1. Introduction

Optical interferometers have been used for a wide range of applications [1–7], including precision measurement technologies and frequency standard disseminations. The long-armed fiber-optic interferometer is of particular interest in the fields of quantum cryptography and quantum communications [8,9]. While most applications do only require short-armed interferometers [10], some of the proposed protocols of quantum key distribution rely critically on interferometric effects [11–13], and the development of a long-armed interferometer, by extending the reach of communications, is essential for delivering such protocols to real-world applications. Some quantum repeater schemes also require the development of a long-armed interferometer [14–22]. However, various environmental effects such as thermal, mechanical, and acoustic disturbances make it difficult to stabilize the interference, especially in a long-armed interferometer made of optical fibers.

On the other hand, most quantum communication protocols need a stable operation of the interferometer at extremely low light intensity; that is, at the single-photon level. Quantum information is usually carried by the single-photon level signals that travel through the quantum channel. The phase reference information, as well as the clock synchronization and the classical data information, is carried by the strong light signals that travel through the classical channel. When the quantum and the classical channels are multiplexed into a single fiber using the wavelength-division multiplexing technique, it is hard to separate the quantum channel from the classical one because a small amount of photons induced from the Rayleigh and Raman light scattering in the classical channel can severely degrade performance of the quantum channel [23].

Both the stabilization of a long-armed fiber interferometer and the stable operation of the interferometer at the single-photon level present many technical challenges. The motivation of the current work is to develop a single-photon interference stabilization technique in a long-armed interferometer made of single-mode fibers, targeting future experiments on quantum key distribution protocols in which interferometric effects play a crucial role. This differs from previous single-photon interference experiments in which the arm lengths of the interferometer are usually as short as several meters [24,25].

In this paper we report on single-photon interference experiments in a Michelson-type interferometer built with two 6-km-long fiber arms, as well as on the active stabilization of the interferometer. The signal and the reference light share the same optical paths in the interferometer and are (de-) multiplexed using the wavelength-division multiplexing technique. A real-time active feedback control technique is developed and applied for the reference light to maintain the optical path length difference between the two arms. The signal light can be locked in a stabilized interference state with an arbitrarily chosen phase difference. We demonstrate a stable operation of single-photon interference in the stabilized interferometer. The high visibility obtained in the single-photon interference shows that practical implementation of various quantum protocols are feasible.

2. Experimental setup

Figure 1 shows the experimental setup. The Michelson-type interferometer was specially designed for future experiments on quantum cryptography protocols. A few fiber optic components not shown in Fig. 1 were additionally inserted into the horizontal arm of the interferometer for future experiments. We had verified that those hidden components had no considerable effect on the present experiments except that optical losses and path lengths were increased because of them.

 

Fig. 1 Schematic of the experimental setup. LD, distributed feedback laser diode; OVA, optical variable attenuator; WDM, wavelength-division multiplexer; Cir, optical circulator; BS, 50/50 fiber-optic beam splitter; FST, fiber stretcher; ODL, optical delay line; SMF, single-mode optical fiber; FM, Faraday rotator mirror; D1 and D2, linear photodetectors or single photon detectors; D3, linear photodetector.

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Each arm of the interferometer was made of a spool of 6-km-long single-mode optical fiber. When measured without the spool, the length of each arm was about 40 meters, including the hidden components. At the initial stage of experiments, the length difference between the two arms was manually adjusted with an optical delay line (ODL) so as to be on the order of 1 mm, which is much less than the coherence lengths of the signal and the reference lights. An optical variable attenuator (OVA) was inserted into the vertical arm to balance the optical losses between the two arms. The total optical round trip loss from the input port of 50/50 beam splitter (BS) to the entrances of detectors D1 and D2 was about 17 dB for each of the 6 km long arms. We placed the fiber spools inside a polystyrene box to avoid fast thermal fluctuations caused by ambient air flows in our laboratory environment. The other components, except the light sources and the photodetectors, were placed inside another box made of styrofoam and acrylic plates.

It has been known that fluctuations of the phase difference and the polarization alignment between two interferometer arms are two major factors to be considered when attempting to stabilize a fiber interferometer. However, since the polarization fluctuation is generally not so fast and is quite stable compared to the phase fluctuation [22], we focus on the control of phase fluctuations in the present work. For the setup shown in Fig. 1, a polarized light wave entering the BS is split into two light waves that travel along two different arms. When the split light waves reenter the BS after reflection from the two FMs, they have an equal polarization state, orthogonal to the initial polarization. Thus, the polarization fluctuations can be automatically compensated for by the use of FMs if they are not too fast [26,27].

Two distributed feedback laser diodes (LDs) operating at 1550.12 nm (linewidth 2 MHz) and 1552.93 nm (linewidth 0.5 MHz) were used at continuous wave modes for the signal and the reference light sources, respectively. The signal light intensity was adjusted by using an optical variable attenuator (OVA) to fit the purpose of each experimental run. However, for all of the experiments presented in this paper, fixed power of −28.70 dBm was used for the reference light when measured at the output port of the circulator (Cir) that was connected to the input port of the BS.

