Introduction

Optical photons are ideal carriers of quantum information, as exemplified by their widespread and indispensable use in quantum information science. Compared to commonly used degrees of freedom such as polarization1 and path2, encoding and processing quantum information in the frequency domain of a photon promises massive channel capacity and operation parallelism in a single waveguide3,4. The ability to manipulate photon spectra is a prerequisite to implement frequency-domain protocols and schemes, such as spectral linear optical quantum computing4, as well as frequency-multiplexed quantum repeaters5 and quasi-deterministic single-photon sources6,7. In addition, different sources of single photons, produced by heralding photon pairs8,9 or from solid-state emitters10, vary largely in frequency and bandwidth. Spectral control of single photons is therefore crucial for matching frequency/bandwidth differences and inhomogeneities among these photon sources, and for interfacing them with spectrally mismatched quantum memories and stationary qubits11,12,13.

Quantum spectral control, however, has proved difficult as it requires altering photon energies without introducing loss or noise. The most common approaches rely on optical nonlinearities14, such as four-wave mixing Bragg scattering15,16,17, sum-/difference-frequency generation18,19,20,21, and cross-phase modulation22. These processes can achieve large frequency shifts but involve strong optical pumps, which are prone to generating noise photons and require stringent pump filtering. Optomechanical frequency shifters have also been explored, featuring small device footprint and on-chip integrability23,24. However, they require suspended waveguides and high-Q mechanical resonances, which can only operate over a very narrow radio-frequency (RF) bandwidth. Alternatively, electro-optic (EO) phase modulation allows deterministic spectral-temporal control by directly interfacing microwave and optical fields25,26,27. Unfortunately, most integrated photonic platforms, such as silicon and silicon nitride, do not offer low-loss, high-bandwidth, and efficient electro-optic phase modulation. As a result, EO quantum spectral control has only been demonstrated using discrete, bulk modulators6,25,26,28,29, hindering their scalability towards complex, large-scale quantum systems.

In this work, we report on-chip spectral control of nonclassical light pulses using a thin-film lithium niobate (TFLN) modulator. As an emerging integrated photonic platform, TFLN offers a low-loss and wide transparency window, as well as large EO, piezo-electric, and χ(2)-nonlinear coefficients30. Notably, TFLN EO modulators have demonstrated significant advantages over their traditional bulk counterparts in terms of half-wave voltage (\(V_\pi\)), bandwidth, footprint, and integrability31. Here, we use a specially designed double-pass TFLN phase modulator to demonstrate electro-optic spectral control of heralded single-photon pulses at telecom wavelengths. The novel modulator design significantly reduces the voltage requirement for phase modulation, making it possible to drive multiple \(V_\pi\) with readily available RF sources. This technology advancement enabled us to achieve terahertz-scale (± 641 GHz or ± 5.2 nm) frequency shifts—the largest shifting by electrical means demonstrated to date—along with an 18-fold bandwidth compression through spectral shearing and time lensing, respectively (see Supplementary Table S1 for performance comparison). Our results not only show a substantial performance breakthrough but also hold great promise for future large-scale, multi-functional integration with other essential classical and quantum components that have already been developed on the TFLN platform30,32.

