Long-distance distribution of time-bin entanglement generated in a cooled fiber

This paper reports the first demonstration of the generation and distribution of entangled photon pairs in the 1.5-um band using spontaneous four-wave mixing in a cooled fiber. Noise photons induced by spontaneous Raman scattering were suppressed by cooling a dispersion shifted fiber with liquid nitrogen, which resulted in a significant improvement in the visibility of two-photon interference. By using this scheme, time-bin entangled qubits were successfully distributed over 60 km of optical fiber with a visibility of 76%, which was obtained without removing accidental coincidences.

The entangled states of quantum particles constitute the quintessential feature of quantum mechanics because they highlight its non-locality most vividly [1]. Moreover, entanglements form the basis of quantum information, and facilitate such applications as quantum key distribution (QKD) [2,3], quantum teleportation [4], and quantum repeaters [5]. Of the many forms of entanglement, entangled photons are important because they are suitable for distributing quantum information over long distances. Although several good sources are available in the short wavelength band [6,7], an entangled photon-pair source in the 1.5-µm band is needed if we are to realize quantum information systems over optical fiber networks. Recently, spontaneous four-wave mixing (SFWM) in a dispersion shifted fiber (DSF) has been drawing attention as a promising method for generating entanglement in the 1.5-µm band [8,9,10]. Polarization [8,9] and time-bin entangled photons [10] have already been generated and successfully distributed over optical fibers [9,10,11]. The merit of this scheme is the good coupling efficiency it provides between nonlinear medium (i.e. a DSF) and transmission fibers.
Despite the series of successful experiments described above, a serious problem has been reported regarding the fiber-based photon-pair source, namely the existence of noise photons generated by spontaneous Raman scattering [8,9,10,12,13]. The pump light used for the SFWM process also works as the pump for the spontaneous Raman scattering process, by which Stokes and anti-Stokes photons are generated in wavelength bands longer and shorter than the pump wavelength, respectively. Consequently, accidental coincidences are caused by the Stokes and anti-Stokes photons whose wavelengths coincide with those of the idler and signal channels of photon pairs generated by SFWM. In the two-photon interference measurement, such accidental coincidences seriously degrade the visibility. As a result, the visibilities reported in the previous experiments were obtained after subtracting accidental coincidences [8,9,10,11].
This large number of noise photons prevented the fiber-based photon-pair source from being applied to quantum information experiments such as QKD, because accidental coincidences result in a large bit error rate. Thus, the suppression of accidental coincidences caused by spontaneous Raman scattering is a very important issue as regards making the fiber-based photon-pair source useful in real quantum information systems.
To solve this problem, Inoue and I recently demonstrated that noise photons caused by spontaneous Raman scattering were suppressed by cooling a DSF with liquid nitrogen [14].
We observed a significant enhancement of the quantum correlation characteristics in a timecorrelation measurement. However, entangled states have yet to be generated using a cooled fiber, and so the improvement in the visibility has not been confirmed directly in a degree-ofentanglement measurement.
In this paper, I report the first experiment on time-bin entanglement generation in a DSF cooled by liquid nitrogen. With an average photon number per pulse of ∼0.06, a significant improvement in the visibility from 65% to 80% was achieved by cooling the DSF, without subtracting accidental coincidences. In addition, time-bin entangled qubits were successfully distributed over 60 km (30 km x 2) of optical fiber with a visibility of 76%. This distance exceeds the previous record for the long-distance distribution of entanglement set by a group from Geneva University (25 km x 2), in which they used a lithium triborate crystal as a nonlinear medium [15].
Spontaneous Raman scattering is a process in which a spontaneous photon is generated by a nonlinear interaction between a pump photon and a phonon. The numbers of Stokes, n s , and anti-Stokes photons, n as as a function of temperature T are expressed as [14] n s (T ) = gLe −αL where g, α, L, h, ν and k B are a gain coefficient proportional to the pump power, a fiber loss coefficient, the fiber length, Planck constant, photon energy, and Boltzman constant, respectively. It is apparent that we can reduce the number of spontaneous Raman photons by lowering the fiber temperature. If the fiber loss coefficient is independent of temperature, the ratio of the Stokes photon number at liquid nitrogen (77 K) and room temperature (293 K) with the same pump power is calculated to be n s (77)/n s (293) = 0.29. For anti-Stokes photon numbers it is n as (77)/n as (293) = 0.24. Here, I assumed that ν = 400 GHz, which corresponds to the frequency difference between the pump and signal/idler channels in the experiment. Thus, the number of noise photons is expected to be reduced by cooling the fiber with liquid nitrogen. .