We used several wavelength-division multiplexers (WDMs) to (de-) multiplex the signal and the reference light. The WDMs were comprised of two serially connected dense wavelength-division multiplexers (DWDM) that were centered at 1550.12 nm with 100 GHz channel spacing (channel isolation 50 dB). Thus, the overall isolation level between the signal and the reference light was about 100 dB. The signal light was detected by photodetectors D1 and D2. We had at our disposal two types of the photodetectors: linear photodetectors and single photon detectors (SPDs), for the detection of the signal light depending on its intensity. On the other hand, the reference light was detected by a linear photodetector (D3) only. The output photocurrent of the D3 (New focus, 2053FC) was fed into the feedback control system composed of a real time controller (NI, PXI-8106), an analog in-out card (NI, PXI-6259), and an NI-LabView-based feedback control algorithm. Thus, the feedback control system monitors the intensity of the reference light, and drives a fiber stretcher (FST) to control the phase difference of the reference light between the interfering arms.

We made the FST using two identical piezoelectric tube transducers (piezo-tubes) and a single-mode bare optical fiber. The resonant frequency of the piezo-tube was 22 kHz in the radial direction [28]. We manually wound a bare fiber of about 20 meters onto the two piezo-tubes sequentially. An epoxy-type adhesive was used to prevent the bare fiber from slipping on the surfaces of the piezo-tubes. We drove the FST by applying an equal voltage of up to 10 V to each of the piezo-tubes. When the two piezo-tubes were driven together, the half-wavelength voltage $V_{\pi }$ for the reference light was 67 mV. Thus, optical path delay range of the interferometric stabilization system was about 116 μm.

The phase difference ${\phi }_r$ of the reference light is obtained by measuring the photocurrent $I_r$ of the D3,

The signal light has an interference phase ambiguity even though the phase difference of the reference light is kept fixed at a preset value. That is, given the optical path difference $\Delta L$ of the interferometer, the phase differences of the signal and the reference light have the following relation:

3. Experimental results

We first demonstrated the active stabilization of phase fluctuation for the 6-km-long fiber interferometer. Figure 2(a) shows a typical measurement result of the phase noise of the signal light for a stabilized condition [29]. In this measurement, we adjusted the power of the signal light to −8.79 dBm when measured at the input port of the BS. A linear photodetector (New Focus, 1811) was used for D1, and its output photocurrents were sampled at 100 kHz with a data acquisition card (NI, PCI-6259). In Fig. 2(b) we show the distribution of the phase noise. The best-fit curve is a Gaussian distribution with a width σ = 0.06 rad. This phase noise implies that the optical path length fluctuation is maintained as small as about 15 nm between the 6-km-long interfering arms. The expected interference visibility $V=\exp (-{\sigma }^2/2)$ is given at 99.8%, provided that no additional noise is included [22]. We verified that the stabilized condition could be maintained for about 20 minutes on average before the optical path delay range of 116 μm was reached.

 

Fig. 2 A typical example of active stabilization for the 6-km-long Michelson-type fiber interferometer. (a) The phase noise of the signal light. (b) The distribution of the phase noise of (a).

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We performed single-photon interference experiments in the stabilized 6-km-long fiber interferometer. Two SPDs (idQuantique, id201) made of InGaAs/InP avalanche photodiodes were used for signal light detection at D1 and D2, respectively. Each of the SPDs was operated in a gated Geiger mode with an internal trigger rate of 1 MHz, a gate window of 2.5 ns, and a quantum efficiency of about 3.5%. The dark counts of the SPDs with a dead time of 1 μs were measured at 7.5 ± 2.6 Hz and 7.8 ± 2.7 Hz, respectively. When the reference light was injected alone, the count rates were slightly increased to 8.8 ± 2.8 Hz and 9.1 ± 3.1 Hz because of the Raman scattering. We reduced the power of the signal light to −63.88 dBm at the input port of the BS, which corresponds to 8 photons/gate. The count rates of the SPDs were increased to 32.7 ± 5.5 Hz and 29.6 ± 5.1 Hz, respectively, if the signal light was injected alone and the Faraday rotator mirrors were replaced with 50 dB attenuators to avoid reflections of the signal light at the ends of the interferometer arms. These increases of the count rates were largely attributed to the Rayleigh backscattering in the fibers, as the reflections from other optical components were negligible. Thus, we could expect noise counts of the SPDs at D1 and D2 to be about 34.0 ± 5.7 Hz and 30.9 ± 5.5 Hz, respectively, including the dark counts and the error counts caused by stray photons. We could also expect a maximum count rate of about 5600 Hz after interference by considering the trigger rate, the quantum efficiency, and the optical round trip loss.

Figure 3 shows results of the single-photon interference experiments. In Fig. 3(a) we show the count rates measured at D1 and D2, respectively, for a stabilized and a nonstabilized condition. The raw visibility was measured at 98.4 ± 0.2% for stabilized conditions. The net visibility obtained after subtraction of the noise counts was 99.5 ± 0.1%, which is consistent with the phase noise of 0.06 rad. Figure 3(b) demonstrates the stabilized evolution of the count rates for different chosen values of the phase difference ${\phi }_s$.

 

Fig. 3 Single-photon interference experiments in the 6-km-long fiber interferometer. (a) Measured count rates for a stabilized and a nonstabilized condition. (b) Stabilization of the single-photon interference for different chosen values of the phase difference between two interfering arms.

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4. Conclusion

In conclusion, we have demonstrated the active stabilization of single-photon interference in a long-armed fiber interferometer. The interferometric stabilization system showed a phase stability of 0.06 rad for the Michelson-type interferometer made of 6-km-long fiber spools. A high visibility of more than 98% was obtained (without subtracting the noise counts) in the single-photon interference experiments using a weak coherent light signal. While most quantum communication experiments employing fiber interferometers have already been demonstrated, a range of the proposed quantum protocols requiring long-armed interferometers still present technical challenges. Our results suggest experimental realizations of such quantum protocols are feasible.