Results

The fundamental Fourier relation between frequency and time allows spectral control of light through temporal phase modulation (Fig. 1). A linear temporal phase \(\phi \left( t \right) = - Kt\) applied to a photon wavepacket will lead to a Fourier shift that converts the photon frequency from \(\omega\) to \(\omega + K\), where \(t\) is time in the moving frame of the wavepacket (Fig. 1a). This Doppler-like frequency shift is often called spectral shearing26,33. On the other hand, a quadratic phase modulation, \(\phi \left( t \right) = Bt^2/2\), can enable spectral compression or expansion of a photon wavepacket with a properly applied quadratic spectral phase, \(\varphi \left( \omega \right) = {{{\mathrm{{\Phi}}}}}\left( {\omega - \omega _0} \right)^2/2\), where \(B\) is the chirp factor, \({{{\mathrm{{\Phi}}}}}\) is the group delay dispersion (GDD), and \(\omega _0\) is the center frequency25 (Fig. 1b). This method is widely used for spectral-temporal control of ultrafast pulses and can be explained by exploiting the space-time duality between paraxial diffraction of a spatially confined optical beam and spectral dispersion of a temporally confined optical pulse34,35. Specifically, mapping to a spatial imaging system, the quadratic temporal phase resembles a lens in time domain (referred to as time lens), and the spectral dispersion is analogous to spatial diffraction in free-space propagation. As a result, for instance, a broadband optical pulse can be “collimated” to narrowband when it is placed at the “focal point” of the time lens (\({{{\mathrm{{\Phi}}}}} = 1/B\)). It is worth mentioning that both spectral shearing and time lensing rely on pure phase modulation and are fundamentally unitary and deterministic. The shearing rate and lens curvature, given a certain RF drive power, are ultimately determined by the half-wave voltage (\(V_\pi\)) and operating frequency of the phase modulator, which is why our TFLN modulator can provide significant performance advantage in EO spectral control.

Fig. 1: Frequency and bandwidth control of light through temporal phase modulation.
figure 1

a A linear phase modulation, referred to as spectral shearing, results in a Doppler-like frequency shift. b A quadratic phase modulation, known as time lens, applied to a properly dispersed optical pulse can lead to bandwidth compression/expansion

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In our experiment, we generated pulsed photon pairs at ~1560 nm through spontaneous parametric down-conversion (SPDC)36 (Fig. 2). The orthogonally polarized signal and idler photons were separated using a polarization beam splitter, and the signal photon was sent to an integrated TFLN phase modulator. Notably, the TFLN modulator features a novel double-pass design37, in which the optical waveguide passes through the velocity-matched coplanar waveguide electrode twice, doubling the interaction length between RF and optical fields and thereby enhancing the modulation efficiency (see Supplementary Information). It had a measured Vπ between 2.3–2.8 V at phase-matched frequencies from 10 to 40 GHz, which is significantly lower than commercially available discrete bulk LN modulators (typically > 7 V at 30 GHz for telecom wavelength; see, for example, Thorlabs LN27S-FC) as well as previously demonstrated single-pass TFLN phase modulators38. We note that the double-pass modulator only reaches minimum \(V_\pi\) at specific frequencies due to the loopback waveguide (see Supplementary Information for detailed discussion). This non-flat frequency response is not ideal for general-purpose applications such as telecommunications, but well suited for applications where the modulator only needs to work at a fixed RF frequency, such as spectral shearing, time-lens, and frequency comb generation. The sinusoidal RF drive for the modulator was phase-locked to the pump laser, and the phase relative to the optical pulses was controlled using a tunable RF delay. Since the temporal extent of the optical pulse (< 1 ps) was much shorter than the RF period (tens of ps), the phase modulation experienced by the optical pulse can be reliably tuned from nearly linear (photon arrival synchronized to the rising/falling edges of the sinusoidal drive) to predominantly quadratic (photon arrival synchronized to the valley/peak of the RF drive) by controlling the relative RF phase. After the TFLN modulator, the photons were either sent to time-based spectrum measurement36,39 or a beam splitter for quantum interference (see Fig. 2).

Fig. 2: Experimental set-up.
figure 2

Orthogonally polarized photon pairs were generated by pumping a type-II phase-matched periodically poled potassium titanyl phosphate (PPKTP) crystal with a mode-locked Ti:sapphire laser. After being separated by a fiber polarization beam splitter (PBS), the signal photons (horizontally polarized, H) went through a double-pass TFLN modulator (EOM) with Vπ as low as 2.3–2.8 V in 10–40 GHz range. The output either passed through a 20 km fiber (labeled Dispersion) followed by superconducting nanowire single-photon detectors (SNSPDs) for dispersion-based spectrum measurement or a 50:50 beam splitter (BS) for quantum interference with the idler photon (vertically polarized, V), which passed through a polarization controller (PC) and a tunable delay. The RF drive of the modulator was phase-locked to the pump laser with a tunable phase delay. Waveshapers (WS) were used to apply spectral filtering or spectral phase; LPF long-pass filter, BFP bandpass filter, PLO phase-locked oscillator

