Abstract
The quantum noise of light, attributed to the random arrival time of photons from a coherent light source, fundamentally limits optical phase sensors. An engineered source of squeezed states suppresses this noise and allows phase detection sensitivity beyond the quantum noise limit (QNL). We need ways to use quantum light within deployable quantum sensors. Here we present a photonic integrated circuit in thin-film lithium niobate that meets these requirements. We use the second-order nonlinearity to produce a squeezed state at the same frequency as the pump light and realize circuit control and sensing with electro-optics. Using 26.2 milliwatts of optical power, we measure (2.7 ± 0.2)% squeezing and apply it to increase the signal-to-noise ratio of phase measurement. We anticipate that photonic systems like this, which operate with low power and integrate all of the needed functionality on a single die, will open new opportunities for quantum optical sensing.
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Introduction
Squeezed states of light exhibit fluctuations in their quadrature amplitude below that of the quantum vacuum1. This property makes them indispensable resources for increasing the sensitivity of optical measurements. In interferometry with classical light, signal-to-noise-ratio scales as \(\sqrt{N}\) with the total number of detected photons N. As a result, the imprecision in determining the optical phase, or phase sensitivity, follows \(1/\sqrt{N}\), referred to as the quantum noise limit (QNL). In this case, the signal-to-noise-ratio (SNR) is limited by photon shot noise. To increase the SNR within the confines of the QNL, we must increase N—by using more optical power or extending the measurement time. These approaches are often undesirable or impossible due to technical or fundamental limitations. Intriguingly, the QNL can be overcome by injecting squeezed states of light into the dark port of the interferometer2. Ultimately, this approach may lead to a truly quantum-limited Heisenberg scaling 1/N of sensitivity2,3,4. Over the past forty years, impressive efforts have been put into designing squeezed light sources and integrating them into gravitational wave detectors. These detectors now routinely obtain quantum-enhanced sensitivity exceeding 2 dB5,6. Similar ideas were also extended into other laboratory demonstrations, e.g., in distributed phase sensing7 and enhanced signal-to-noise-ratio in biological sensing8 and microscopy9.
We aim to demonstrate an integrated quantum optical sensor that generates and uses squeezed light to perform measurements beyond the QNL. Our sensor moves much of the functionality often implemented on the optical table—e.g., generating pump light, locking phases, and implementing an interferometer, onto the chip itself. We use thin-film lithium niobate (LN)10 to achieve all of the functions in a monolithic circuit. In the last few years, integrated thin-film LN devices have demonstrated efficient light generation covering wavelengths from mid-infrared to blue11,12,13,14, optical parametric oscillators15,16, dispersion engineering17,18,19, EO modulation, tuning20,21, and frequency combs22. This article combines nearly all of the aforementioned capabilities in a single LN chip and demonstrates an integrated quantum sensor. We leverage the strongest electro-optic coefficient of LN (r33 = 31 pm/V)23 to actively control the power and phase of light within a photonic integrated circuit (PIC) and interface it with periodically poled LN (PPLN) waveguides that support efficient nonlinear processes. The strong second-order optical nonlinear coefficient
In the degenerate parametric amplification process, photons are generated in pairs with a fixed phase relationship through the interaction \({\hat{H}}_{{{{{{{{\rm{I}}}}}}}}}\propto ({\hat{a}}^{2}+{\hat{a}}^{{{{\dagger}}} 2})\). The resulting state of the light is squeezed. Following the first demonstration of a squeezed light source by parametric down-conversion (PDC) in an optical cavity24, numerous other approaches, including single-pass PDC25,26, semiconductor lasers, optical fibers, atomic ensembles1, and ponderomotive squeezing with mechanical oscillators27 have successfully demonstrated varied amounts of squeezed light. Optical materials with intrinsic second- or third-order nonlinearities may be the most versatile integrated sensors approach. Recent demonstrations of integrated photonic circuits in silicon nitride28,29,30 proton-exchanged LN31, and thin-film LN32,33 have shown that low power and scalable sources of quantum light are possible.
