Interference at the Single Photon Level Along Satellite-Ground Channels

Quantum interference arising from the superposition of states is striking evidence of the validity of quantum mechanics, confirmed in many experiments and also exploited in applications. However, as for any scientific theory, quantum mechanics is valid within the limits in which it has been experimentally verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored conditions such as moving terminals at large distances in space. Here, we experimentally demonstrate single photon interference at a ground station due to the coherent superposition of two temporal modes reflected by a rapidly moving satellite a thousand kilometers away. The relative speed of the satellite induces a varying modulation in the interference pattern. The measurement of the satellite distance in real time by laser ranging allows us to precisely predict the instantaneous value of the interference phase. We then observed the interference patterns with a visibility up to 67% with three different satellites and with a path length up to 5000 km. Our results attest to the viability of photon temporal modes for fundamental tests of physics and quantum communication in space.

Figure 1

Scheme of the experiment and satellite radial velocity. In the top panel we show the measured radial velocity of the Beacon-C satellite ranging from $-6$ to $+6\mathrm{km}/\mathrm{s}$ as a function of time during a single passage. In the bottom panel we show the unbalanced MZI with the two $4f$ systems used for the generation of the state and the measurement of the interference. The light and dark green lines, respectively, represent the beams outgoing to and ingoing from the telescope. In the inset, we show the expected detection pattern: the number of counts $N_c$ in the central peak varies according to the kinematic phase $\phi$ imposed by the satellite. The right photo shows the MLRO with the laser ranging beam and the Beacon-C satellite (not to scale). The phase $\phi (t)$ depends on the satellite radial velocity as described in the text.

Figure 2

Kinematic phase and interference pattern. Top panel: we show the measured satellite distance and the predicted kinematic phase $\phi (t)$ estimated by Eq. (2) as a function of time for a passage of the Ajisai satellite. The shaded area represents the temporal window of data acquisition. Bottom panel: kinematic phase $\phi (t)$ and theoretical probability $P_c(t)$ in the shaded area. The interference pattern is modulated according to the value of $\phi (t)$ determined by the satellite velocity.

Figure 3

Constructive and destructive single photon interference [Beacon-C satellite, 11.07.2015 h 1.33 central european summer time (CEST)]. (a) Histogram of single photon detections as a function of time $\mathrm{\Delta }=t_{\text{meas}}-t_{\text{ref}}$ realized by selecting only the returns characterized by $\phi (\mathrm{mod}2\pi )\in [4\pi /5,6\pi /5]$ that lead to constructive interference. The solid line shows the tri-Gaussian fit. By evaluating the Gaussian integrals we obtained the counts $N_{\ell }=112\pm 11$ for the sum of lateral peaks and $N_c=196\pm 14$ for the central one. (b) Histogram of single photon detections realized by selecting only the returns characterized by $\phi (\mathrm{mod}2\pi )\in [-\pi /5,\pi /5]$. Here, $N_{\ell }=112\pm 11$ and $N_c=46\pm 7$. (c) Histogram of single photon detections without any selection on the phase. As expected, the interference is completed washed out and we measured $N_c=1245\pm 35$ and $N_{\ell }=1306\pm 36$, fully compatible with $P_c=1/2$. In all panels, the dotted red lines represent the expected counts in case of no interference.

Figure 4

Experimental interference pattern. Experimental probabilities $P_c^{(\exp )}$ as a function of the kinematic phase measured for three different satellites. By fitting the data we estimate the visibilities ${\mathcal{V}}_{\exp }=67\pm 11\%$ for Beacon-C, ${\mathcal{V}}_{\exp }=53\pm 13\%$ for Stella, and ${\mathcal{V}}_{\exp }=38\pm 4\%$ for Ajisai. The dashed lines correspond to the theoretical value of $P_c$ predicted by Eq. (1). The points are obtained by considering ten intervals of the phase defined by ${\mathcal{I}}_j\equiv [(j-1/10)\pi ,(j+1/10)\pi ]$. For each interval we selected the data corresponding to $\phi (\mathrm{mod}2\pi )\in {\mathcal{I}}_j$: from such data we determined the experimental probability of detection in the central peak $P_c^{(\exp )}$ and we averaged the corresponding phase $\phi$. We note that at the point $\phi =0$ and $\phi =2\pi$ the same subset of data was selected.