Here, |k x represents a state in which there is a photon in a time slot k in a mode x, signal (s) or idler (i). φ is a relative phase term that is equal to 2φ p , where φ p is the phase difference The photons output from each bandpass filter are transmitted over a 30-km DSF with a loss of 0.2 dB/km and then input into a 1-bit delayed Mach-Zehnder interferometer fabricated using planar lightwave circuit (PLC) technology [17,10]. A state |k x is converted as follows by the interferometer.
Here, a and b denote two output ports of the interferometer. θ x is the phase difference between the two paths of the interferometer for channel x, and can be tuned by changing the temperature. As a result, the time-bin entangled state |Ψ is converted to where θ = θ s + θ i and 16 non-coincident terms in the parentheses are not shown because they are not observed in a coincidence measurement. We can observe a two-photon interference fringe by changing θ and measuring the coincidence counts in the second time slot. This experiment uses two detectors connected to port a of the interferometers, so only the fifth term in parentheses in Eq. (5) is observed in a two-photon interference measurement.
This means that a time-bin entangled photon pair is detected with a probability of 1/8 when a constructive interference occurs (i.e. θ = φ). When the average number of correlated photon pairs per pulse is µ c (which means that the average number per time-bin qubit is 2µ c ), the count rate of correlated events in a constructive interference, R c , is expressed as where α s and α i denote transmittances for the signal and idler channels including the quantum efficiency of the photon counters, respectively. On the other hand, the accidental coincidence rate R acc is given by where µ x and d x denote the average number of photons per pulse and the dark count rate of the detector for channel x with x = s, i, respectively. If the average number of noise photons per pulse for channel x is given by µ nx , µ x is expressed as two-photon interference fringe. Therefore, the visibility V is expressed as First, I confirmed the effectiveness of fiber cooling for improving the visibility of two-photon interference without connecting 30-km DSF spools. I changed θ i by changing the temperature of the interferometer for the idler, while fixing θ s , and recorded the coincidence counts. µ s and µ i were set at approximately 0.05 and 0.06, respectively, for both the cooled and uncooled experiments [18]. The average count rates of the signal and idler channels, respectively, were approximately 1500 and 1600 Hz throughout measurements. Without cooling the DSF, the visibility of the two-photon interference fringe was 64.7%, which was obtained without removing the accidental coincidences ( Fig. 2 (a)). Fig. 2 (b) shows the fringe when the DSF was cooled. The level of the minimum points of a fringe corresponds to the number of accidental coincidences, which is proportional to µ s µ i as shown in Eq. (7). Because µ s and µ i were set at the same value for both measurements, the minimum points of both fringes were at almost the same level, as seen in Fig. 2. However, the peak level of the fringe increased significantly when the DSF was cooled. This implies that the number of noise photons is suppressed and so the portion of correlated photon pairs is effectively increased by cooling the DSF. As a result, the visibility increased to 80.0% with the accidental coincidences included. The average number of correlated photon pairs per pulse µ c can be estimated from the obtained visibilities and Eqs.
(6)- (9). As a result, µ c was ∼0.02 when the DSF was uncooled and ∼0.04 when cooled. Thus, it is experimentally confirmed that fiber cooling is effective for improving the visibility of a two-photon interference fringe.
I then inserted a 30-km DSF spool between the bandpass filter and the interferometer in both the signal and idler arms, and undertook a two-photon interference experiment. The result is shown in Fig. 3. µ s and µ i were again set at around 0.05 and 0.06, respectively.
Squares show the coincidence rate per start pulse and x symbols show the idler count rate as a function of interferometer temperature. The average count rate for the signal was ∼430 Hz.
The average coincidence rate at the peak of the fringe was as low as ∼0.3 Hz, which resulted in a long measurement time (the measurement shown in Fig. 3 took more than three hours to complete). The visibility of the fringe that includes accidental coincidences was 75.8%, which exceeds the value associated with the violation of Bell's inequality (∼ 71%). I would like to emphasize that the result presented here sets a new record for long-distance distribution of quantum entanglement.
In summary, I have reported the first experimental generation of time-bin entanglement using a cooled fiber. A significant improvement in the visibility was observed by cooling the DSF with liquid nitrogen. As a result, entangled photons were successfully distributed over 60-km (30 km x 2) fibers with a fair visibility of 75.8%. The results show that a 1.5-µm band entanglement source based on a cooled fiber is a promising technology for realizing advanced quantum information systems over optical fiber networks.
The author thanks K. Inoue for helpful comments and T. Honjo for help in making the measurement software. This work was supported in part by National Institute of Information and Communications Technology (NICT) of Japan.