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Abstract
Photonic integrated circuits (PICs) have enabled novel functionality in quantum optics, quantum information processing and quantum communication. PICs based on Silicon Nitride (Si3N4) provide low-loss passive components and are compatible with efficient superconducting nanowire single-photon detectors (SNSPDs). For realizing functional quantum photonic systems, the integration with active phase-shifters is needed which is challenging at the cryogenic temperatures needed for operating SNSPDs. Here we demonstrate a cryo-compatible phase shifter using a low-voltage opto-mechanical modulator and show joint operation with SNSPDs at 1.3 K. We achieve a half-wave voltage of 4.6 V, single-photon detection with 88% on-chip detection efficiency (OCDE) and a low timing jitter of 12.2 ps. Our approach allows for operating reconfigurable quantum photonic circuits with low dissipation in a cryogenic setting.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photonic-integrated circuits (PICs) are widely considered to be an important building block for the advancement of information processing due to their advantages in terms of speed, scalability, and power consumption. Furthermore, in the area of quantum information processing and quantum optics, PICs provide substantial advantages compared to traditional bulk-optical setups and offer alignment-tolerant and interferometrically stable setups [1]. Silicon nitride (Si3N4) has emerged as an attractive platform for CMOS-compatible PICs because of its low absorption over a broad transparency window from ultraviolet (UV) to infrared (IR) wavelengths and a good refractive index contrast [2]. While silicon nitride is very convenient for realizing passive devices, implementing active elements remains more challenging. Phase shifters are essential elements in PICs because they allow for active circuit reconfiguration required for a variety of application areas such as microwave photonics, quantum information processing [3,4] and artificial neural networks [5]. For this reason, they have been studied intensively over the last decade. Thermo-optic phase shifters can be realized on Si3N4 and allow for short interaction lengths in the range of 100 µm but are relatively slow compared to other physical mechanism [6–8]. Importantly, inducing phase shifts in dielectrics via heat is largely incompatible with integrating optical and superconducting elements in close proximity. In addition, the thermo-optic coefficient of silicon nitride, which is essential for efficient modulation, decreases by several orders of magnitude when going from room to cryogenic temperatures [9]. In contrast, modulators based on the electro-optic effect in alternative material platforms are exceptionally fast and allow for operation in the GHz regime with low half-wave voltages and low loss [10–12]. However, due the negligible electro-optic coefficient in silicon nitride, electro-optic phase shifting is not viable on this platform. As an alternative, micro-electro-mechanical system (MEMS) based phase shifters are well suited for a range of applications, as they offer a low half-wave voltage of a few volts, while having loss below 1 dB [13–16]. In addition, MEMS devices require around 100 µm - 200 µm length for appreciable phase shifts and are therefore much more compact compared to electro-optic modulators (EOMs), while outperforming other mechanisms in terms of power consumption [13,16,17].
Detectors that are directly integrated into PICs constitute another crucial building block for holistic chip-scale signal processing solutions. Further, single-photon detectors are highly desirable to expand the number of possible use cases to experiments in quantum optics, photonic quantum computing and quantum communication as well as several classical applications, such as high-resolution light detection and ranging and lifetime imaging. Within the last decade, superconducting nanowire single-photon detectors (SNSPDs) have emerged as a superior detector technology with excellent performance characteristics such as high efficiency, low dark-count rates and low timing jitter, which were also integrated with several PIC platforms [18,19], such as Si3N4-on-insulator [20,21]. Such waveguide-integrated SNSPDs allow for combining state-of-the-art single-photon counting with complex photonic integrated circuit functionalities, while even offering some benefits over conventional SNSPDs, such as ultra-short dead times [22].
The desired integration of both, low-voltage phase shifters and SNSPDs on a single chip limits the choice of phase modulation techniques, because SNSPDs require temperatures well below the critical temperature of the superconducting nanowire for operation (typically around 1-4 K). Because of both, the diminishing thermo-optic coefficient of silicon nitride at low temperatures and thermal heating of nearby superconducting nanowire devices, thermo-optical phase shifters are not suitable for this task [9]. In this respect, MEMS modulators can be operated at cryogenic temperatures without introducing thermal dissipation as they are essentially electro-static devices. However, MEMS devices require more involved nanofabrication processes, posing additional challenges when combined with superconducting materials (such as NbN or NbTiN). For example, the hydrofluoric acid typically employed for releasing mechanical structures can damage superconducting nanowires when direct contact occurs and therefore additional protection layers are necessary.
