Entanglement between a Photonic Time-Bin Qubit and a Collective Atomic Spin Excitation

Entanglement between light and matter combines the advantage of long distance transmission of photonic qubits with the storage and processing capabilities of atomic qubits. To distribute photonic states efficiently over long distances several schemes to encode qubits have been investigated—time-bin encoding being particularly promising due to its robustness against decoherence in optical fibers. Here, we demonstrate the generation of entanglement between a photonic time-bin qubit and a single collective atomic spin excitation (spin wave) in a cold atomic ensemble, followed by the mapping of the atomic qubit onto another photonic qubit. A magnetic field that induces a periodic dephasing and rephasing of the atomic excitation ensures the temporal distinguishability of the two time bins and plays a central role in the entanglement generation. To analyze the generated quantum state, we use largely imbalanced Mach-Zehnder interferometers to perform projective measurements in different qubit bases and verify the entanglement by violating a Clauser-Horne-Shimony-Holt Bell inequality.

Figure 1

(a) Schematic overview of the experimental setup. $W$, write pulse; $R$, read pulse; $w$, write photon; $r$, read photon; $L$, interferometer lock light; PC, polarization controller; PZ, piezoelectric fiber stretcher; $D_{w(r)}^{+(-)}$, single photon detectors; FS, fiber switch; PD, photodiode; PID, proportional-integral-derivative controller. (b) Energy levels relevant for the photon generation process. (c) Expected behavior of the read photon transfer efficiency of the early (green line) and late (brown line) atomic excitations as a function of the readout time $t_R$. The blue pulses indicate the times of the early ($E_W$) and late ($L_W$) write pulse peaks required to create the light-matter entangled state. The orange pulses indicate the times of the early and late read pulse peaks ($E_R$ and $L_R$) required to subsequently convert the atomic qubit into a read photon time-bin qubit.

Figure 2

(a) Measured read photon transfer efficiency of the atomic excitation as a function of the readout time. The green open circles show the case without magnetic field dephasing, while the blue dots show the case with the magnetic field on. For both traces, the write (read) detection gates are 40 ns (60 ns) and the data are only corrected for the detection efficiency of the single photon detectors. (b) Atomic excitation readout selectivity as a function of the write pulse power. Here, the write and read detection gates were set to 30 and 40 ns, respectively. The error bars are smaller than the size of the data points. The inset shows the time-bin correlation for one particular write pulse power. Error bars correspond to $\pm 1$ standard deviations of the photon counting statistics.

Figure 3

(a) Write and read photon histograms at the interferometer outputs (photon durations are 20 and 30 ns FWHM, respectively). The detection events in each of the bins correspond to a projection to a different state as indicated in the figure. (b) Representation of the different orthogonal time-bin states on the Bloch sphere. (c) Write-read photon correlation coefficients taken at $P_W=7\mu \mathrm{W}$. The phase of the read photons interferometer is scanned, while the phase of the write photons interferometer is fixed at two different values ($U_{w1}=0\mathrm{V}$ for the blue dots and $U_{w2}=0.268\mathrm{V}$ for the green open circles). The detection gate widths were set to 30 ns for the write photons and 40 ns for the read photons [cf. blue area in (a)].

Figure 4

(a) Visibility of the two-photon interference fringes as shown in Fig. 3 (blue dots) and detected photon coincidence rate (green open circles) versus write pulse power. The dashed line represents the visibility required to violate a Bell inequality ($V>1/\sqrt{2}$). (b) Values of the four correlation coefficients taken at $P_W=3.5\mu \mathrm{W}$ and with the four basis settings ($U_w=0.268\mathrm{V}$, $U_w^{\prime }=0\mathrm{V}$, $U_r=0.333\mathrm{V}$, and $U_r^{\prime }=0.099\mathrm{V}$) that are optimal for a Bell inequality violation.