Entangling Different-Color Photons via Time-Resolved Measurement and Active Feed Forward

Entangling independent photons is not only of fundamental interest but also of crucial importance for quantum-information science. Two-photon interference is a major method for entangling independent identical photons. If two photons are different in color, perfect two-photon coalescence can no longer happen, which makes the entangling of different-color photons difficult to realize. In this Letter, by exploring and developing time-resolved measurement and active feed forward, we have entangled two independent photons of different colors for the first time. We find that entanglement with a varying form can be identified for different two-photon temporal modes through time-resolved measurement. By using active feed forward, we are able to convert the varying entanglement into uniform entanglement. Adopting these measures, we have successfully entangled two photons with a frequency separation 16 times larger than their linewidths. In addition to its fundamental interest, our work also provides an approach for solving the frequency-mismatch problem for future quantum networks.

Figure 1

Experimental setup. Two cavity-enhanced spontaneous parametric down-conversion (CSPDC) sources are being used to create two pairs of entangled photons. The pumping beam is generated though second-harmonic generation (SHG) of a Ti:sapphire laser working at 795 nm and stabilized through rubidium spectroscopy. Two acousto-optic modulators (AOM) are used to chop the pumping beam into short pulses with a repetition rate of 2 MHz and to tune the frequencies of the narrow band entangled photons. Each entanglement source is basically made up of a linear cavity with a 25 mm long nonlinear crystal (PPKTP) and a 5 mm long KTP crystal inside. The KTP is utilized to achieve double resonance for both CSPDC photons through temperature tuning [15]. The measured linewidths for the two cavities are ${\gamma }_1/2\pi =4.2\mathrm{MHz}$ and ${\gamma }_2/2\pi =5.6\mathrm{MHz}$, respectively. Within each source, by controlling the double-resonance condition and making use of additional filtering etalons [16], the two down-converted photons are configured to have the same frequency, which is exactly one-half of the pumping beam. Photons $A$ and $a$ are polarization entangled, and so are $B$ and $b$. A polarizing beam splitter (PBS) along with two polarizers (POL) are utilized for the Bell-state measurement. Detection-time differences between $D_1$ and $D_2$ are fed forward to a Pockels cell to cancel the random phase shifts in order to recover the entanglement between photons $A$ and $B$. To compensate the feedback delay due to the single-photon detectors, the time-to-amplitude convertor (TAC), and the high-voltage driver of the Pockels cell, a single-mode (SM) fiber loop with a length of 150 m is inserted for photon $A$.

Figure 2

Measured correlation visibilities and fourfold count rates as a function of the coincidence time window. (a),(b) Pumping pulse width is set to 50 ns. (c),(d) Pumping pulse width is set to 300 ns. Data points in black filled squares are measured in the basis of $|H⟩/|V⟩$, and data points in red filled circles are measured in the basis of $|+⟩/|-⟩$. In this measurement, twofold coincidence count rates are 310 and $190{\mathrm{s}}^{-1}$, respectively, for the two CSPDC sources. Error bars represent statistical errors.

Figure 3

Visibilities in the basis of $|+⟩/|-⟩$ for photons $A$ and $B$ as a function of detection time delay $\delta t$. (a),(b) Active phase feed forwarding is applied. (c),(d) Active phase feed forwarding is not applied. Error bars represent statistical errors. For a given value of $\mathrm{\Delta }\omega$, all data points are measured with the same setting for the feed-forward circuitry. In these measurements, the fourfold count rate is $24{\mathrm{h}}^{-1}$ and the twofold count rates are 200 and $140{\mathrm{s}}^{-1}$, respectively.

Figure 4

Measurement results of ${\sigma }_i\otimes {\sigma }_i$ for photons $A$ and $B$ with $i=x$, $y$, and $z$. (a),(b) Active phase feed forward is applied. (c),(d) Active phase feed forward is not applied. Error bars represent statistical errors.