Here we show how to overcome these challenges and present the integration of an electro-optomechanical phase shifter with a waveguide-integrated SNSPD in a common circuit, enabling joint operation of both devices at cryogenic temperatures. Our phase shifter is based on the mechanical displacement of the rails of a slot waveguide [13]. We show a low half-wave voltage below 5 V at both, room temperature and cryogenic temperatures with a supported modulation frequency up to the MHz regime. For phase shift measurements, we embed the device in a Mach-Zehnder Interferometer (MZI), which yields an extinction ratio (ER) of 30 dB at a wavelength of 1550 nm and an estimated insertion loss of 0.5 dB. We show that the nanofabrication process maintains excellent SNSPD performance yielding high on-chip detection efficiencies (OCDE) of 88% with an exceptionally low timing jitter of 12.2 ps.
2. Device concept
The device consists of one phase shifter and one SNSPD and is shown in Fig. 1(a). Light is coupled into the photonic structures via a grating coupler (P1) optimized for TE-polarized light with a wavelength of 1550 nm. It is then guided to a MZI with a built-in path difference of 120 µm. Two symmetric 1 × 2 Multimode Interferometers (MMIs) are used to split and combine the light with a splitting ratio of 50/50. The phase shifter is placed in the shorter upper arm of the MZI and consists of a free-standing slot waveguide made of two rails, the upper one of which is connected to a free-standing movable gold electrode via a narrow Si3N4 bridge (see Fig. 1(b)). A second, fixed ground electrode is placed nearby. By applying a voltage to the electrodes, the movable electrode is displaced towards the fixed electrode and thereby increases the slot gap size. As shown by the 2D finite element simulation in Fig. 1(c) (COMSOL Multiphysics), the effective refractive index of the slot mode decreases with increasing slot gap width. Therefore, a voltage-induced rail displacement yields a phase shift in the upper arm of the MZI. We use two strip-to-slot/slot-to-strip mode converters [23,24] with a taper length of 10 µm to convert the strip waveguide mode to a slot waveguide mode and vice versa.
Fig. 1. (a) Microscope image of the fabricated device consisting of one phase shifter (PS), one SNSPD and multiple fiber-to-chip grating couplers (P1, P2, R1-R3). (b) False color SEM image of the phase shifter consisting of slot waveguide, bridge, and electrodes (photonics: blue, gold electrodes: yellow). (c) Effective refractive index of the slot waveguide mode as function of the slot gap width. The inset depicts the mode profile of the fundamental TE mode at a wavelength of 1550 nm (rail width of 450 nm and 500 nm, slot width of 150 nm). (d-e) False color SEM images of (d) the top of the SNSPD covered by HSQ (purple) on the waveguide and (e) the tip of the SNSPD. Both SEM images are taken under an angle of 40°. (f) Electronic circuitry for operation of the phase shifter (Vps) and for biasing and reading out the SNSPD.
After combining the light at the second MMI, it is guided to a third 50/50 beam splitter, from which one channel terminates in a second reference grating coupler (P2), where we analyze the MZI signal with a calibrated power meter (Agilent HP Keysight 81635A). The second channel guides the light to a U-shaped 110 nm wide superconducting nanowire on top of the waveguide with an overall detector length of 80 µm (measured from tip to base) (Fig. 1(d) and 1(e)). In this way, the incident light intensity onto the SNSPD can be estimated by measuring the output power at the reference grating coupler P2. Our design comprises four contact pads with a ground-signal-ground-signal (GSGS, common ground) configuration, where the left signal pad is used for applying a voltage to the phase shifter and the right signal pad is connected to the readout circuitry of the SNSPD (Fig. 1(f)). For calibration measurements, we also place some fully passive circuits (consisting of MMIs and grating couplers) on the sample for an estimation of the insertion loss of the various optical elements on the chip.