Here, we focus on integrating these developments into a complex photonic circuit that can be used as a cost-effective and self-contained sensor. Because of this goal, we limit the optical power to the typical range of a commercial diode laser. Our goal, like those of the first integrated analog electronic circuits, is to demonstrate a path towards a deployable technology as opposed to realizing record-breaking performance. From a photonic system perspective, the squeezed source is only one part of a larger optical sensor. Combining emerging squeezed light sources with more complex PICs is a promising avenue for developing deployable optical sensors with quantum-enhanced sensitivity. So far, achieving sub-shot-noise sensitivity in optical metrology has required complex setups with multiple modulators, lasers, and optical cavities. This has limited the domain of quantum optical sensing to experiments with high complexity5,6,9 that can address only a few of the possible application spaces—even for experiments that use new integrated quantum light sources. Our work combines emerging squeezed light sources with a complex PIC to realize a nearly complete on-chip quantum sensor, thus opening a promising avenue for deployable optical sensors with quantum-enhanced sensitivity.
Results
In this work, we use the X-cut thin film of lithium niobate on an insulator (LNOI) platform to build a sensor with an integrated source of squeezed light for quantum-enhanced measurement. Figure 1a outlines a scheme of the PIC implemented in our chip with three major components—input tunable beam splitter, squeezer, and signal interferometer. We pattern eight such PICs in a single chip, which we show on a microscope picture in Fig. 1b. We design the squeezer to generate a sub-shot noise state of light at the same frequency as the pump light, enabling interference with the local oscillator (LO) extracted from the original beam. Active EO circuitry controls interferometers and the LO phase, which enables using the system for both squeezing characterization and quantum measurement. Using lensed SMF-28 fiber, we interface our device with an off-the-shelf, ultra-low noise DBR laser and operate the system in CW mode at 1544 nm. The output ports of the beam splitter out-couple light into two lensed multimode fibers, which we connect to a balanced photoreceiver off-chip. Both the laser34,35 and detectors36 can be further integrated with the PIC to increase the system efficiency and improve the squeezing visibility.
Device design
The squeezer subsystem comprises two PPLN waveguides and a series of directional couplers for spectral filtering. We design the waveguide geometry to maximize the nonlinear normalized efficiency (see Methods for details). Fundamental harmonic (FH) light first enters a PPLN waveguide designed to phase match a second harmonic generation process using periodic poling with a period of around 3.7
where \(\langle \delta {\hat{{{{{{{{\rm{Y}}}}}}}}}}^{2}\rangle\) is the variance of the quadrature squeezed with respect to vacuum \(\langle \delta {\hat{{{{{{{{\rm{Y}}}}}}}}}}_{{{{{{{{\rm{vac}}}}}}}}}^{2}\rangle,L\) is the length of the poled waveguides,
Active EO circuitry controls optical power splitting and the LO phase within the PIC. The tunable beam splitter at the input and the signal interferometer at the output are both intensity modulators. Both consist of a Mach–Zehnder interferometer (MZI) with a phase modulator in one arm. The former is typically DC-biased at phase ϕ1 either close to zero, to direct most of the input light into the squeezer, or set to
Subsystem characterization
We calibrate the shot noise level by routing all the optical power to the local oscillator path. For this purpose, we bias the tunable beam splitter at the input with a DC voltage bias of 47 V. In this configuration, we use the local oscillator to probe the vacuum state sent to the opposing port of the signal interferometer. For the BHD measurement, we lock the signal interferometer to a splitting ratio of 50:50. We achieve this by controlling the difference between the intensity of two outputs and locking its DC part to zero. Next, we step the power of the input laser using an external variable optical attenuator (VOA), such that the power in the local oscillator waveguide varies between 0 and 8.8 mW and record the RF spectra of the balanced homodyne detector, as shown in Fig. 2a. Finally, we integrate the noise power and plot it against the LO power in Fig. 2b, observing a linear dependence as expected from a shot noise-limited measurement. Note that the linearity of our measurement implies that there is no excess intensity noise from the laser. Hence, we measure only shot noise and can use it as a reference for further squeezing measurements. The mean squared error of the linear fit defines our uncertainty of the shot noise measurement. Based on the shot noise calibration, we choose LO power for the squeezing experiments at around 7.84 mW, where the optical shot noise dominates our detection. We highlight this operating point in Fig. 2b. Note that the noise and LO power are recorded simultaneously, and the detector noise determines the uncertainty of the LO power below a relative deviation of 3 × 10−5.
