Experimental Demonstration of Conjugate-Franson Interferometry

Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate, for the first time, the complementary technique in the time basis called conjugate-Franson interferometry. It measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of $96\pm 1\%$ without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the quantum-classical threshold by 25 standard deviations and validates the conjugate-Franson interferometer (CFI) as an alternative method for certifying time-energy entanglement. Moreover, the CFI visibility is a function of the biphoton’s joint temporal intensity, and is therefore sensitive to that state’s spectral phase variation: something that is not the case for Franson interferometry or Hong-Ou-Mandel interferometry. We highlight the CFI’s utility by measuring its visibilities for two different biphoton states: one without and the other with spectral phase variation, observing a 21% reduction in the CFI visibility for the latter. The CFI is potentially useful for applications in areas of photonic entanglement, quantum communications, and quantum networking.

Figure 1

Experimental setup of our conjugate-Franson interferometer. Time-energy entangled signal-idler photon pairs generated by cw pumped SPDC were coupled into an optical fiber and routed to their respective MZIs. The signal’s frequency shifter was configured to blue shift its input, whereas the idler’s shifter was configured to red shift its input. The polarization and the path lengths between the two arms of each MZI were made to be the same. The fiber-based CFI was placed inside a custom-built two-stage thermal box for phase stabilization. The MZI outputs were detected with SNSPDs, and their arrival times were recorded for coincidence measurements. LPS: long-pass filter; PBS: polarizing beam splitter; PC: polarization controller; FS: frequency shifter for $\mathrm{\Delta }\mathrm{\Omega }$ ($-\mathrm{\Delta }\mathrm{\Omega }$) frequency shift; AG: tunable air gap; BS: $50/50$ beam splitter; and $\mathrm{DCM}+(-)$: dispersion module with normal (anomalous) dispersion.

Figure 2

(a) Log-scale display of frequency shifters’ output spectra, measured using classical light, that shows signal-to-noise ratios of at least 20 dB limited by higher-order sidebands. Maximum intensities of both spectra normalized to 0 dB. (b) Measured CFI coincidences vs inferred signal-idler frequency sum: central peak location determines zero detuning of signal-idler sum frequency. Thirty-second integration time for each data point; measurement taken with MZI phase sum of ${\varphi }_T\approx \pi /2$. (c) Coincidences (blue) as a function of MZI phase sum ${\varphi }_T$, with calculated uncertainties assuming Poisson statistics. Least-squares fit (solid red line) to the form $A[1+V\cos ({\varphi }_T)]$ yields a fitted CFI visibility $V$ of 93%. No background counts are subtracted from measured data. (d) Singles count rates for both detectors as functions of MZI phase sum ${\varphi }_T$, showing no meaningful variations.

Figure 3

(a) JSI calculated for a biphoton with 320-GHz-wide flat-top spectrum. Spectral phase $\varphi$ (none, set to zero) applied to blue (red) shaded region outside (within) the $\pm 80\mathrm{GHz}$ span of signal and idler frequency detuning. JSI does not depend on $\varphi$. (b) JTI of same biphoton state with $\varphi =0$ or $2\pi$. (c) JTI of same biphoton state with $\varphi =\pi$. Maximum of JTI normalized to one.

Figure 4

Conjugate-Franson fringe visibility as a function of applied spectral phase $\varphi$ of Eq. (5). Measured data points (blue) closely follow calculated values (solid red line) obtained from Eq. (3), with a rectangular spectrum of 320 GHz span shown in Fig. 3. Error bars represent one standard deviation of three measurements.