Coherent Ultrafast Measurement of Time-Bin Encoded Photons

Time-bin encoding is a robust form of optical quantum information, especially for transmission in optical fibers. To readout the information, the separation of the time bins must be larger than the detector time resolution, typically on the order of nanoseconds for photon counters. In the present work, we demonstrate a technique using a nonlinear interaction between chirped entangled time-bin photons and shaped laser pulses to perform projective measurements on arbitrary time-bin states with picosecond-scale separations. We demonstrate a tomographically complete set of time-bin qubit projective measurements and show the fidelity of operations is sufficiently high to violate the Clauser-Horne-Shimony-Holt-Bell inequality by more than 6 standard deviations.

Figure 1

Measuring time-bin qubits. (a) In typical time-bin measurement schemes, an input time-bin state is sent through an unbalanced interferometer matched to the bin separation. High-fidelity measurement requires isolating the middle output pulse, necessitating a large delay ${\tau }_{e\ell }$. (b) A photon encoding a time-bin qubit is chirped and undergoes SFG with an equal and oppositely chirped strong laser pulse. The SFG contains two peaks separated in frequency by an amount proportional to the time delay, ${\tau }_{e\ell }$. (c) If the chirped strong laser pulse is itself in a superposition of two time bins, the output spectrum contains three peaks. In this case, high-fidelity measurement requires isolating the middle frequency. The process is directly analogous to conventional time-bin measurement, with the signal converted from time to frequency.

Figure 2

Experimental setup. Polarization-entangled photon pairs (signal and idler) are generated via down-conversion (SPDC) in orthogonally oriented nonlinear crystals (extra crystals used for compensation not shown). The signal photon is converted to a time-bin qubit using a birefringent crystal (5 mm $\alpha$-BBO) and polarizer. The signal acquires a positive chirp in 34 m of optical fiber. The strong laser pulse is prepared using an identical birefringent crystal and a series of wave plates to set the phase, then negatively chirped using gratings. The photon and laser pulse are combined in a nonlinear crystal to produce SFG. The middle frequency is detected using a photon counter after a monochromator.

Figure 3

Sum-frequency spectrum, in arbitrary units (a.u.). The up-converted signal spectrum (background subtracted) taken using our spectrometer, with $\beta$ set to 0. A fit to the data is shown in blue. The monochromator selected those wavelengths that fall between the dotted lines.

Figure 4

Coincidence counts versus $\beta$. The idler is projected into the diagonal basis in (a) ($|D⟩$ in blue and $|A⟩$ in red) and the circular basis in (b) ($|L⟩$ in orange and $|R⟩$ in green). The CHSH-Bell inequality was violated using the data points indicated by the gray lines with a value $S=2.54\pm 0.08$.

Figure 5

Quantum state reconstruction. (a) Coincidence counts between the idler and the SFG photon in each peak from Fig. 3, for $\beta =0$ and the indicated polarization measurement of the idler. (b) Real part of the reconstructed density matrix of the initial two-photon polarization state produced from the SPDC source, which has a fidelity of 94% with $|{\Phi }^{+}⟩$. (c) Real part of the reconstructed density matrix of the time-bin-encoded signal and polarization-encoded idler using chirped-pulse up-conversion to measure the time-bin states; the state has 95% fidelity with the reconstructed density matrix of the initial state. Imaginary parts of both matrices were negligibly small and are in the Supplemental Material 26.