Cryogenic Photonic Readout Based on Thin-Film Lithium Niobate Mach–Zehnder Modulators

Cryogenic data transfer has numerous applications at 4.2 K for extracting data from supercomputers and quantum computers to address interface bottlenecks. The external modulation of data transmission across temperature zones is achieved through the use of electro-optic modulators. The performance of a thin-film lithium niobate (TFLN) Mach-Zehnder modulator was examined at cryogenic temperatures. Low-frequency measurements indicate that the Vπ (voltage needed for π phase shift) of the modulator increases as the temperature decreases from 298 K to 4.2 K. A comparison was conducted between the readout performance of the electrical wire link and the optical fiber link, spanning from 4.2 K to 298 K. Additionally, high-speed data transmission was successfully demonstrated in a 4.2 K environment without the need for cryogenic electric amplifiers, achieving signals of up to 30 Gbps. The proposed solution holds potential benefits for both classical and quantum computers in alleviating interface bottlenecks.

links, comprising external and internal modulation, are proposed for the optical output of weak electrical signals from cryogenic devices [6].The performance of the optical readout, based on external modulation, is directly affected by the electrical-optic (EO) modulator at cryogenic temperatures [7].
Several cryogenic electro-optical modulators have been demonstrated on various material platforms to meet the demanding needs of cryogenic interfaces.A CMOS-compatible silicon electro-optic modulator was demonstrated to operate at 4.8 K with data rates of up to 10 Gbps [8].However, silicon modulators are limited by the inefficient electro-optic modulation at cryogenic temperatures.A BaTiO 3 thin-film modulator has also been investigated across a temperature range from room temperature to 4 K, where a drive voltage of 1.7 V enables 20 Gbps data modulation.Although the results are encouraging, there are challenges posed by high propagation losses and switching voltages [9].A silicon modulator based on the DC-Kerr effect was fabricated in commercial silicon photonics foundries and operated at 5 K with GHz speed.However, the required modulation signal operates on the scale of volts [10].High-speed InP-on-Si electro-optic resonator modulators achieving Gbps with low modulation voltages (ten millivolts) operate at 4 K.Nevertheless, the demonstrated data rates for cryogenic transmitters have been limited to 4 Gbps [11].A silicon-organic hybrid (SOH) modulator exhibits 50 Gbps OOK data transmission with a BER of 7 × 10 −4 at a peak-to-peak drive voltage of 1.6 V [12].This represents the highest data rate achieved by an electro-optic modulator at 4 K.However, the modulation voltages of these EO platforms are 2-3 orders of magnitude higher than those typically provided by SC circuits (<∼10 mV) [13].A graphene-based ring modulator was also demonstrated to operate with a bandwidth of 14.7 GHz at 4.9 K [14].Other examples, such as a SiN thermo-optic modulator [15], a superconducting acousto-optic phase modulator [16], and an integrated magneto-optic modulator [17], were shown to operate at cryogenic temperatures with limited performance and various disadvantages.
In comparison to other solutions, lithium niobate modulators, with various superior characteristics, have received wide attention and have been extensively studied in different fields [18], [19].An annealed proton exchange LiNbO 3 modulator was measured at cryogenic temperatures, and its half-wave voltage increased by 9.25%, in close agreement with the theoretical prediction [20].Cryogenic electro-optic modulation in titanium in-diffused lithium niobate waveguides was investigated for integrated quantum optics [21].The photorefractive effect in high-Q lithium niobate ring resonators was studied at 1.8 K [22].Furthermore, we previously reported a high-speed optical link based on a commercial LiNbO 3 modulator at rates up to 32 Gbps from 3.4 K to room temperature [7].However, thin-film lithium niobate modulators have not been extensively studied in terms of cryogenic performance.
In this study, we examined the half-wave voltage of a thinfilm lithium niobate modulator at two different temperatures: 298 K and 4.2 K. Using this modulator, we constructed and measured both electrical wire link and optical fiber link readouts, spanning from 4.2 K to 298 K. Additionally, we compared the frequency response (S21) of the two data transmission schemes as mentioned earlier.Moreover, we assessed the bit error rate (BER) performance and total bit energy consumption of data transmission between the cryogenic environment and room temperature.