The squeezer relies on the performance of the periodically poled waveguides in the SHG and OPA sections. We characterize our periodic poling by measuring the quasi-phase-matching transfer function of a diagnostic waveguide patterned adjacent to our SHG and OPA segments such that it passes through the same poling region (see Methods for measurement details). An example QPM transfer function is shown in Fig. 2c. This measurement gives us the SHG response decoupled from the rest of the PIC components. Because the SHG and OPA take advantage of the same nonlinearity and poled waveguides are identical, we can directly use the nonlinear efficiency obtained in the SHG measurements to benchmark the OPA performance. Note that the diagnostic waveguide is 8.1 mm long, whereas the one in the primary device is 10 mm long. Given the significant length of the fabricated waveguide, nonuniformities distort the ideal sinc2 shape of the nonlinear transfer function37 and reduce the peak nonlinear efficiency. We measure the intensity of generated SH light as a function of pump power controlled by external VOA. In Fig. 2d, we plot data and linear fit to extract a maximum normalized efficiency of about 1000%/(W ⋅ cm2), lower than the simulated 4000%/(W ⋅ cm2) for an ideal poled structure. We use this number further to estimate the amount of parametric amplification and the expected squeezing level. Because of the nonuniformities, the quadratic scaling of the efficiency with length is not exact. However, we neglect this because the length difference between the test and device waveguides is small. The inset of Fig. 2d shows a second harmonic microscope image of periodic poling used in the fabrication process. Black stripes on the sides of the picture are metal finger electrodes, and light gray shapes stretching between them correspond to inverted crystal domains.
Squeezing and quantum-enhanced sensing
We characterize squeezing by directing most of the laser light into the squeezer and holding the LO power constant. We drive the squeezer subsystem with 18.4 mW of optical power. Given the calibrated normalized efficiency, we estimate SH power at around 3.4 mW to generate about (1.5 ± 0.1) dB of squeezing on the chip. We perform a BHD measurement to verify this by beating the squeezed state with the local oscillator at the signal interferometer. We lock the phase shift within the output interferometer such that the DC part of the difference signal is zero. At the same time, we lock the input beam splitter to keep the sum of photodiode readouts at a constant value, ensuring the LO power is fixed at around (7.84 ± 0.03) mW. We follow this locking scheme to work around the slow phase drift observed in EO devices38,39. A simple procedure that periodically updates the voltage at the input beam splitter and signal interferometer at a low frequency (around 1 Hz) is sufficient. Finally, we measure the power spectral density, as shown in Fig. 3a, and reference it to the shot noise measurement (black line). We perform this measurement as a function of the LO phase, controlled through a DC voltage applied to a phase shifter in the LO path. Blue and orange traces in Fig. 3a correspond to the maximum anti-squeezing and maximum squeezing, respectively. In addition to probing broadband noise, we introduce two RF signals corresponding to peaks at 72 and 60 MHz. The former originates from an RF signal applied to the LO phase shifter, which we highlight in blue, and the latter corresponds to a tone on the signal interferometer, which we highlight in orange.
