We performed a quantum interference experiment using two polarization-entangled photon pairs at 1550 nm, created in periodically poled lithium niobate waveguides. Using four-fold coincidences, a Hong−Ou−Mandel dip at diagonal polarization was observed with a visibility of 74.5% before subtracting accidental coincidences. This experiment lays a foundation for demonstrating polarization-based entanglement swapping and for realizing a quantum relay.
© 2010 OSA
When two initially separated photons are mixed using a beamsplitter, photon bunching will be observed if and only if they have identical polarizations and spatial, temporal and spectral modes; i.e., if they are indistinguishable . This phenomenon is known as a Hong−Ou−Mandel dip and it was first confirmed experimentally by Mandel’s group . Observation of a Mandel dip using two photon pairs from spatially separated entanglement sources is becoming increasingly important for both realizing quantum teleportation  and demonstrating entanglement swapping . Several research groups have reported related experiments [5–10]. Time-bin-based fiber-optic entanglement swapping has been demonstrated in the telecom band [11–13], which is a suitable band for distributing entangled photons in low-loss optical fibers. In this paper, we discuss a Mandel-dip experiment using two polarization-entangled photon pairs in the 1550-nm band, created in two separately located lithium niobate waveguides with periodic poling. In the following, we first describe the experimental setup for generating polarization-entangled photon pairs and we discuss their quantum interference to evaluate the Mandel-dip visibility. The experimental results are then presented and discussed. Four-fold coincidences were recorded for different polarizations, and visibilities of around 75% were observed.
2. Experimental setup and design
Figure 1 shows the quantum interference scheme for observing a Mandel dip using two initially separated photon pairs. The two independent entanglement sources used are labeled as Modules 1 and 2. Two photons from each module will emerge at the same output port of the beamsplitter (BS), if they are indistinguishable. Coincidence detection of the two photons at the single-photon detectors B and C is then forbidden, giving rise to a perfect Mandel dip. However, if two pairs are accidentally created in a single source (either Module 1 or 2), the visibility of the Mandel dip will be reduced . Thus, four-fold coincidence measurements using four single-photon detectors (A−D) are essential for evaluating dips. Polarizers (P1-4) are tilted to ensure that all photons have identical polarizations before detection.
Figure 2 sketches the experimental setup. We use a Ti:sapphire mode-locked femtosecond laser (High Q Laser) as the pump laser (see blue arrows in Fig. 2). It has a center wavelength of 775 nm, an average power of 240 mW and a pulse duration of 230 fs. The repetition frequency is 72.9 MHz. The pump beam is then split into two beams by a non-polarizing beamsplitter (NBS1). These beams are incident on spatially separated entanglement sources, Modules 1 and 2. Attenuators (ATTs) and polarization controllers (PCs) after NBS1 are used to adjust the powers and polarizations of the pump beams onto the modules. Module 1 has a 1-mm-long, type-0, MgO-doped, periodically poled lithium niobate (PPLN) waveguide (HC Photonics) placed at the center of a polarization Sagnac loop  formed by two polarization-maintaining fibers (PMFs).The pump beam is diagonally polarized and is incident on a polarizing beamsplitter (PBS). It is then split into two beams of equal intensity but orthogonal polarizations. The loop with a 90-degree twist allows the PPLN waveguide to be bidirectionally pumped in the same polarization mode. Module 2 has the same configuration as Module 1. A dichroic mirror (DM1) offers high transmission for the pump beam and high reflection for the photon pairs. To separate signal and idler photons, a second dichroic mirror (DM2) is optically coated for high reflection between 1500 and 1550 nm and high transmission between 1550 and 1585 nm (see red arrows in Fig. 2). Transmitted and reflected photons are respectively referred to as signal and idler photons. The polarization-entangled state is created in each module, where H and V respectively indicate horizontal and vertical polarization states, and the subscripts s and i represent the signal and idler, respectively. A phase compensator (PCM), which consists of two quarter-wave plates and a half-wave plate, is introduced to adjust the relative phase, θ. After θ = 0 is achieved, a fiber-optic delay line (DL) and a second non-polarizing beamsplitter (NBS2) are employed to evaluate the visibility of a Mandel dip observed in quantum interference. Polarization controllers (PCs) are also inserted for signal and idler photons to compensate for birefringence in the single-mode fibers (SMFs) used in the experiment. In addition, pump rejection filters (PFs) are used to filter unwanted photons from the pump beam. Bandpass filters (BFs) with a 5-nm bandwidth increase the coherence time of photons to 0.71 ps; the center wavelengths of these bandpass filters are 1562 and 1538 nm for the signal and the idler, respectively. Polarizers (PLs) determine the polarization states of signal and idler photons in four-fold coincidence measurements. The single-photon detectors (D1-4; id Quantique) have identical gate frequencies of 4.05 MHz. Since the laser frequency is 18 times as high as the gate frequency, we use a frequency divider (AVTECH) for external control of D1-4 by the pump laser. The gate width is 2.5 ns. A dead time of 10 μs is imposed to cut off unwanted after-pulses in detection. Table 1 shows the quantum efficiencies and the dark-count probabilities.