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We first demonstrated spectral shearing by driving the modulator with ∼8.1 \(V_\pi\) at 27.5 GHz (i.e., ~ 4 W on-chip RF power). By synchronizing the photon to the steepest rising (falling) slope of the RF drive, we obtained redshifted (blueshifted) versions of the original spectra (Fig. 3a). With RF modulation, no added insertion loss was observed beyond fiber-to-chip coupling drift. There was a slight spectral broadening (7.1% for the redshifted photons and 4.9% for the blueshifted photons), mainly due to shift frequency fluctuation caused by timing jitters between the photon pulse and RF drive (see Methods). Since the optical pulse has a much smaller duration than the RF period, the magnitude of frequency shift is proportional to the ramp rate of the phase modulation and can be adjusted continuously by tuning the RF phase, following \(K = - 2\pi \times \pi \frac{V}{{V_\pi }}f_{{{{\mathrm{RF}}}}}\cos ({{{\mathrm{{\Delta}}}}}\phi )\), where \(f_{{{{\mathrm{RF}}}}}\) is RF frequency, and \({{{\mathrm{{\Delta}}}}}\phi\) is the RF phase with respect to the optical pulses. Figure 3b shows the measured single-photon spectra with increasing \({{{\mathrm{{\Delta}}}}}\phi\), and their center wavelengths were extracted in Fig. 3c. The frequency shift underwent a sinusoidal change with a maximum range of ± 5.2 nm (± 641 GHz). This shift frequency is about 3× higher than previous demonstrations using discrete, bulk LN modulators at visible wavelength (~6× higher when adjusted for wavelength since modulator \(V_\pi\) decreases with wavelength). Equivalently, the RF power on the bulk modulator would need to be increased by 36× (~70 W based on ref. 26) to achieve the same shift frequency, which would likely exceed its power handling capability. Our result is also more than 4× higher than that based on optomechanical shearing23. A more detailed performance benchmarking can be found in Supplementary Table S1.

Fig. 3: Single-photon spectral shearing.
figure 3

a Measured single-photon spectra when the photon was locked at the rising and falling slopes of the sinusoidal RF drive. b Waterfall plot of the measured single-photon spectra with increasing RF phase delay (~0.13π step), showing that the center frequency can be tuned continuously. The spectra were normalized to their maximum value to account for coupling drift during measurement and displaced vertically for ease of visualization. Due to timing jitter between the RF drive and optical pulse, we observed a spectral broadening of photon bandwidth, especially near zero-shift positions. Black solid lines are Gaussian fittings. c Extracted frequency shift as a function of RF phase delay, showing maximum shift of ±5.2 nm (± 641 GHz). The input photon was at 1560 nm with a FWHM bandwidth of 6.5 nm. The modulator was driven at 27.5 GHz with an amplitude of 8.1 Vπ (Vπ ≈ 2.5 V)

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To verify that the frequency shearing process does not introduce unintended modifications to the photons, we performed Hong-Ou-Mandel interference between twin photons with different frequencies. We first prepared nondegenerate photon pairs with a frequency detuning of 154 GHz by tuning the temperature of the nonlinear crystal (see “Methods”). Both signal and idler photons were filtered to a full-width half-maximum (FWHM) bandwidth of 200 GHz. The red photon went through a tunable delay, and the blue photon passed through the TFLN modulator. They then interfered at a beam splitter, and the coincidences at the two output ports were measured as a function of delay time (Fig. 4). High-visibility HOM interference requires the two photons to be indistinguishable. Without correcting their frequency differences, the two photons had a low interference visibility of 23.1 ± 3.1% (background subtracted, see Methods), due to partial spectral overlap. By turning on the spectral shearing and redshifting the blue photon to erase the frequency distinguishability, we observed a high interference visibility of 90.5 ± 4.3%. The maximum achievable visibility was limited by the measurement setup instead of the shearing process (see “Methods” and Supplementary Information). In this experiment, we reduced the RF drive on the modulator to 13.6 GHz and ~4.0 \(V_\pi\) (i.e., ~0.85 W RF power on the modulator), which optimized the tradeoff between intended frequency shift and temporal jitter-based spectral broadening as mentioned above. The high visibility two-photon interference between unshifted and shifted photons, which is a prerequisite for frequency-domain quantum computing and networking, indicates that shearing did not introduce unwanted distortion or noise to the photons.