We verify the phase-sensitive nature of the generated squeezed light by stepping the LO phase shifter bias. Due to a small power leakage of the FH in the squeezer path,
Limited squeezing visibility and squeezing/anti-squeezing asymmetry result from the detection chain efficiency of 20% (see Methods for more details) and squeezer leakage
Finally, we use the signal interferometer to perform a quantum-enhanced measurement of an RF signal. The classical approach to increasing SNR is by using more optical power. However, this strategy is limited —increasing optical power in electro-optic-modulators causes a series of parasitic effects related to the second- and third-order nonlinearity. Especially the photorefractive effect can cause instability of electro-optic modulators. Moreover, photodetectors suffer from saturation and nonlinearity, and can be damaged with large optical power. Using the additional power to generate squeezing offers an alternative. In this case, the chip configuration is the same as in the squeezing measurement; most light pumps the squeezer, and the LO power is fixed at (7.84 ± 0.03) mW. We use the signal interferometer to perform a quantum-enhanced measurement by injecting squeezed state into its dark port, as shown in Fig. 3d. Based on our squeezing calibration, we set the LO phase to align with the maximum observed squeezing and perform the measurement. For that purpose, we apply a small RF tone to the output interferometer electrode. We set the RF amplitude to −83 dBm, corresponding to the root-mean-square voltage of 15.8
Discussion
Complex quantum photonic integrated circuits, like the one presented in this work, extend the reach of quantum technologies into new domains. The integration allows us to generate quantum light and leverage its properties within the same circuit, enabling more stable and lower power operation. These critical advantages point toward new classes of mobile and deployable sensors that are natively “quantum-compatible”. In the work we present here, we benchmark a sensor by detecting voltage signals imparted as phase upon an optical field. Many other interferometric measurements are today limited by shot noise. These measurements, including refractive index sensing, optomechanical force, acceleration43, and mass sensing44, will directly benefit from integrating the quantum apparatus, as demonstrated here. Moreover, squeezing and squeezed light are crucial elements of numerous quantum sensing, communications45, and computing protocols46,47. Quantum PICs, such as those shown here, are promising and scalable approaches for building these systems.
Methods
Fabrication
We fabricate our device with X-cut thin-film LNOI (lithium niobate on insulator, NanoLN), following the procedure outlined in Fig. 4. The material stack consists of 500 nm of lithium niobate bonded to a 2
The photonic circuit is patterned with a FOX-16 mask and electron beam lithography and transferred to the LN layer with an argon ion mill (Fig. 4d). The etch depth is 300 nm, and the waveguide width is 1.2
Metal electrodes for EO tuning are patterned with the same process as the poling electrodes but made out of 100 nm gold (Fig. 4e). The bottom layer of electrodes and waveguides are covered with SiO2 deposited with a high-density plasma process (Fig. 4f )49. To provide electrical contact to the buried electrodes, we pattern vias by standard SiO2 etch with fluorine chemistry and photolithography (Fig. 4g). Finally, we pattern a top metal layer with the electron beam. This layer provides access to the buried electrodes with an external probe and consists of 200 nm of gold and a 10 nm chromium adhesion layer (Fig. 4h).
In the final step, we prepare the chip facets for light coupling by stealth dicing with a DISCO DFL7340 laser saw17. High-energy optical pulses are focused on the substrate to create an array of damage sites. They act as nucleation sites for crack propagation, resulting in a uniform and smooth cleave.
Waveguide design
We design the waveguide geometry to maximize the normalized nonlinear efficiency for the SHG pumped at 1540 nm and OPA pumped at 770 nm. We find a geometry that results in the normalized efficiency of around
Electro-optic simulation
We design the geometry of our electro-optic devices to provide phase-tuning functionality without introducing excess loss to the quantum state of light. We model our system using a finite-element mode solver (COMSOL). We first define the electric field-dependent refractive index23 as:
The elements of the electro-optic tensor r33 = 31 pm/V and r13 = 10 pm/V modify ordinary and extraordinary indices of the crystal as a result of the static field. We solve for the static electric field and follow with eigenmode analysis in the system with a modified refractive index, as shown in Fig. 5c.
We find the half-wave-voltage-length product from the relationship between the effective index and applied voltage V
Experimental setup
We characterize fabricated PICs in two different setup configurations, one for BHD and one for SHG characterization. In both cases, the chip temperature is controlled with a thermistor (Thorlabs TH10K) and thermo-electric cooler (Thorlabs TECF2S, MTD415TE, MTDEVAL1). We operate our device at 45 ∘C to maximize SHG intensity at the low noise laser operating wavelength.
