In recent years, thin-film lithium niobate (TFLN) has emerged as a material of significant importance in the cryogenic quantum domain, finding applications in both cryogenic modulators for the photonic link and room-temperature electronics and a photonic integrated platform for quantum information processing^[1–3]. Cryogenic quantum applications are highly sensitive to temperature fluctuations, making the thermo-optic (TO) behavior of the chip crucial in cryogenic quantum information processing and computing^[4]. Understanding the refractive index variation with temperature, specifically the TO coefficient, is crucial for the precise design and operation of modern optoelectronic integrated devices and circuits. Although there are some reports of temperature dependence on the refractive index of lithium niobate, most cases focus on the TO effect of the bulk lithium niobate above room temperatures^[5,6]. Previous research on the TO effects of the TFLN has often indicated linear relationships between temperature and refractive index changes in conventional temperature regimes^[7,8]. While the electro-optic performance of TFLN at cryogenic temperatures has been investigated^[9,10], but studies on the TO performance of lithium niobate (TN)-integrated photonics in these conditions remain scarce. Recently, an optical filter on a TFLN platform was characterized under cryogenic conditions, but the temperature-dependent effective index was not explored from room temperature to cryogenic temperature^[11]. As one of the most important components for integrated photonics, the aMZI on the TFLN platform offers excellent versatility, which makes it suitable for preparing various optical devices^[12]. To our knowledge, limited research exists on the TO characterization of TFLN asymmetric Mach–Zehnder interferometers (aMZIs) at cryogenic temperatures.

In this work, we prepare an aMZI on a TFLN platform and study its TO characterization with the influence of temperature. The aMZI at different temperatures will give us a better understanding of the TO properties of the TFLN, and the cryogenic-compatible aMZI will further increase the application scenarios of TFLN devices.

Different techniques have been developed to measure the refractive index change of LN as a function of temperature. Both methods demand meticulous sample preparation of the crystal material and precise alignment of a free-space optical path. Any variations in sample preparation can significantly affect the measurement results, and careful alignment of the optical path is essential to ensure reliable outcomes^[13,14]. In contrast to the abovementioned conventional methods using discrete optical devices, photonic integration (ring resonator and Mach–Zehnder interferometer) opens a new path toward measuring TO coefficients at cryogenic temperatures.

Compared with the ring resonator, the Mach–Zehnder interferometer (MZI) has the advantage of a more stable response and has served as one of the fundamental and important structures in photonic integrated circuits^[15,16]. The proposed aMZI operates based on the principle that temperature variations induce differential phase shifts in the transmitted modes of the two interferometer arms, stemming from their distinct waveguide lengths. The TO coefficient of the waveguide materials could be acquired by detecting the wavelength shift of the interference dips of the aMZI. Figure 1(a) shows the schematic structure of the aMZI on a TFLN platform. The S-bends were introduced into the structure to generate the length difference between the two interferometer arms and balance the extra bending loss to achieve a high extinction ratio (ER). Figure 1(b) shows the microscope image of a part of the aMZI structure, and Fig. 1(c) shows the zoomed-in scanning electron microscope (SEM) image of the bending waveguide region.

The proposed device is fabricated on a 600-nm-thick x-cut single-crystalline LN thin film with a 2-µm-thick buried silicon oxide layer sitting on a silicon substrate (from NANOLN). All devices were designed to work with the TE mode and the guided wave propagated along the $y$-axis direction. Considering both the transmission losses and fabrication processes, the etching depth of the LN ridge waveguide is 300 nm, and the width of the ridge waveguide is 1.5 µm^[17]. The sidewall angle of the waveguide is approximately 73° in Fig. 1(d). The aMZI is covered with a 1.6-µm-thick silicon dioxide layer. The detailed process flow of the fabrication and packaging procedure is described in Ref. [17]. The aMZI is designed with two unbalanced arms having a 550 µm length difference, yielding a 1.74 nm free spectral range (FSR). A polarization-maintaining (PM) fiber and a single-mode fiber terminated by blocks of optical glass were aligned and glued directly to the input and output interfaces of the chip with cryo-compatible epoxy (GA700H, NTT), respectively.