II. THE CHARACTERISTICS OF THE TFLN MODULATOR AT CRYOGENIC AND ROOM TEMPERATURE
A typical thin-film lithium niobate Mach-Zehnder modulator was designed and fabricated using a 600-nm-thick x-cut single-crystalline lithium niobate (LN) thin film.This film was layered with a 2-µm-thick buried silicon oxide layer on a silicon substrate (obtained from NANOLN), as previously described [23].To ensure stability during low-temperature testing, the pigtailed fibers were aligned and directly attached to the chip interfaces using cryo-compatible epoxy (GA700H, NTT).The experimental setup involved custom-built cryogenic systems equipped with cable feed-throughs for applying electrical signals and fiber feed-throughs for connecting the modulators, as reported in prior work [7].To maintain TE polarization input into the modulator within the cryostat, a tunable laser (Santec TSL-710) and a polarization controller were employed.The modulated output signal was detected using a 1 GHz photodiode (PDA10CF-EC, Thorlabs) and subsequently recorded on an oscilloscope (DSOX3104T, Keysight) at room temperature.
To assess the performance of the TFLN modulator at both room temperature and cryogenic temperature, we conducted measurements of the half-wave voltage (V π ) using a 1 kHz triangular wave signal generated by an arbitrary function generator (AFG3152C, Tektronix).Fig. 1(a) and (b) illustrate that the V π increased from 3.97 V at 298 K to 4.64 V at 4.2 K, indicating a V π increase of approximately 16.9%.This observed increase aligns with the expected change of V π , which corresponds to 14% between 300 K and 20 K as reported previously [24].The change in V π at cryogenic temperature is primarily influenced by the temperature-dependent index of refraction and the birefringence of lithium niobate [24].The temperature dependence of the electro-optical coefficient, known to be linear with a magnitude of around 5 × 10 −4 /K, also contributes to the observed variations [25].It is worth noting that the impact of the index of refraction temperature dependence on V π is two orders of magnitude smaller than the effect of the electro-optical coefficient temperature dependence [24].Thus, the latter exerts a significantly greater influence on V π in TFLN modulators.The performance of the modulator is greatly affected by the driving voltage, which directly impacts energy consumption, sensitivity, and noise, all of which scale quadratically with V π [26].
It is worth noting that we observed a reduction in the peakto-peak voltage of the received signal at 4.2 K.This decrease is anticipated due to the higher insertion loss of the modulator at cryogenic temperatures, resulting in a lower extinction ratio.The coupling efficiency between the chip and fibers is diminished due to the mismatch caused by the cryogenic temperatures [27].Consequently, this measurement indicates a partial degradation in modulator performance at low temperatures.