The setup for BHD measurements is shown in Fig. 1a. For squeezing and quantum-enhanced measurements, we use an ultra-low noise, integrated DFB laser with an emission wavelength of around 1544 nm (Thorlabs ULN15PC). The laser is followed by a high extinction ratio fiber isolator (Thorlabs IOT-G-1550A) and a fiber polarization controller. We introduce an additional variable optical attenuator (HP 8156A) for the shot noise measurement to control the laser power. Then, we couple light to the chip with a lensed SMF-28 fiber (OZ Optics). We collect light into a balanced photoreceiver (Thorlabs PDB425C with RF output conversion gain 1.25 × 105 V/W) using multimode fibers lensed (in-house) and mounted on a v-groove chip with a pitch matching the PIC output waveguide separation. We collect RF spectra with an electronic spectrum analyzer (Rohde & Schwarz FSW26) with a resolution bandwidth set to 60 kHz. Tap ports for FH and SH light filtered within the squeezer subsystem are collected into another lensed multimode fiber, separated by a combination of a 50/50 splitter and optical edge pass filters, and monitored with photodiodes: Newport 1623 Nanosecond Photodetector for FH and Thorlabs APD440A for SH. Electro-optic components on the chip are controlled with DC voltage supplied with three TTi PLH250-P sources. LO phase modulator and the signal interferometer receive RF signal from an arbitrary waveform generator (Rigol DG4102). We mix RF signals and DC bias with bias-tees (ZFBT-4R2G+) and connect to the chip with a triple ground-signal-ground (GSG) probe. We estimate the total insertion loss of RF input at 1.22 dB by combining the loss of two SMA cables (FLC-4FT-SMSM+), DC block (Inmet 8039), and the bias-tee.
We evaluate the system’s stability during balanced homodyne measurements based on the DC readout of the individual photodiodes of the balanced detector. We convert the readouts to optical power and plot it for the squeezing measurement dataset in Fig. 6a. Figure 6b shows the same dataset normalized to the mean power of each channel in the BHD. The standard deviation of the relative power is below 0.3%, which allows us to detect small changes to the noise power on the order of a few percent. We also use the DC readouts from the homodyne detector to normalize the data plotted in the main part of the article.
For the second harmonic characterization, we reconfigure the setup to work with a continuously tunable c-band laser (Santec TSL-550, 1480–1630 nm) passing through a variable optical attenuator (HP 8156A). Next, we tap off 5% of the light for power calibration using a power meter (Newport 918D-IR-OD3R) and pass the light through a polarization controller. Light couples to the chip through an SMF-28 lensed fiber and is collected by the same kind of fiber at the output facet. Then, we out-couple light into free space and split with a 1000 nm short-pass dichroic mirror (Thorlabs DMSP1000) and filter to avoid cross-talk. Finally, we measure light intensity with avalanche photodiodes (Thorlabs APD410A and Thorlabs APD410). We use variable optical attenuators before APDs to prevent saturation and increase the dynamic range of our measurement (HP 8156A and Thorlabs FW102C).
Squeezer performance
The integrated squeezer proposed in the main text takes advantage of the second-order nonlinearity in LN waveguides. In this system, both SHG and OPA can be described with coupled-mode equations for the degenerate three-wave mixing process23:
where A(z) and B(z) are amplitudes of the FH and SH modes with frequency relationship 2
In the squeezer subsystem, FH light is filtered out after pumping the SHG, and the SH stays in the waveguide to generate squeezing through OPA. To find the amount of squeezing generated, we will first define field quadratures for the FH mode as follows:
Next, we can use equation (4) to find the evolution of the field quadratures X and Y along the waveguide length as follows:
In the last line, we have chosen to set the phase of B(z) to −
Solving these equations yields:
It is clear that the Y quadrature is deamplified while the X quadrature is amplified. This amplification and deamplification process, when applied to shot-noise-limited light, leads to anti-squeezing and squeezing of the quadrature fluctuations. In other words, the variance for quadrature operators under the action of amplification/deamplification is given by:
where \(\langle \delta {\hat{{{{{{{{\rm{X}}}}}}}}}}_{0}^{2}\rangle\) and \(\langle \delta {\hat{{{{{{{{\rm{Y}}}}}}}}}}_{0}^{2}\rangle\) are variances of the quantum state entering the OPA. In the proposed PPLN squeezer subsystem of length L, combining equations (6) and (15) defines squeezing as:
Coherent leakage into the squeezer and LO phase calibration
In our system, we observe non-perfect filtering of the squeezer subsection pump at the fundamental frequency. This results from the limited extinction ratio of the filter used on the chip to separate FH from SH after the SHG section. This section explains how we quantify this leakage and use it to calibrate the local oscillator phase.
