1. Introduction

In quantum communications, information may be encoded in a variety of degrees of freedom such as polarization, phase, angular momentum, etc. The two main qubit degrees of freedom which are utilized in fiber are based on optical polarization and phase. Polarization is an excellent qubit for free-space, though in fiber optical networks several polarization-based effects such as polarization dependent loss (PDL) and polarization mode dispersion (PMD) make its use more challenging. Even if PDL and PMD are not a problem, active polarization stabilization or tracking of the entire quantum communications channel is required to successfully transmit polarization qubits [1]. To avoid many of the difficulties associated with polarization impairments, the phase difference between adjacent pulses or time-bins has been used in both entanglement-based and prepare-and-measure quantum communications experiments [2–11]. The temporal separation between pulses is typically much shorter than the time scale of the fiber perturbations, which leads to natural resilience to channel impairments [2,3]. These phase-based protocols can be configured in a polarization insensitive way, but they do require alignment of optical interferometers for qubit analysis. This is an advantageous trade-off, as the interferometer lengths requiring stabilization are many orders of magnitude shorter than the quantum channel itself. Optical interferometers can be implemented in either free-space or wave-guided configurations, however, fiber-based interferometers are more convenient.

Passive stabilization techniques for phase-based qubits in prepare-and-measure systems have been demonstrated, including the “plug and play” architecture [9]. However, as noted by Yuan and Shields [8], the optical pulses must make a round trip between the users and hence this architecture’s performance will be limited relative to one-way systems. Therefore, the development of active stabilization techniques for one-way quantum communications systems is of great importance. Reported techniques include active thermal management of photonic integrated circuits [4] or adding ports and single-photon detectors to interferometer outputs for tomography [5]. Most of the active techniques involve the injection of an additional reference signal, usually at a wavelength differing from the quantum signal, which is monitored and used to cancel relative path length drifts in the interferometers [7,9,12–15]. Though effective, adding an entirely dedicated control wavelength to the system requires additional optics that results in more loss, and does not necessarily ensure the system can be stabilized during quantum measurements.

We describe a novel scheme for actively locking the relative phases of three fiber-based time-bin interferometers in a manner suitable for quantum communication systems. In this system, we utilize time-bin entangled photon pairs, reusing the entangled source pump to stabilize the interferometers. This technique adds only two additional low speed classical detectors, avoiding undesirable lossy optics in the quantum channel or extra single-photon detectors. Furthermore, the interferometers are continuously stabilized even during quantum communications, thereby improving potential throughputs by eliminating the need to stop transmission to allow for a tuning period, for example as in [10]. This approach leverages work in the coexistence of classical and quantum signals [6] as the pump pulse is maintained at a relatively large power level in all parts of the system; in this case there are approximately eight orders of magnitude difference between the quantum and classical signal strengths. Interestingly, despite the presence of the relatively intense co-propagating pump pulse, the transmitted entangled photons are only slightly degraded over the 50 km end-to-end link. This approach to interferometer stabilization was first introduced briefly over a single 5 km fiber [16]. In this paper, we describe the technique in greater detail and extend it to stabilize two independent fiber links over a total end-to-end length of 50 km and measure the visibility of the entangled pair.

2. Experimental setup

The experimental setup is shown in Fig. 1. One source and two analysis fiber-based Michelson interferometers [17] are utilized to generate and analyze time-bin qubits. Each interferometer employs a tunable delay line (General Photonics VDL001-35-60) in one arm (τ₀, τ₁, τ₂) so the relative path-length delays of all three interferometers can be matched to each other. The delay lines provide a continuously tunable delay from 0 to 600 ps with a readout resolution of 0.1 ps. The τ₁ and τ₂ delays are also varied to provide the local phase shifts which enable two-qubit analysis. A piezo-based fiber phase shifter in each interferometer tweaks the phase bias in the interferometer to provide the active stabilization. Details on these mechanisms are discussed below.

