Low-latency switchable coupler for photonic routing
Photonic switching is a key building block of many optical applications challenging its development. We report a 22 photonic coupler with arbitrary splitting ratio switchable by a low-voltage electronic signal with 10 GHz bandwidth and tens of nanoseconds latency. The coupler is based on a single Mach-Zehnder interferometer in dual-wavelength configuration allowing real-time phase lock with sub-degree stability. The coupler can be set to any splitting ratio from 0:100 to 100:0 with the extinction ratio of 26 dB. We show 100 ps switching between various coupling regimes such as balanced 50:50 beam splitter, 0:100 switch, and a photonic tap. Furthermore, using the reported coupler, we demonstrate for the first time the perfectly balanced time-multiplexed device for photon-number-resolving detectors and also the active preparation of a photonic temporal qudit state up to four time bins.
Fast splitting, switching, and routing of light are critical tools of photonic technology in the rapidly developing fields of optical communication and optical information processing including demanding applications like quantum cryptography Lukens et al. (2018), neuromorphic computing Shen et al. (2017); Cheng et al. (2017), photonic simulations Schreiber et al. (2012), scalable boson sampling Motes et al. (2014); He et al. (2017), universal quantum computing Takeda and Furusawa (2017), and photon counting Tiedau et al. (2019). In the last few years, high-efficiency single-photon generation has been demonstrated employing active time multiplexing Xiong et al. (2016); Mendoza et al. (2016); Kaneda and Kwiat (2018). Optical switching has also facilitated a recent pioneering demonstration of postselection-loophole-free violation of Bell’s inequality with genuine time-bin entanglement Vedovato et al. (2018).
A basic routing device switches the input signal between two or more output ports. Such on-off switches find their application in optical networks and data centers. They typically require a high extinction ratio (low crosstalk) but not ultra-high-speed performance, with 1 s response being sufficient for the vast majority of switching systems Cheng et al. (2018). The most advanced modulation, processing, and detection schemes, however, require ultra-low latency between the control signal and the switch response, together with a large bandwidth and high extinction. Furthermore, the continuous tunability with arbitrary splitting ratio is required Takeda and Furusawa (2017); He et al. (2017); Lukens et al. (2018). The universal routing device would also be able to coherently superpose two incident signals acting as a coupler switchable between various splitting ratios.
Various switching techniques are used like liquid crystal devices, microelectromechanical systems, semiconductor optical amplifiers, and Mach-Zehnder interferometers (MZI) with electro-optic phase modulator (EOM). The MZI operates as a variable beam splitter and allows the continuous tunning of its splitting ratio. The main drawbacks of MZI based switchable coupler are the extinction ratio limited by visibility of the MZI and its phase instability causing the drift of the splitting ratio. The visibility optimization is particularly challenging in the case of a spectrally broad signal, like short optical pulses and the majority of single-photon sources, and with dispersion elements utilized as a part of the MZI. The phase stability issue can be addressed by active phase locking, though it is notoriously uneasy at a single-photon level or with fluctuating input signal. The deteriorating effect of manufacturing imperfections on the MZI visibility can be diminished by cascading more MZIs, which has been demonstrated recently Miller (2015); Wilkes et al. (2016); Liu et al. (2017). Unfortunately, increasing the number of MZIs per single routing step decreases the stability of the whole system significantly and makes the phase stabilization even more difficult.
In this Letter, we present a low-latency switchable coupler employing a high-visibility fiber MZI. An auxiliary light beam is injected to the MZI, co-propagates with a single-photon signal, and enables real-time continuous phase locking with a unique sub-1 deg long-term stability. The picowatt-level auxiliary beam is wavelength separated with virtually no crosstalk to the signal. We demonstrate fast switching of the coupler by changing its operation between any splitting ratios in a fraction of nanosecond. The splitting ratio is controlled using low-voltage electronic signal compatible with the output of the majority of photodetectors, which is crucial for utilization of the coupler in optical feedback and feedforward circuits. We show outstanding performance of the reported device in two demanding applications, namely a balanced time-multiplexed device for photon-number-resolving detectors and an active preparation of a photonic time-bin encoded 4-level state with time-bin separation in the range of tens of nanoseconds.
Ii Experimental methods
The developed coupler is based on fiber MZI where the splitting ratio can be switched by changing an optical phase using an integrated waveguide EOM, see Fig. 1. The MZI was implemented to have high interference visibility resulting in high extinction ratio, exceptional phase stability enabling a long-term continuous operation, and fast modulation with low overall latency between a control electronic signal and the response of the switching. In what follows we will discuss these design goals and the corresponding features of the presented solution.
