N$: simultaneous output $N$-photon events detected per second. We integrate over a coincidence window of 3 ns. Uncertainties are obtained from Poissonian counting statistics and are too small to be visible for smaller $N$.

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4. DISCUSSION AND CONCLUSION

In this work, we presented a resource-efficient scheme for temporal-to-spatial mode demultiplexing, and use it in combination with a highly efficient quantum dot based single-photon source. Our architecture requires only one active element for obtaining, in principle, an arbitrary number of outputs, thus significantly reducing the amount of resources compared to former implementations. At present, our demultiplexer enables up to eight-photon coincidence events measured at a rate of ${\sim }6$ mHz. This constitutes a significant improvement in number of output channels and count rates compared to alternatives, locating our work at the state-of-the-art for multi-photon sources.

Moreover, count rates following this approach can still significantly improve for the same source efficiency by addressing the factors affecting the channel efficiencies. The main limiting factor is the leakage of photon events in incorrect time bins during the loading process. This is due to the diagonal propagation of the single-photon modes relative to the central axes of the birefringent crystal, causing a small but accumulative polarization walk-off. While individually controlling the polarization of each path entering the EOM mitigates this effect to some extent, optimized channel efficiencies will require making use of compensation crystals, or modified trajectories that exploit near-recurrent geometries while imposing normal incidence along the birefringent element. Furthermore, reducing the path delay, using an EOM with faster rise time is largely beneficial: smaller distances allow for smaller beam diameters and Rayleigh ranges; therefore, many more trajectories can fit within limited optics’ clear apertures. As proof-of-principle, we also built a demultiplexer unit that outputs sixteen modes using standard one-inch optical elements; see Supplement 1 for more information. With these modifications in mind, our approach can be used to build multi-photon sources at larger scales.