 

Fig. 1 Experimental setup for time-bin qubit generation and analysis. The two analysis interferometers are stabilized with respect to the source interferometer. MLL: Mode-locked laser, FRM: Faraday rotator mirror, DSF: dispersion-shifted fiber, PBS: polarization beam splitter, SMF: single-mode fiber; SPD: Single photon detector; PI: proportional-integral.

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The source time-bin interferometer (TBI) splits picosecond pulses from a fiber-based passively mode-locked laser (~1550 nm, ~50 MHz repetition rate) into two pulses that are time delayed by ~5 ns with a relative phase shift of ϕ₀. The double pulses pump a short length of dispersion-shifted fiber (DSF) which creates signal-idler photon pairs. The pump power is carefully chosen to minimize multi-photon pair emission (measured mean photon number at source output is ~4·10⁻³ per pump pulse). Photon pairs are created with equal probability in either pump pulse, corresponding to early and late time-bins. To reduce accidental coincidences arising from spontaneous Raman scattering in the DSF, the fiber is cooled by submersion in liquid nitrogen [18]. A polarizer is also utilized to suppress cross-polarized spontaneous Raman noise from the source DSF. A Finisar Waveshaper optical filter routes the signal photons to the first 25 km fiber spool (SMF₁ in Fig. 1) and the idler photons to the second 25 km fiber (SMF₂ in Fig. 1). The signal and idler photons are chosen approximately ± 400 GHz ( ± 3.2 nm) from the central pump wavelength. The 3 dB bandwidths of the pump, signal, and idler are ~1 nm. The pump is also split and injected into each fiber along with the quantum signals. The Waveshaper provides ~30 dB of additional loss to the pump only, so that approximately −42 dBm of pump power enters each of the two fiber spools.

Previous experiments used fiber with low dispersion at the transmission wavelengths to minimize the pulse spreading and maintain good visibility at the output [7]. In contrast, the 25 km fiber spools used here contain standard single-mode fiber (Corning SMF 28) with ~17 ps/nm/km dispersion at 1560 nm and total loss per spool of ~6 dB. No measures were taken to thermally isolate these fibers spools from the lab environment. As the pulse bandwidths in our experiment are relatively small (corresponding to pulsewidths of a few ps) and the time-bin separation (~5 ns) is sufficiently larger than the pulse width, inter-time-bin crosstalk arising from chromatic dispersion is avoided.

After passing through the fiber, the signal and idler photons, along with the co-propagating pump, pass through the analysis time-bin interferometers. At this point both the signal and the pump (from SMF₁) accumulate phase shifts of ϕ₁, and the idler along with the pump (from SMF₂) accumulate phase shifts of ϕ₂ from these interferometers. The pump pulses are filtered from the interferometer outputs using a double cascade of standard telecom thin-film filters with 0.5 dB and 3 dB bandwidths of ~0.9 nm and ~1.1 nm, respectively, providing greater than 80 dB of pump suppression. The filtered pump pulses are routed to classical photodetectors while the signal and idler photons are measured using avalanche photodiode single-photon detectors (SPD). The experiments employ Princeton Lightwave InGaAs Geiger mode APDs. At a trigger rate of 50 MHz, the detection efficiencies are approximately 20% on both SPDs. The corresponding dark count probability of each detector is ~3·10⁻⁶ /ns, and the gate duration is set to 1 ns. The detection events from the SPDs are then analyzed in coincidence. Note that all of the interferometers relative phase shifts, ϕ₀, ϕ₁, and ϕ₂ will wander due to thermal drifting when left free-running. Our stabilization system locks the analysis interferometers’ phases to the slowly varying source interferometer phase ϕ₀ so that its effect on the coincidence counting rates is suppressed.

