Characterization of coherent quantum frequency combs using electro-optic phase modulation

We demonstrate a two-photon interference experiment for phase coherent biphoton frequency combs (BFCs), created through spectral amplitude filtering of biphotons with a continuous broadband spectrum. By using an electro-optic phase modulator, we project the BFC lines into sidebands that overlap in frequency. The resulting high-visibility interference patterns provide an approach to verify frequency-bin entanglement even with slow single-photon detectors; we show interference patterns with visibilities that surpass the classical threshold for qubit and qutrit states. Additionally, we show that with entangled qutrits, two-photon interference occurs even with projections onto different final frequency states. Finally, we show the versatility of this scheme for weak-light measurements by performing a series of two-dimensional experiments at different signal-idler frequency offsets to measure the dispersion of a single-mode fiber.

Figure 1

Depiction of biphoton frequency comb (BFC). (a) Spectrum of BFC with a free spectral range labeled as $\mathrm{\Delta }\omega$. (b) Time correlation function, with fast substructure arising from coherent interference between the different biphoton frequency components. If the phase between different biphoton frequency components is random, there will be no time-average interference, and we would get only the longer envelope.

Figure 2

Basic schematic for phase coherence measurements and illustration of biphoton spectral progression at different steps. (a) Experimental setup. (b) Broadband continuous biphoton spectrum. (c) Biphoton frequency comb after carving continuous spectrum with pulse shaper 1. The blocked frequencies were attenuated by 60 dB, making contamination from undesired frequencies negligible. (d) Sidebands projected from phase modulation of comb lines. (e) Using pulse shaper 2, selected sidebands could be routed to a pair of single-photon detectors. SPDC: spontaneous parametric downconversion; PM: phase modulator; rf: radio frequency.

Figure 3

Qubit and qutrit interference patterns. The two-photon interference as a result of applying (a) ${\varphi }_2$ relative phase on ${\mathrm{S}}_2{\mathrm{I}}_2$ with respect to ${\mathrm{S}}_1{\mathrm{I}}_1$, (b) ${\varphi }_2$ relative phase on ${\mathrm{S}}_3{\mathrm{I}}_3$ with respect to ${\mathrm{S}}_2{\mathrm{I}}_2$, (c) 0 phase on ${\mathrm{S}}_1{\mathrm{I}}_1$, $\varphi$ phase on ${\mathrm{S}}_2{\mathrm{I}}_2$, and $2\varphi$ phase on ${\mathrm{S}}_3{\mathrm{I}}_3$, (d) ${\varphi }_2$ phase on ${\mathrm{S}}_2{\mathrm{I}}_2$ while setting the sideband amplitude such that $|C_3|=\frac{|C_1|}{2}$. The red error bars are the standard deviation of three measurements for each phase and the blue curves indicate the theoretical predictions taking into account the visibility calculated from the maximum and minimum data points. The coincidence-to-accidental ratio in our measurements was 3:1, but accidentals were subtracted in these plots.

Figure 4

(a) Shift in the interference pattern as a result of added dispersion; the dashed vertical line indicates the relative shift of ${\varphi }_5=0.74\pi$. The blue curve indicates the theoretical prediction taking into account the visibility calculated from the maximum and minimum data points. (b) Coincidences as a function of $f_{\mathrm{os}}$ when ${\varphi }_k={\varphi }_{k+1}=0$. The blue curve is the theoretical prediction normalized to the maximum number of coincidence counts. (c) Phase shift of the interference pattern as a function of $f_{\mathrm{os}}$. The blue line is the linear fit to the data points. The red error bars are the standard deviation of three measurements. The coincidence-to-accidental ratio was also 3:1 in these measurements and the accidentals were subtracted in the plots.