3. Fabrication
We design our PICs using the open-source Python toolkit gdshelpers [25]. All lithographic steps are performed using electron beam lithography (EBL) with 100 kV (Raith EBPG5150). We employ silicon nitride (330 nm, high tensile stress Si3N4) on buried oxide (3.3 µm) silicon wafers (525 µm), which are diced into 15 µm x 15 µm samples. 5 nm NbTiN are sputter-deposited (Aja Orion 8 UHV) as superconducting layer [26]. We coat the sample with AR-P 6200.13 positive resist (CSAR 62, Allresist). After the development, a Cr-Au-Cr (5 nm, 80 nm, 5 nm) layer stack is deposited, using electron beam physical vapor deposition, followed by a lift-off process. Using the same deposition technique, we cover the sample with 5 nm SiO2 as adhesion layer. We pattern the nanowires with XR-1541-006 negative resist (HSQ 6%, Dow Corning) and, using dry etching with CF4 chemistry, transfer the pattern into the underlying superconducting layer. Subsequently, we cover the nanowires with a second layer of HSQ 6% as passivation layer. We use AR-N 7520.12 negative resist (Allresist) and dry etching with CHF3 chemistry to pattern the photonic structures. The Si3N4 layer is not fully etched but 50nm remain, which is needed as a hard mask during the wet etching step. To pattern the windows where the structures are released, we use AR-P 672.045 positive resist (PMMA 4.5, Allresist) and remove the remaining Si3N4 in this region via dry etching. The AR-N 7520.12 and PMMA 4.5 resists are subsequently removed via oxygen plasma. To protect the nanowires during the following wet etching step, we cover them with AR 300-80 adhesion promoter (Allresist) and AR-P 672.08 positive resist (PMMA 8%, Allresist). We use a resist thickness of approximately 1.5 µm to reduce the chances of resist peeling due to diffusion, which would result in uncovered nanowires. The sample is dipped in buffered oxide etchant (1:7, Microchemicals) and transferred to acetone to remove the SNSPD protection layer. Finally, the sample is dried using critical point drying (Leica EM CPD300) to prevent stitching of the free-standing rails of the phase shifter’s slot waveguide.
4. Characterization and results
We characterize the phase shifting behavior of two devices on the same chip, with a design slot width of 150 nm (250 nm) and a slot length of 250 µm (300 µm) for device 1 (device 2), respectively. The sample is placed in a closed-cycle cryostat with a base temperature of around 1.3 K and contacted electrically via a radio frequency (RF) probe (Cascade Microtech) and optically with a fiber array consisting of SMF28 single-mode fibers. The read-out circuit for the SNSPD is depicted in Fig. 1(f). The detector is biased with a low-noise voltage source (Keithley 2400) over a series resistor of 992 kOhm. The RF signal is split off with a Bias-Tee (ZZFBT-6GW+) and amplified with low-noise electronic amplifiers (ZFL-1000LN+). To characterize our devices, we sweep the wavelength from 1540 nm to 1550 nm for multiple different bias voltages and extract the phase shift from the position of the fringes in the MZI spectrum, which originate from destructive interference at the second MMI. We focus on a wavelength range of 10 nm, but our phase shifter as well as the SNSPD yield also similar results outside this window, as shown previously [13,27]. The intensity is measured both, with a conventional power meter through the output grating coupler P1 (Agilent HP Keysight 81635A), (Fig. 2(a), dashed lines) as well as the on-chip SNSPD (Fig. 2(a), solid lines). By applying bias voltages between 0 and 6 V, we are able to measure phase shifts between 0 and 1.75 π. Similar to previous work [15], we measure a quadratic dependency between the phase shift and the applied voltage (Fig. 2(b)). A phase shift of π is achieved at a voltage of 6.1 V and 4.6 V for device 1 and device 2, respectively, corresponding to half-wave voltage length products of 0.15 Vcm and 0.14 Vcm. The measured ER obtained with the power meter measurement for device 1 is 30.2 ± 1.9 dB, yielding an upper limit for the insertion loss of the phase shifter of 0.5 dB ± 0.1 dB.