The stabilization control system injects a low-frequency (~1 kHz) and low-amplitude dither signal into the source interferometer piezo controller, which adds a small phase modulation in addition to the quasi-static ϕ₀. This low-frequency modulation should be chosen high enough so that the control system integration time is sufficiently shorter than the time scale of the phase fluctuations, which are typically on the order of a second in our fiber-based interferometers. Because the path length delays in each TBI are significantly greater than the pulse width, three copies of the pump pulse will exit the analysis TBIs. The second timeslot is where the quantum two-photon interference is observed and is exclusively selected using the SPD gating window. The pump pulses exhibit classical interference in the second timeslot, and the phase dither from the source TBI is converted into an amplitude modulation which is detected by the classical photodetectors. For simplicity, the classical detector integrates all pump pulses; the DC offset resulting from the first and last pump pulses is later rejected in the control system. The closed-loop control system monitors the amplitude of the 1 kHz dither signal using synchronous demodulation, which is accomplished by mixing the dither tone clock with the recovered photodetector signal, both of which are locked in phase. The signal is integrated over a 34 ms window, which was sufficiently short to track and compensate fiber phase fluctuations and provide stable, high visibility measurements. The phase shifters in the analysis TBIs are adjusted appropriately to minimize the recovered dither signal amplitude, which serves as an error signal in our control loop.

A standard proportional-integral (PI) control [19] can be used here because the dithering process produces a signal proportional to the slope of the cascaded interferometer output. This signal goes to zero at either the minimum or maximum of an interference fringe and changes sign on either side of it. Also, given that the control algorithm is simply minimizing the recovered dither tone at either the minimum or maximum as opposed to setting it to a fixed value, no power calibration is required. The resulting pump signal can be configured to either a maximum or minimum of an interference fringe by setting the closed-loop proportional feedback gain to either a positive or negative value, respectively. The result is that by adjusting the piezo controllers in the interferometers, the cascaded source-signal and source-idler TBI pairs are simultaneously maintained at either a minimum or maximum transmission at the pump wavelength. However, the transmission of the TBI pairs at the signal and idler wavelengths will be different than that for the pump wavelength, but stabilized to a constant value. This constant value is adjusted via a different control to sweep out TPI fringes. Specifically, the relative phase shift between the signal and idler interferometers is varied by adjusting the interferometer time delays and is described further below. The result is repeatable, stable coincidence counting rates for the entangled signal/idler pairs for any given TPI analysis setting.

The coincidence counting rate for time-bin entangled pairs is given by the following expression [3,4]:

where ${\tau }_0$, ${\tau }_1$, and ${\tau }_2$ are the absolute time delays in the pump, signal-analysis, and idler-analysis interferometers respectively, ${\varphi }_0$, ${\varphi }_1$, and ${\varphi }_2$ are the corresponding absolute phase shifts, and ${\omega }_S$, ${\omega }_I$ are the signal and idler frequencies. When the control system is configured to lock the pump-signal and pump-idler interferometers for maximum interference at the pump frequency (${\omega }_P$), the following conditions are held:

As a result, by adjusting the delay line in either of the analysis interferometers, the relative phase between the signal and idler analysis interferometers may be varied in order to scan the two-photon interference fringe. The phase resolution of the TPI scan depends on Δω and the minimum signal-idler relative time delay possible with the delay lines. In the experiment, the phase resolution achievable for the TPI fringe scan is 0.2 radians. Furthermore, in order to ensure accurate visibility measurements, the pulse temporal width should be greater than the time delay scanning range. The observed fringe period is ~2.8 ps, which is less than the estimated pulse width. In order to reduce the possibility of introducing timing distinguishability the interferometer relative delays are the same in the middle of the fringe.

3. Results

The performance of the stabilization system is shown in Fig. 2, which contrasts the stability of the source-signal and source-idler interferometer cascades with the control system feedback first disabled and then enabled. The pump monitor signal amplitude is recovered from the classical detectors followed by synchronous detection at the dither frequency. Without stabilization, the monitor signal amplitude varies considerably with time, which in the 200 second interval shown here, corresponds to a phase drift of ~360 degrees, which makes entanglement visibility measurements under such conditions considerably difficult. By adding modest thermal insulation surrounding the interferometers and enabling the stabilization control system, the phase drift can be minimized to a small fraction of a wavelength as shown in Fig. 2. The standard deviation of the phase stability, which is computed from the recovered monitor signal amplitude, is only 0.2 degrees.