For studying the TO performance of the aMZI from room temperature to cryogenic temperature, the sample is then mounted in a cryostat, as reported previously^[9]. The schematic diagram of the experimental setup to study the TO effects of the aMZI is shown in Fig. 2. As shown in Fig. 2, the fibers were in/out of a vacuum enclosure by a vacuum fiber. The input signal of the aMZI was supplied by the built-in calibration light source of an optical spectrum analyzer (OSA, Yokogawa AQ6375B). Because this light source has a lower output power and is less likely to interfere with testing in a low-temperature environment, this built-in reference light source is originally used to align the optical path for alignment adjustment of the OSA. Its polarization was adjusted with a polarization controller to align with the quasi-TE polarization of the guide mode of the sample. The output of the aMZI is sent into the same OSA. Additionally, a temperature sensor is installed close to the aMZI for measuring the temperature. After the OSA was warmed up, alignment adjustments were made using the built-in reference light source. During the measurement, the transmissions and temperatures were recorded simultaneously by a computer.

Using the aforementioned experimental setup, we measured a series of transmission spectra for the aMZI at different temperatures. Figure 3 shows segments of the normalized transmission spectrum at different temperatures, from 290 to 10 K in steps of 10 K, plotted in different colors. As can be seen, a temperature variation from 290 to 10 K causes blue shifts of the interference dips from 1550.48 to 1545.6 nm, causing a total blue shift of the spectrum by 4.88 nm. This wavelength shift is attributed to temperature-dependent variations in the effective index of the two arms of the aMZI^[11]. Additionally, the shift diminishes gradually below 50 K. This phenomenon is caused by the reduction in the TO coefficient at cryogenic temperatures^[18]. Additionally, the maximum output light intensity of the transmission spectra decreases by 6 dB as the temperature drops from 290 to 10 K. It is induced by the increase in the total losses of the device due to coupling loss and propagation loss^[19].

It is well known that the wavelength shift of the aMZI is induced by the thermal expansion and TO effects. The temperature could change the dimension of the device and the refractive index of the material. However, due to the extremely tiny thermal expansion coefficients of the LN, which are on the order of ${10}^{-6}/\mathrm{K}$^[20], the length difference between the two arms and the variation of the cross-section of the device at different temperatures can be considered insignificant. Additionally, the optical energy is dominantly preserved inside the LN waveguide core^[7]. Therefore, the contribution caused by the ${\mathrm{SiO}}_2$ cladding and the ${\mathrm{SiO}}_2$ substrate can be neglected. The response variation of the aMZI can be considered to be mainly caused by the mode index discrepancy at different temperatures. Thus, the variation of $n_{\mathrm{eff}}$ with temperature is described by the modified expression^[21]$$\frac{\partial n_{\mathrm{eff}}}{\partial T}=\frac{n_g}{\lambda }\times \frac{\partial \lambda }{\partial T},$$(1)where $\frac{\partial n_{\mathrm{eff}}}{\partial T}$ represents the TO coefficient of the TFLN, $\partial T$ is the temperature variation, $\lambda$ is the wavelength in vacuum, $n_g$ is the group refractive index of the TFLN waveguide mode, and $\frac{\partial \lambda }{\partial T}$ is the changed wavelength with temperature. It is worth noting that such a method is not dependent on the path length difference between both arms.

The calculated TO coefficient of the TFLN based on the measured transmission spectra from 290 to 10 K is shown in Fig. 4. It can be derived that the variation of the refractive index versus the temperature is $3.95\times {10}^{-5}{\mathrm{K}}^{-1}$ at 290 K, which shows good agreement with the values in the existing literature^[6]. Below 50 K, the TO coefficient continuously decreases and reaches a value as low as $5.29\times {10}^{-8}{\mathrm{K}}^{-1}$ at 10 K. This continuous decrease of the temperature dependence of the refractive index agrees with the third law of thermodynamics, which states that all temperature-dependent parameters have to become constant going towards 0 K^[18]. The inset in Fig. 4 gives the dip wavelength shift concerning the temperature for the data shown in Fig. 3. The purple solid line corresponds to the fitted result. We can see that it has a nonlinear shift with decreasing ambient temperature, and the shift decreases slowly when the temperature is below 50 K.

In conclusion, we study the TO characterization of an on-chip TFLN aMZI across a temperature range of 290 to 10 K. Our experimental results demonstrate that the aMZI maintains stable performance even under cryogenic conditions, underscoring the high potential of the TFLN devices for effective operation at low temperatures. Its transmission spectrum exhibits a temperature-dependent blue shift, decreasing by 4.88 nm at cryogenic temperature (10 K) compared to the results at room temperature (290 K). Our findings not only advance the understanding of the TO properties of TFLN but also highlight TFLN’s potential as a robust platform for applications in extreme environments.