Fig. 4: Hong-Ou-Mandel (HOM) interference between two photons with different frequencies.
figure 4

a HOM interference set-up. The two input photons have FWHM bandwidth of 200 GHz and frequency difference of 154 GHz. The TFLN modulator was used to redshift the blue-detuned photon and erase the spectral distinguishability. The modulator was driven at 4.0 Vπ with a 13.6 GHz sinusoidal RF signal. b Normalized coincidence rates after background subtraction as a function of path length delay. When the shearing was turned on, the interference visibility increased from 23.1 ± 3.1% (due to partial spectral overlap) to 90.5 ± 4.3%. Error bars indicate one standard deviation assuming Poisson counting statistics. Solid lines: Gaussian fitting

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Next, we configured the TFLN modulator as a time lens and demonstrated single-photon bandwidth compression. We first applied a quadratic spectral dispersion, \({{{\mathrm{{\Phi}}}}}\left( {\omega - \omega _0} \right)^2\)/2, to a nearly transform-limited single-photon pulse using a waveshaper, which introduced programmable phase delays at different wavelengths. We then directed the dispersed photons to the TFLN modulator and synchronized them to the valley of the sinusoidal phase modulation, imposing a nearly quadratic temporal phase of \(\phi \left( t \right) = Bt^2/2\), with \(B = 4\pi ^3\frac{V}{{V_\pi }}f_{{{{\mathrm{RF}}}}}^2\) (see Fig. 5a). Intuitively, the spectral phase separates different frequency components in time, which then experience different amounts of frequency shearing and therefore lead to bandwidth compression. During the measurement, we kept the RF drive at 13.6 GHz and ~4.0 \(V_\pi\), corresponding to \(\frac{1}{B} \approx 10.9\) ps2. The uncompressed input photon had a FWHM bandwidth of 6.55 nm (807 GHz). We gradually increased the group delay dispersion, \({{{\mathrm{{\Phi}}}}}\), by re-programming the waveshaper. Doing so is equivalent to moving the “object” away from the lens and towards the “focal point” (\({{{\mathrm{{\Phi}}}}} = 1/B\)). As expected, the measured single-photon spectra and their FWHM bandwidths were compressed tighter and tighter with increasing \({{{\mathrm{{\Phi}}}}}\), as shown in Fig. 5b and c. Note that when Φ becomes too large, the dispersed pulse will start to overfill the time lens’ aperture (\(\sim 1/f_{{{{\mathrm{RF}}}}}\)), causing spectral distortion and spurious sidebands (see simulated spectra in Supplementary Fig. S6). The slight frequency shifts in the measured spectra were likely caused by parasitic group delays added by the waveshaper at different spectral phase settings, which caused optical pulses to move away from the valley of the RF drive. We also observed spectral broadening after engaging the modulation (from 6.55 nm to 6.95 nm, without adding spectral dispersion), which was due to the timing jitter between the RF drive and optical pulse. Here, the spectral resolution was 0.53 nm (determined by the timing jitter of the SNSPD and dispersion given by the 20 km single-mode fiber), which artificially broadened the measured spectrum. To uncover the actual bandwidth of the compressed photons, we performed high-resolution spectroscopy at \({{{\mathrm{{\Phi}}}}} = 1/B\) using a Bragg grating based dispersion module, achieving a spectral resolution of ∼0.11 nm36. The measured FWHM bandwidth was 0.35 nm (43.1 GHz), corresponding to a compression factor of 18.7 (inset of Fig. 5b and star in Fig. 5c), about 3× what was demonstrated using discrete bulk LN modulators with similar driving schemes25.