III. THE TRANSMISSION CHARACTERISTICS OF THE ELECTRICAL WIRE LINK AND THE OPTICAL FIBER LINK
After determining the cryogenic modulation properties of the TFLN modulator, we proceeded with a cryogenic interconnect experiment to read out the microwave output signals electrically and optically.Fig. 2 illustrates the two measurement setups based on a dilution refrigerator, which were utilized to characterize the readout characteristics of the electrical wire link and the optical fiber link from 4.2 K to 298 K.The cryostat contains two cold stages (40 K and 4.2 K).For the transmission of gigahertz microwave signals from the cryogenic temperature, RF signals are conveyed to the cold stages (4.2K) through coaxial cables (30 cm Fig. 2. Simplified schematics of the readout of the electrical wire link and the optical fiber link from 4.2 to 298 K, respectively.and 25 cm).In both measurement setups, an RF cable connection and the TFLN modulator are situated on the cold stage.In the case of the electrical wire link readout, coaxial cables (100 cm and 100 cm) are employed to transfer the output signals to the room temperature, as depicted in Fig. 2(a).Conversely, the optical fiber link readout is conducted using fibers (100 cm and 100 cm), as shown in Fig. 2(b).The additional components of the optical fiber link setup include a polarization-maintaining (PM) fiber for injecting light into the modulator, a photodetector (U2t Photonics MPRV1331A) for receiving the output signal, and an electronic amplifier (MINI-ZVA-403GX+) for signal amplification.To ensure a steady-state temperature, the setups were maintained at 4.2 K for at least 12 hours before each measurement.To prevent additional thermal loading on the cryostat, the TFLN modulator was not set to the quadrature bias point by its thermo-optic phase shifter.Throughout the subsequent tests, the TFLN modulator maintained a fixed phase shift induced by an imbalance between its two arms.
To characterize the frequency response (S21) of both the electrical wire link and the optical fiber link described earlier, a radio-frequency input signal with a power level of 0 dBm is generated using a PNA network analyzer (Keysight N5227B) and swept across the range of 100 MHz to 30 GHz.Prior to measurement, an electrical calibration kit is employed to compensate for attenuations in the external wires.The input optical power is set at 2.5 mW for a wavelength of 1550 nm.Fig. 3 depicts the normalized small signal bandwidths of the two data transmission channels (the electrical wire link and the optical fiber link described in Fig. 2(a) and (b), respectively) from 4.2 K to 298 K.The electrical wire link exhibits 3-dB and 6-dB bandwidths of 1.6 GHz and 5.6 GHz, respectively.If the coaxial cables of the readout are replaced by fibers carrying the optical signal from the modulator, the 3 dB and 6 dB bandwidths are extended to 5.6 GHz and 18.1 GHz respectively.The electronic amplifier following the photodetector was not utilized in this bandwidth measurement.The channel length of the electrical wire link affects short-distance data transmissions, whereas the optical fiber link is not affected.Consequently, short-distance data transmission experiences greater benefits from optical fiber links.Furthermore, the bandwidth in current experiments is restricted by the RF signal path into the cryostat.Fig. 3.The measured bandwidth of the electrical wire link and the optical fiber link from 4.2 to 298 K, respectively.(Input and output of the electrical wire link are via coaxial cables; input of the optical fiber link is identical to that of the electrical wire link, but the output of the optical fiber link is via fibers).Fig. 4. The BER versus driving voltage for data rates at 25 Gbps and 30 Gbps.Total bit energy consumption for data transmission at 25 Gbps and 30 Gbps, respectively.The input optical power is 2.5 mW.The HD-FEC and SD-FEC limits are indicated by dashed grey lines.
Even better performance should be achieved with improvements to the measurement setup.
To evaluate the performance of the optical link for high-speed digital data transmission from 4.2 K to 298 K, as shown in Fig. 2(b), the TFLN modulator is placed on the second stage (4.2 K) inside the cryostat.In the BERT measurement, pseudorandom bit sequences (PRBS) are used in the non-return-to-zero (NRZ) mode with lengths of 2 15 −1 and peak-to-peak voltage amplitude (V pp ) ranging in the hundreds of millivolts.The mentioned electronic amplifier amplifies the output signal of the photodetector to ensure its amplitude exceeds the lowest input signal limit of the BER tester (Keysight M8040A).Fig. 4 illustrates the correlation between the BER and the driving V pp for the readout of the optical fiber link operating at 25 Gbps and 30 Gbps.The measured BER curves at 25 Gbps and 30 Gbps, shown in Fig. 4, are well both below the tolerance of the softdecision forward error correction (SD-FEC) limit of 2.4 × 10 −2 [28].The measured BER curve at 30 Gbps is even below the HD-FEC (3.8 × 10 −3 ) limit in the measurement [29].The BER performance can be enhanced if the input RF cable connection of the transmission system does not have electrical bandwidth restrictions.Additionally, the results demonstrate the expected trend of a decreasing BER with an increasing driving signal amplitude, which is attributed to the enhancement of the output optical signal-to-noise ratio resulting from the increased driving V pp .Moreover, the results indicate that the BER increases as the data rate rises while maintaining a constant driving V pp .
In a cryogenic system, the cryocooler primarily contributes to the overall energy consumption, which is proportional to the power dissipation at the lowest temperature stage [30].Low power consumption is essential to meet the demanding needs of cryogenic interfaces.In practical implementation, the energy consumption per bit for data transmission arises from two sources: the power consumption of the switching modulator and the insertion loss of optical paths in the cryostat.Additionally, the power consumed by electrical and optical components at room temperature can be disregarded.The power consumption of the switching modulator encompasses dynamic switching energy and static power consumption.The dynamic switching energy is generated by the applied electric field on the arms of the electro-optic modulator, corresponding to the energy required to switch a capacitor.Given our modulator's traveling wave electrode configuration with a 50 Ω terminator, the electrical energy per bit dissipated in the modulator can be estimated as P E,bit = V pp 2 /(B × R), where V pp is the peak-to-peak voltage amplitude, B is the bit-rate, and R is the equivalent resistor of 50 Ω [31].The static power consumption results from the thermo-optic phase shifter that maintains the modulator at the quadrature bias point.To avoid additional thermal loading on the cryostat, we did not use the thermo-optic phase shifter to set the TFLN modulator to quadrature bias.The loss of fiber-tochip coupling within the refrigerator significantly impacts the energy consumption allocation at low temperatures.Based on our calculations, we considered the most pessimistic scenario where all the input optical power is lost within the cryostat.The optical energy per bit dissipated in the modulator can be estimated as P O,bit = P in /B, where P in is the optical power into the cryostat, and B is the bit-rate.Fig. 4 also presents the total bit energy consumption for data transmission in our proposed cryogenic setup at 25 Gbps and 30 Gbps, respectively.The electrical part of the total energy per bit exceeds the actual value due to a significant portion of energy consumed in the coaxial line feeding the cryogenic system.Notably, the optical energy consumption for 25 Gbps and 30 Gbps amounts to 100 fJ/bit and 83.3 fJ/bit, respectively, with an optical input power of 2.5 mW.If the additional insertion loss caused by the cryogenic temperature is reduced and the photodetector's sensitivity is increased, the optical energy per bit dissipated in the modulator will decrease.

IV. CONCLUSION
We conducted a study on a thin-film lithium niobate (TFLN) Mach-Zehnder modulator at cryogenic temperatures.Despite the degradation of modulator performance at low temperatures, it continues to exhibit satisfactory performance at 4.2 K. Additionally, the results underscored the broader frequency range over which the optical fiber link can operate.Moreover, we successfully demonstrated high-speed data transmission using signals of up to 30 Gbps in a 4.2 K environment, without the need for electrical amplifiers within the cryostat.It is our belief that the driving voltage can be further minimized through the optimization of the TFLN modulator's structure.The proposed solution has the potential to eliminate a significant obstacle in scaling emerging cryogenic systems for classical and quantum information processing and sensing.

Fig. 1 .
Fig. 1.The EO characterization of the TFLN modulator with 1 kHz triangular voltages sweep at 298 K and 4.2 K, showing V π of 3.97 V (a) and 4.64 V (b), respectively.