Fig. 2. (a) Wavelength sweep for different bias voltages applied at the phase shifter electrodes for device 1. The dashed line indicates the power measurement through output coupler P2, while the solid lines are obtained by measuring the count rate with the SNSPD. The extinction ratio is slightly lower for the SNSPD measurement because of stray light scattered at the grating couplers. (b) Phase shift as a function of voltage applied to the phase shifter electrodes and a quadratic fit (dashed lines). For a voltage of Vπ = 6 V (4.6 V) the phase is shifted by π in the case of device 1 and 2, respectively.
The intensity measurement with the SNSPD yields a lower ER of 25.0 dB ± 0.8 dB, meaning that in the case of destructive interference the SNSPD registers more clicks than expected. These additional clicks are explained to a small extend by the dark-count rate of the detectors (see below) and to a larger extend by light being scattered at grating couplers and other photonic elements. Since the dark-count rate can be directly measured by blocking all incident light one can estimate the stray-light fraction. While the dark counts cannot be eliminated easily, we note that in a real-use scenario the counts originating from scattered stray-light can be avoided to a large degree by using low-loss fiber-to-waveguide coupling solutions, such as side-coupling or 3D polymer couplers [27–29]. The influence of scattering at other photonic elements (phase shifter and MZI) is estimated to be one order of magnitude smaller than that of the grating couplers. The hypothesis was verified by also measuring the count rate of the SNSPD when light is only incident on grating coupler R1 with a similar distance to the SNSPD as couplers P1 and P2, but not connected via a waveguide (see Fig. 1(c)). This caused count rates in a similar order of magnitude as opposed to the dark count rate, which is measured when all input light is blocked.
To study the temperature dependence and long-term stability of the phase shifter we repeatedly perform phase-shift measurements using the same procedure as described before over a period of 16 hours at cryogenic temperatures and 26 hours at room temperature (see Fig. 3(a)). The half-wave voltage is relatively stable over time with a standard deviation of 0.01 V at room temperature and 0.02 V at cryogenic temperature but exhibits a decrease of the voltage required for a π phase shift from 4.6 V at cryogenic temperature to 3.9 V at room temperature in the case of device 2.
Fig. 3. (a) Evaluating Vπ of device 2 over time at cryogenic temperatures (1.3 K) and room temperature (295 K, vacuum) shows a stable behavior of the phase shifters. (b) Resonance frequency of the phase shifter at cryogenic temperature of 1.3 K and at room temperature.
We further characterize the dynamic properties of the phase shifter driven by thermal noise. The resonance frequency of the phase shifter depends on the mechanical properties of the electrode and waveguide structures as well as the temperature and can be measured by directing a strong continuous-wave laser signal through the MZI and monitoring the output with a spectrum analyzer. The fundamental mechanical in-plane resonance frequency was determined as 778 kHz at cryogenic temperatures and 794 kHz at 300 K, as shown in Fig. 3(b). These values are in good agreement with the eigenfrequency of 779 kHz, which we measured for a device with the same length at room temperature in previous work [13]. The resonance peak is slightly broader at the higher temperature measurement, corresponding to an overall lower Q factor. We attribute this mainly to a change of pressure inside the sample chamber as both measurements were performed in a helium gas environment, used for thermalization of the device at cold temperatures, correspondingly expanding at higher temperatures [30,31].