Fig. 5: Bandwidth compression of single photons.
figure 5

a Experimental implementation and illustration of the temporal and spectral evolution of the photon. A waveshaper first applies a quadratic spectral phase (or group delay dispersion, GDD) to the input photon, which stretches the wavepacket in time. The TFLN modulator then adds a quasi-quadratic temporal phase to the photon by synchronizing the photon arrival time to the valley of the sinusoidal phase modulation. This modulation acts as a time lens and compresses the photon bandwidth. b Measured single-photon spectra with different GDDs. At the “focal point” (\({{{\mathrm{{\Phi}}}}} = 1/B\)), the 6.55 nm FWHM input photon (blue curve) was compressed to 0.35 nm (inset; black solid line: Gaussian fitting), corresponding to a compression factor of 18.7. c Extracted FWHM bandwidths (from Gaussian fitting) of the output photons with different GDDs. Spectra in the main panel of (b) and blue circles in (c) were measured using 20 km fiber, which has an instrument response function (IRF)-limited resolution of 0.53 nm; inset of (b) and purple star in (c) were measured using a high dispersion module made of a chirped fiber Bragg grating, which has an IRF-limited resolution of 0.11 nm. The TFLN modulator was driven at 13.6 GHz and 4.0 Vπ

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Discussion

As the ultrafast photon pulses travel through the integrated TFLN modulator, it is worth considering the effects of dispersion and group delay. At telecom band, our modulator introduces a total group delay of ∼562 ps and dispersion of -16.8 fs/nm (See Supplementary Information). Taking the largest-bandwidth photons used in our experiments (6.5 nm), assuming transform-limited pulses, this dispersion effect will only broaden the pulse from 550.7 fs to 560.7 fs. Regarding microwave modulation, in the single-pass case, optical group delays do not affect modulation because optical and microwave signals will travel at the same speed (velocity matching). However, in the double-pass case, there is a section where the optical wavepacket loops back to catch a different microwave cycle (Fig. S1a). Effective modulation only happens if the photon re-enters the electrode in-phase with its first entrance, resulting in an oscillating \(V_\pi\) as a function of RF frequency (see Supplementary Fig. S1b and supplementary notes). This is acceptable since we only need to operate at a single RF frequency, and the shearing amplitude and time lens curvature can be controlled by RF amplitude.

Our shift frequency is currently limited by the frequency synthesizer and power amplifier instead of the device’s bandwidth or power handing threshold. Larger frequency shifts can be achieved with even higher RF power and frequency, but more stable pump laser and better locking methods are needed to alleviate timing-jitter-induced bandwidth broadening25,40. Higher RF power and frequency may also cause more severe on-chip heating, making it challenging to operate multiple devices on the same chip. To address this problem, thicker metal, wider center conductor width, and advanced electrode design such as capacitive loading are needed41. In addition, gated or pulsed microwave drives with low duty cycle, or those directly amplified from reference photodetector’s output40, may help reduce on-chip heating.

We have focused on spectral control of ultrafast quantum light pulses in the current work. Extending them to narrowband (GHz) single photons, such as those from cavity-embedded quantum emitters, would require a much slower RF drive (MHz to kHz) and larger modulation depth. In this case, the modulator no longer needs to operate in traveling-wave mode, and high-voltage amplifiers are more accessible in this frequency range. Instead of sinusoidal drive, one may also employ serrodyne modulation with a saw-tooth drive5,6. Alternatively, combining EO modulation with resonant structures can significantly improve the modulation efficiency for narrowband operation42. Moreover, because spectral shearing performs unidirectional and full frequency shifts, it is not sufficient for frequency-domain quantum information processing4, which requires frequency-domain beam splitter that allows bi-directional and partial frequency shifting. This can be implemented by combining phase modulators and waveshapers43,44 or using advanced coupled-resonator modulators42. Nonetheless, efficient on-chip phase modulators are essential components for realizing these functionalities and for interfacing spectrally mismatched photons.