3. Experimental results
All the polarizers were initially set to the same diagonal polarization. The idler photons after NBS2 in Fig. 2 become indistinguishable when the two optical path lengths are equal. In this case, the time delay between them becomes zero, and the coincidence count rate of photons in detectors D2 and D3 drops to zero. We measured the two-fold coincidence counts at different time delays. Counts over a period of 20 s were measured five times at each delay. The average values and standard deviations are plotted in Fig. 3 (circles) as a function of the time delay. The measured data were fitted to a Gaussian function determined by the spectral transmission of the bandpass filter BF:15]. The fit indicates a visibility of 26.2% for two-fold coincidences, which is comparable to the theoretical value of 33.3% , even though we did not subtract accidental coincidences. The temporal width was σ = 0.46 ps, corresponding to a full width at half maximum of 1.08 ps, which is close to the expected value. For reference, two-fold coincidence counts of photons measured by D1-2 and D3-4 and their single-photon counts are given in Table 2 . They are independent of the time delay. To observe a Mandel dip, it is necessary to use four-fold coincidences that contain two signal photons. Three different time delays were chosen to measure the number of four-fold coincidence counts occurring in 4000 s. The measurement was repeated only four times for each delay because of a lack of long-term laser stability. We fitted the data using the same temporal width as that of the two-fold coincidences, as plotted in Fig. 3 (squares). A raw visibility of 74.5% for four-fold coincidences was observed. From the measured visibility for two-fold coincidences, we have a fraction 26.2/33.3 = 0.787. The obtained visibility of 74.5% for four-fold coincidences is nearly equal to 78.7%, demonstrating the validity of the data obtained in this experiment. We also measured four-fold coincidence counts when the polarizers were adjusted to vertical and horizontal polarizations. The results were fitted using Eq. (1), as shown in Fig. 4 . Both curves exhibit a clear Mandel dip. Visibilities of 74.7% for the horizontal polarization (circles) and 75.3% for the vertical polarization (squares) were observed. These results demonstrate that quantum interference was observed using two spatially separate polarization-entangled pairs in the 1550-nm band. This setup as demonstrated will allow to perform an entanglement swapping experiment at 1550 nm if a Bell-state measurement is undertaken at NBS2 in Fig. 2. Thus, our experiment represents an important step toward achieving polarization-based entanglement swapping in the telecom band.
We consider the case where three photon pairs are generated at the same time in Fig. 2 (one pair in Module 1 and two pairs in Module 2, and vice versa). If propagation loss is high, a chance of all three idler photons reaching NBS2 becomes small. However, to record four-fold coincidence counts, two of three idler photons must survive. If such photons are coming from the same module, we will record four-fold coincidence counts. Also, four-fold coincidence counts will be observed if all three idler photons survive. These counts are not related to photon bunching and reduce the Mandel-dip visibility. Detailed theoretical and experimental investigations of such four-fold accidental coincidence counts are our future task.
The number of four-fold coincidence counts is proportional to the product of all four quantum efficiencies of the single-photon detectors used in the experiment and also proportional to the gate frequency. On the other hand, increasing the pump power raises the number of accidental coincidence counts, which reduce the Mandel-dip visibility. Performance improvement of single-photon detectors promises dramatic increase of the number of four-fold (not accidental) coincidence counts.
A Mandel dip was observed using two spatially separated polarization-entangled pairs in the 1550-nm band. Dips in the four-fold coincidences were obtained at different polarizations. A visibility of around 75% was obtained for each polarization-entangled state without subtracting accidental counts. These experiments lay a foundation for realizing a quantum relay in the 1550-nm band and for demonstrating polarization-based entanglement swapping.
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