When operated as an on-off switch, the signal injected in the first input port is reproduced by an ideal MZI either at its first output port with no signal at the second one (ON state) or at the second port with no signal at the first one (OFF state) for the phase set to 0 or , respectively. The corresponding constructive or destructive interference is not perfect under real conditions and the switching has limited extinction ratio directly given by the interference visibility. The desired high visibility operation requires perfect indistinguishability of interfering optical signals at the output of the MZI in all relevant degrees of freedom, namely path, spatial mode, polarization, time, and frequency. The path information is reduced by making the signals in both arms of the MZI of the same intensity by slight tuning of losses. Also, the splitting ratio of the output fiber splitter has to be close to 50:50. Spatial distinguishability is inherent in single-mode fiber implementation. Polarization-maintaining fibers are utilized throughout the setup to keep the polarization constant in time and the same for both the MZI arms. All connector splices are made to minimize polarization crosstalk between the fiber axes, and additional polarization filtering is also included. The MZI arms are carefully adjusted to have the same optical path length using tunable air gaps. The difference between the MZI arms is further minimized by placing the components symmetrically in both the arms. This is particularly important for the components exhibiting strong dispersion such as integrated EOMs and dispersion compensators. Having all these degrees of freedom under control and precisely adjusted, we have reached the interference visibility of 99.55% in the optical bandwidth of 3 nm around 810 nm (equivalent to pulse length down to 300 fs). It results in switching with the extinction ratio of 26 dB for continuous as well as pulsed optical signals.
A usual problem of interferometric circuits is a random phase fluctuation caused by temperature changes, airflow, and vibrations. These adverse effects can be partially eliminated with passive methods such as thermal stabilization and acoustic and vibration isolation. An active stabilization is necessary to keep the phase fluctuation small enough for advanced applications. Particularly, the long-term switching operation with the ultimate extinction ratio requires the phase stability better than 1 deg. Comparing the output signal to a fixed setpoint and adjusting the phase based on the error signal represents a common solution in the case of the strong classical signal. However, such an approach is fundamentally limited by a photocounting noise when a weak optical signal is used Pulford et al. (2005). Inherently stable interferometers Mičuda et al. (2014) or repeating the stabilization and measurements steps Miková et al. (2012) are possible solutions at the single-photon level. The best performing technique uses an auxiliary strong optical reference co-propagating with the signal through the MZI and enabling the real-time phase lock. In fibers, the reference and the signal overlap spatially and have to be multiplexed in different degree of freedom with the wavelength being the typical choice Carvacho et al. (2015). We utilize 100 pW reference at 830 nm obtained from a spectrally and single-mode filtered luminescent diode. Its large spectral width of 10 nm allows for locking not only the optical phase but also the autocorrelation maximum, which signifies zero relative optical path of the interferometer. The reference is separated at the output of the MZI using a sequence of a polarizing beam splitter (PBS), quarter wave plate (QWP), and a 3 nm interference filter centered at 810 nm (IF) acting together as wavelength selective optical isolator. The transmitted signal is detected by single-photon avalanche diodes while the reflected reference impinges an ultra-sensitive photodiode (PD) with NEP=9 fW/. The amplified photodiode signal from both the MZI output ports is processed by a custom proportional-integral-derivative (PID) controller with the setpoint set at the maximum fringe slope and adaptively corrected for amplitude fluctuations of the reference. The produced electronic error signal is fed to a fiber stretcher (FS) with the dynamic range of 35 m Nováková et al. (2019). The overall stabilization bandwidth of 1 kHz given primarily by the response of the stretcher has been reduced to approximately 30 Hz for some measurements to further improve the signal-to-noise ratio of the lock. The crosstalk from the reference to the signal is below 10 photons/s (i.e. photon crosstalk probability below for 100 ns time bin). To manipulate the relative phase between the reference (locked to ) and the signal, we insert in the MZI a custom-made dispersion compensator formed by two tilted high-dispersion SF10 glass plates.
The reaction time, also termed latency, of the realized switchable coupler is given by the propagation delay of the optical signal from the input to the output of the device and, also, by the response of the phase modulator employed. The coupler is approximately 9 m long, which corresponds to the delay of 45 ns. It can be decreased below 20 ns easily by reducing the pigtail length of the constituent components and shortening the fiber stretcher sacrificing its dynamic range. Further decreasing the latency of the device seems to be superfluous especially when triggered by free-running single photon detectors considering their typical recovery time 10-30 ns. The waveguide integrated LiNbO EOM features 10 GHz bandwidth with negligible impact on the overall latency. The modulator is controlled by voltage signals within 0 – 2.2 V using electronic pulse generator with 3.5 ns pulse width and 0.4 ns rise time for the response characterization, and a field-programmable gate array (FPGA) with 10 ns clock period to control complex measurement protocols. The FPGA was supplemented with a GaAs FET 6-bit digital attenuator with the 0.5 dB step to generate pulse sequences used for switching the coupler between arbitrary splitting ratios.
Iii Results and discussion
We have verified the stability of the splitting ratio during continuous wave operation and characterized the time response of the coupler to a fast-changing control signal, to demonstrate the outstanding performance of the developed coupler. The long-term stability was characterized by acquiring the output intensity for various fixed splitting ratios, particularly the most sensitive 50:50 ratio. Noise spectrum of the coupler transmittance shows 60 dB improvement for the actively real-time stabilized coupler. Allan deviation reaches the value of for sub-second acquisitions times (affected by detector fluctuations) and exhibits a plateau at for longer measurement durations (equivalent to phase stability of 0.6 deg).