In summary, we have demonstrated high-performance single-photon spectral shearing and bandwidth compression using an integrated electro-optic modulator. Besides outstanding performance, a major advantage of our approach is its integrability with other essential components on the TFLN platform30,32, such as sources45,46, detectors47, memories48, and a complete set of linear optical components30, for realizing complex photonic circuits and functionalities. By cascading multiple modulators and dispersion units, which may be implemented using dispersion-engineered waveguides or integrated wavelength division multiplexer (WDM) followed by a bank of phase shifters, one may effectively replace the bulk waveshaper and achieve arbitrary spectral control of light fully on-chip. We note that the feasibility of cascading multiple TFLN modulators on a single chip has already been demonstrated recently for on-chip femtosecond pulse generation37. Our work accelerates the development of optical quantum processors and networks, which require low-loss control, and high-visibility interference, of individual photons in the frequency domain to yield an advantage. New functionalities are expected beyond mode matching, for instance, the time lens increases the duration of a photon wavepacket far beyond the temporal resolution of a single-photon detector49, which could allow interference of widely detuned photons50, while the shifter, in combination with a WDM and several such detectors, could allow circumventing rate-limiting detector recovery times. Precise control of the phase of light can also open up new possibilities for high-dimensional quantum information51. Our approach is scalable, does not require optical pumping or filtering, and can be extended to a wide range of operating wavelengths. We expect it to become a useful building block for realizing temporal-spectral control of light in both quantum and classical applications, such as frequency-encoded communication and computation, and ultrafast pulse generation and measurement.

Materials and methods

Modulator design and characterization

The TFLN modulator was fabricated on a 600 nm x-cut lithium niobate on insulator (2 μm buried oxide and 500 μm Si carrier) substrate. The waveguide has a width of 1.5 μm and etch depth of 300 nm, with 0.8 μm PECVD SiO2 top cladding. The electrode is designed to be a velocity-matched coplanar waveguide (CPW), with a center conductor width of 35 μm and a gap size of 5 μm. The modulator features a double-pass design, where the waveguide passes the modulation electrode twice through the two coplanar waveguide (CPW) gaps (Fig. S1a). The CPW is designed to velocity match the optical waveguide and has a length of 2 cm. Effective modulation occurs when the photon wavepacket passes the electrode twice with the same microwave phase, resulting in an oscillating \(V_\pi\) as a function of RF frequency (Fig. S1b, see detailed analysis in Supplementary Information).

The half-wave voltage and bandwidth of the modulator were characterized using a telecom continuous-wave laser. The modulator was driven by a signal generator with calibrated output power. The RF drive was swept from 10 to 40 GHz with 100 MHz steps at two different power levels (13.0 dBm and 19.0 dBm). The output optical signal was captured by an optical spectrum analyzer, and the \(V_\pi\) was estimated by fitting the sideband powers using a Bessel function, \(| {J_n( {\pi \frac{V}{{V_\pi }}} )} |^2\), where n is the sideband number, \(V\) is the drive voltage. The measured \(V_\pi\) as a function of frequency is shown in Supplementary Fig. S1b. Light was coupled in and out of the modulator chip using lensed fibers. The total insertion loss was 11 dB, including fiber-to-chip coupling loss of ~ 4.5 dB per facet. The coupling and on-chip loss could be reduced to as low as 0.5 dB/facet and 2.7 dB/m by optimized design52 and fabrication53. No increase in insertion loss was observed when turning on RF modulation. More details about the double-pass modulator can be found in ref. 37.