 

Fig. 2 The control system monitor signal when the system is disabled (non-solid lines) and enabled (solid lines). The standard deviation of the control signal with the system enabled indicates 0.2 degrees of phase stability is achieved.

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The discussion of this system was initially reported in [16] over a 5 km single-fiber link, and we now extend these results to 50 km where each half of the entangled pair is transmitted down a different fiber. The extension to 25 km fiber links is significant because this length is very close to where one would expect to observe the maximum impact of Raman scattering from the co-propagating classical pump used for stabilization [6]. The raw counting rates are plotted for both the source output (Fig. 3(a)) in a 50 sec counting interval and the output after transmission through 50 km (Fig. 3(b)) in a 400 sec counting interval. Accidental coincidences are not subtracted.

 

Fig. 3 The two-photon interference fringes measured at (a) the output from the source and (b) after transmission through the 2x25 km fiber channels. The green triangles indicate the singles counting rates, and the blue circles the coincidence counting rates. The solid blue lines are sinusoidal fits to the data.

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In order to measure the TPI, only one analysis interferometer delay needs to be scanned. The other interferometer can also be adjusted if more than one measurement basis is desired; see, for example [20]. The singles counts (green triangles) are plotted and, as expected, show little variation with applied phase shift, though we point out in Fig. 3(b) that two outlier data points can be observed at delays around 112 ps. We believe this was due to an intermittent transient event in one of the detectors during those two measurements, though we note that their overall impact on the coincidence counting rates is negligible. The blue circles show how the coincidence counting rates vary with delay, which is consistent with Eq. (5). The fit to the data collected immediately after the source yields visibility of 91% ± 3%. After the entangled photons propagate over 50 km of fiber, the visibility is 83% ± 5%. Due to fiber loss, the measurement interval is increased from 50 sec at the source to 400 sec after 50 km to have similar statistical errors. The measured visibilities exceed the ~70.7% threshold for entanglement by 7 and 2 standard deviations, respectively. We believe the drop in visibility at the channel output may likely be a result of multiple factors. First, the fiber propagation loss results in decreased coincidence rates relative to constant detector dark count rates, which effectively reduces the measurement signal-to-noise ratio. Second, the dither clock reference traverses a separate path relative to the optical signals, so any relative phase jitter in the long fiber paths could potentially increase the noise floor of the control system. One possible solution to this would be to transport the dither clock over the same fiber paths as the optical signals.

Due to the low peak power of the co-propagating stabilization signal (< 1mW), we anticipate its impact on our visibility measurements to be minimal. We have verified this by measuring the change in singles counts, after the fiber spools, on both of the SPDs with the stabilization signal on and off. The increases in singles counts are approximately 0.2·10⁵ and 0.1·10⁵ (in 400 sec) in the two detectors, which are below 7% of the total singles counts observed. Furthermore, we estimate that propagating the source pump in the transmission fiber adds < 1 accidental coincidence count to each of the coincidence counting rate data points shown above in Fig. 3(b). Thus the source pump should have negligible impact on the measured visibility. This estimate of additional accidental coincidences includes those from spontaneous Raman scattering in the SMF fiber. We note that at a distance of ~25 km in fiber, the accumulated spontaneous Raman power reaches a maximum [6]. This suggests that this stabilization technique can be scaled to longer entangled photon separations without degradation in the visibility from Raman scattering of the stabilization signal.

4. Summary

In summary, we have described a novel technique for stabilizing distributed time-bin entanglement interferometers. This is an essential step in enabling high-availability time-bin qubit-based quantum communications applications. This technique is advantageous in that it reuses the bright pump beam already used in typical χ⁽³⁾-based entangled-photon sources instead of introducing other control signals. Finally, because the entangled source pump is used to stabilize the interferometers, the control signal is always present enabling continual phase stabilization with no quantum communications downtime.