In addition to the phase-shifting device, the SNSPD is electronically characterized by recording I-V curves, where we observe a latching current of the nanowire of 21.5 µA with no incident light. For single-photon detectors that are part of complex photonic integrated circuits, an important performance characteristic is the probability of a single photon inside the waveguide being detected by the detector, namely the on-chip detection efficiency (OCDE). Therefore, a good estimation of the photon flux reaching the waveguide of the detector is needed. As described above, by measuring the transmission through the output coupler P2 and considering the loss of the individual photonic components we can estimate the OCDE as
where CR is the measured count rate, DCR is the dark-count rate, ${\mathrm{\Phi }_{\textrm{in}}}$ is the input flux and C < 1 is a correction term accounting for the light which is scattered at the grating couplers and causes additional counts on the detector. C can be estimated from the difference in extinction ratios between power meter and SNSPD measurements (Fig. 2(a)) and was determined to be around 0.998 and therefore almost negligible when measuring at the constructive interference wavelength of the MZI. The input flux ${\mathrm{\Phi }_{\textrm{in}}}$ is calculated asSince the efficiency and the DCR are strongly dependent on the bias current, we measure both as a function of bias voltage (Fig. 4(a)) with the input photon flux set to approximately 106 photons / s (and laser off for the DCR). Saturation of the OCDE can be observed for bias currents approaching the critical current. At 95% of the latching current, an OCDE of (88 ± 8) % is measured. We observe a dark-count rate below 40 cps over the entire bias current range. We assess the timing characteristics of the waveguide-integrated SNSPD by measuring the decay time of an averaged voltage trace of 256 detection events. By defining the decay time τ as the value where the measured voltage reaches 1/e of its maximum, we obtain τ = 3.3 ns (Fig. 4(b), inset). This implies that dead times of well below 10 ns are realistic and indicates that count rates in the order of magnitude of 100 MHz are achievable with the device. The timing accuracy of the detector, on the other hand, is determined by the jitter, which consists of several contributions such as electronic jitter, geometrical jitter and intrinsic detector jitter. We measure the overall jitter of our device by replacing the first amplifier in the read-out circuit (Fig. 1(f)) with a cryogenic low-noise amplifier (Cosmic Microwave Technology, CITLF3) and operate the SNSPD at a bias current of 19 µA. The optical output of a pulsed femtosecond-laser (Pritel) with a repetition rate of 40 MHz is connected to a 50:50 fiber beam splitter, one arm of which is attenuated and connected to the SNSPD, while the other arm is measured off-chip with a fast photo diode (12 GHz New Focus 1544). We record a start-stop histogram between the photo-diode signal and the amplified detector signal with an oscilloscope and fit an exponentially modified Gaussian distribution to the data [32,33]. We observe a full-width half-maximum (FWHM) jitter of 12.2 ps (see Fig. 4(b)).
Fig. 4. (a) On-chip detection efficiency (OCDE) vs. bias current (blue) and dark-count rate (DCR) vs. bias current (orange). The OCDE saturates when approaching the critical current, indicating a high internal quantum efficiency of the nanowire. (b) The jitter of the detector was measured to be 12.2 ps (FWHM). The inset shows the average of 256 voltage traces as produced by the SNSPD and recorded with the oscilloscope. The signal reaches the 1/e value after τ = 3.3 ns. The artifacts after 8.5 ns are attributed to parasitic reflections in the RF signal path.
5. Conclusion
In conclusion, we have demonstrated the simultaneous fabrication and operation of an integrated intensity modulator based on an opto-mechanical phase shifter and a high-performance waveguide-integrated superconducting single-photon detector, thus overcoming limitations imposed by the demanding fabrication requirements for free-standing structures on Si3N4. We achieve a low half-wave voltage of 4.6 V at cryogenic temperatures while maintaining a low insertion loss of 0.7 dB. We monitor the phase shifter output using a waveguide-integrated SNSPD with an on-chip detection efficiency of 88%, low dark-count rate and excellent timing jitter of 12.2 ps. This goes beyond the results of previous works [34].
The use of low-voltage and low-power opto-mechanical phase shifters allows for realizing reconfigurable, cryo-compatible photonic circuits on photonic platforms which would otherwise be limited to fully passive components, such as Si3N4. This enables to implement cryo-compatible programmable nanophotonic processors [35,36]. The combination with high-performance SNSPDs furthermore allows for applications where the detection of light is needed, such as optical neural networks [5,35] as well as applications where single-photon sensitivity is essential, such as fully integrated quantum-optical experiments, quantum information processing, quantum-optical neural networks and linear-optical quantum computing [35,36]. The cryo-compatible device presented herein therefore provides a promising means towards fully integrated and flexible classical and quantum optical photonic processors.
Funding
Ministerium für Kultur und Wissenschaft des Landes Nordrhein-Westfalen (421-8.03.03.02–130428); H2020 Future and Emerging Technologies (101017237); Horizon 2020 Framework Programme (899824); European Research Council (724707).
Acknowledgments
We would like to thank the Münster Nanofabrication Facility (MNF) for their support in nanofabrication related matters.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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