Locking between photon pulse and RF drive

The pump laser for the SPDC photon generation has a repetition rate of ~80 MHz. Its electrical synchronization signal, produced by sampling the laser output with a fast photodetector, was filtered by a bandpass filter around 160 MHz. The filtered signal was then used as a frequency reference for a frequency synthesizer (Analog Devices EV-ADF4371SD2Z) to generate the phase-locked RF drive for the TFLN modulator. The synthesizer did not have a calibrated output power from the manufacturer. To estimate the RF power on the modulator (after power amplifiers, attenuators, and cables), we sent a classical continuous-wave laser into the modulator and measured the generated sideband using an optical spectrum analyzer. The drive voltage was fitted from the sideband distribution (see Supplementary Fig. S4) and calculated using the calibrated modulator \(V_\pi\) (Supplementary Fig. S1b). Due to the drift of laser repetition rate and limited response time of the phase-locked oscillator, there existed timing jitters between the photon pulses and RF drive. This jitter was measured to be ~15 ps FWHM at ~5 GHz and increased with increasing frequency. Direct measurements at 13.6 GHz and 27.5 GHz were not performed due to the limited bandwidth of our oscilloscope. The timing jitter would induce spectral broadening due to the fluctuation in the amount of frequency shifts. This phenomenon became more prominent when the relative RF phase \({{{\mathrm{{\Delta}}}}}\phi\) deviated from integer multiples of π (i.e., fastest rising/falling edges), as observed in Fig. 2b, which is consistent with previous studies and can be alleviated with a more stable pump laser or better locking method25.

Single-photon spectrum measurement

To measure single-photon spectra, the photons were sent through a 20 km fiber. The fiber dispersion performs frequency-to-time conversion (333.8 ps/nm) and was used to reconstruct the spectrum from the measured delay between the photon arrival time and laser trigger36,39. The pump laser had a repetition rate of 80 MHz, and the SNSPDs had a FWHM timing jitter ~180 ps, giving a spectral resolution of 0.53 nm and range of 37 nm. In the time lens experiment (Fig. 5), a fiber Bragg grating based dispersion unit (1.88 ns/nm) was used for high resolution spectrum measurement, which gave a resolution of 0.11 nm and range of 6.6 nm.

Hong-Ou-Mandel interference

In the HOM interference measurement, we tuned the temperature of the crystal to 48.5 °C and set the two waveshapers to be Gaussian filters with FWHM bandwidth of 200 GHz and frequency detuning of 154 GHz. This separation was partly limited by the temperature response of the nonlinear crystal, which was originally designed for degenerate operation. The coincidence rates between the two SNSPDs were monitored as a function of delay (100 μm/0.33 ps steps). The raw coincidence rate far away from the interference dip was 10.94 cps, and the background coincidences (measured by blocking individual beam path) for the airgap and device paths were 1.88 cps and 0.03 cps, respectively. The rate was mainly limited by the narrow filter bandwidth and insertion loss of the two waveshapers. The background coincidences were likely due to multipair events and polarization misalignment. The acquisition time for each data point was 15 s. The measured coincidence curve was fitted using a Gaussian function, and the visibility was calculated as \((N_{{{{\mathrm{max}}}}} - N_{{{{\mathrm{min}}}}})/N_{{{{\mathrm{max}}}}}\), where \(N_{{{{\mathrm{max}}}}/{{{\mathrm{min}}}}}\) are maximum/minimum coincidence rates. In the main text, we presented background-subtracted HOM interference visibility of 23.1 ± 3.1 % and 90.5 ± 4.3 % for the unshifted and shifted cases, respectively. The non-zero visibility for the unshifted case was due to the partial spectral overlap of the two photons. Without background subtraction, the raw values were 19.2 ± 2.6 % and 74.6 ± 3.6%. As a reference, we set the passband of the two waveshapers to be the same while keeping the crystal temperature at 48.5 °C, and measured HOM interference visibility (without frequency shifting) to be 86.2 ± 3.2% with background subtraction and 73.3 ± 2.8% without background subtraction (see Supplementary Fig. S5). This shows that the maximum visibility was not limited by the shearing process, but mainly by the measurement setup, such as the resolution and accuracy of the spectral filters and nonoptimal spectral shape of the source at this operating temperature.

Disclaimer

The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.