The time response was evaluated by setting a fixed initial splitting ratio and sending an electronic control pulse to the coupler. The switching process was observed at the output ports while the single-photon level signal was injected in the first input port of the device. The measurement was repeated many times due to the random nature of the photon detection process, and all detection events were recorded on a time-tagger. The accumulated photon-counting histograms are shown in Fig. 2 for various initial and target splitting ratios to demonstrate arbitrariness of the switching. The data are depicted without corrections, except for SPAD afterpulses subtraction (maximum 1% of the signal) and normalization, to show the temporal evolution of the transmittance and reflectance. The switching speed determined as the rise time (10%-90%) of the measured histograms is 0.7 ns, though the actual response of the coupler switching is much faster. The measurement is affected by the SPAD jitter (0.3 ns), the rise time of the electronic control pulse (0.4 ns), and a resolution of the time tagger (0.16 ns). After correcting for these contributions, the rise time of the coupler switching is estimated to be less than 100 ps, which is compatible with the integrated EOM speed of 10 GHz.
The input optical pulse can be multiplexed in many time bins when reflected part of the signal is fed from the output of the coupler to its input to create a loop, as shown in Fig. 3(a). Electronic control pulses applied to the EOM have to be synchronized with the optical pulse repeatedly passing the coupler. This scheme follows the proposal of a time-multiplexed device for photon-number-resolving detectors Banaszek and Walmsley (2003). Fixed splitting ratio couplers are typically utilized, which yields non-uniform probability distribution of finding a photon in individual time bins Řeháček et al. (2003). Recently, an advanced scheme was experimentally verified, employing a binary switch based on a free-space Pockels cell with the latency of 2.4 s corresponding to a fiber delay loop length of 480 m Tiedau et al. (2019). Employing the low-latency coupler reported here, we were able to decrease this delay to 60 ns corresponding to a 12 m long fiber, i.e. a direct connection between the output and input pigtails of the coupler.
The overall loss of the coupler and the loop represents the main limitation of a photon-number-resolving loop-detector, as the signal is diminished in each cycle in the loop. The extinction ratio of the coupler determines the minimum probability of releasing a photon before the first full cycle. Here, we have focused on the extinction ratio and latency of the coupler and not performed an extensive loss optimization; hence the total loss during a single cycle is approximately 80%. It limits the multiplexing to four balanced time bins, see Fig. 3(b). Using the similar fiber architecture with ultra-low loss components, the loss could be decreased down to approximately 50% with the main contribution stemming from the integrated EOM, which corresponds to 8 balanced round trips. The overall loss slightly below 10% can be reached using a free-space MZI with low-loss components and free-space broadband electro-optic phase modulator. This configuration requires high-voltage driving and would sacrifice other parameters except losses. We estimate time multiplexing to 30-40 of non-saturated equiprobable channels to be ultimately possible.
The reported switching protocol can be generalized to arbitrary time multiplexing. We demonstrate full control over the amplitude of the individual time bins, see Fig. 3(b-g) depicting several examples of time-bin encoded 4-level optical system. The tunable routing of the input signal to the resulting time bins can be complemented by their arbitrary phase modulation using EOMs in both the MZI arms. Starting from single photon input, such the routing represents an efficient way of preparing a photonic multi-level system (qudit). A second switchable coupler would be needed for the qudit analysis at the receiver.
We have presented the 100 ps switchable coupler optimized for routing faint optical signals and single photons. The measured overall latency of the coupler is 45 ns with a possibility of reduction below 20 ns, which is comparable with the recovery time of the state-of-the-art single-photon detectors. We have verified full tunability of the splitting ratio from 0:100 to 100:0 with the exceptional extinction of 26 dB and unparalleled long-term stability of one part in 10,000. We have reached for the first time the balanced operation of loop-based photon-number-resolving detector exploiting the full control over the splitting ratio of the developed coupler. Furthermore, we have demonstrated the deterministic preparation of photonic time-bin four-level qudit with a clock cycle of 60 ns using the presented coupler and a single delay loop. We envision the use of the reported device in advanced feedback and feedforward based schemes of electro-optical control of light, where a detection of a fraction of the light signal changes the splitting ratio of the remaining signal. The low-latency switchable coupler is the key device instantly applicable in a vast number of applications such as time-multiplexed single-photon sources Mendoza et al. (2016), photon-number-resolving detectors Tiedau et al. (2019), and various time-bin encoded communication protocols Vedovato et al. (2018) including quantum key distribution Lukens et al. (2018) and hyper-entangled states preparation and measurement Prilmüller et al. (2018).
Czech Science Foundation (project 17-26143S); MEYS and European Union’s Horizon 2020 (2014-2020) research and innovation framework programme under grant agreement No 731473 (QuantERA project HYPER-U-P-S No 8C18002); Palacký University (project IGA-PrF-2019-010).
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