Our model consists of a tunable beam splitter with two inputs (LO and squeezer output) and two outputs (BHD ports). We calculate a result of a phase modulation imposed on the LO arm on the BHD measurement result, depending on the leakage level. The input state of the system is:
Here,
to find the BHD signal generated. This model is equivalent to the signal interferometer described in the main text. For no power leakage, it is biased such that the phase is around ϕ2 =
We solve for the output port amplitudes and use them to find the BHD differential signal defined as \({P}_{{{{{{{{\rm{BH}}}}}}}}}=|{A}_{out}^{(1)}{|}^{2}-|{A}_{out}^{(2)}{|}^{2}\). The result is given by:
We separate equation (19) into DC and AC parts. The former defines the locking condition:
which is solvable analytically:
In addition to locking, we use the DC term to calibrate the LO phase and directly measure the leakage
VDC is the DC voltage bias at the LO phase shifter. Signal strength depends on the local oscillator power PLO, detection responsivity R, the impedance of the detector Z, and the leakage
Impact of leakage on the squeezing visibility
The AC part of the equation (19) probes both the noise of the prepared quantum state and the noise of the LO. It results in the noise measured in the main text:
Note that it reduces to the usual BHD expression for
This is an expected result for the BHD applied toward phase-sensitive probing of the quadratures of a squeezed state with an additional term that probes the noise of the LO. We assume the LO noise to be phase-insensitive and shot-noise-limited. The signal variance is proportional to the power measured by the spectrum analyzer and given by equation (25). We use this result as a model for our squeezing measurement in the main text.
We illustrate the effects of coherent leakage on squeezing visibility in Fig. 7. We plot the normalized BHD signal using the formula (25) as a function of the local oscillator phase for 1.5 dB of squeezing and anti-squeezing. We assume that the system is locked such that the homodyne detector is balanced, following formula (21) and plot all the values normalized to the shot noise. We plot the results for three squeezer leakage ratios:
Effects of loss in the system
The total detection chain efficiency is a major challenge in characterizing squeezed light. This is especially consequential when working with complex PICs like the one described in the main text. In our experiment, the total detection chain efficiency was around
We summarize all the sources of loss that impact reported total detection efficiency in Table 1. In our measurement, the main limitation is a result of the loss at the interface between the chip facet and collection fibers.
Reducing the overall losses in the system is a straightforward way to improve the device’s performance. Reducing the fiber-to-chip coupling loss down to 0.6 dB has been established by engineering the waveguide termination40,41,42. Moreover, the propagation loss can be reduced to 0.2 dB by reducing the waveguide length where the squeezed state can experience loss. The quantum efficiency of the detector used in this study can be improved to 99.5% using commercially available photodiodes. We use these values to estimate potentially achievable squeezing in the proposed device. In this case, the total detection loss is 0.8
Fundamental harmonic filter design and characterization
We designed the FH filter based on a directional waveguide coupler. We calculate the coupling ratio by simulating a cross-section of two adjacent waveguides in a finite-element mode solver (COMSOL). We extract effective indices for the symmetric and anti-symmetric modes, their difference defines the coupling strength. Then, we find the length of the coupler necessary to transfer 100%. We choose the gap between waveguides to avoid SH light coupling. Our design length is 380
Due to the fabrication imperfections and bend contributions to the coupling, the actual devices differ from the ideal design. We verify the filter performance experimentally by including it inside a racetrack resonator with a total length of around 2 mm, as shown in the inset of Fig. 9a. The filter contributes to the intrinsic loss of the cavity and has a clear wavelength dependence. We measure it by sweeping a tuneable laser coupled to a bus waveguide and fitting lorentzians to the cavity modes. Figure 9a shows the measured intrinsic quality factors. Assuming that the propagation loss of the waveguide is constant across our measurement bandwidth of 1480–1620 nm, we extract the loss contribution from the coupler and plot it in Fig. 9b. The fabricated devices perform best at around 1585 nm and transmit around (8 ± 1)% of light at the squeezer subsystem operation wavelength of 1544 nm. We use three back-to-back filters in the squeezer subsection and observe a suppression of around 18 dB. The excess leakage can result from fabrication imperfections and stray light coupling into the system. The increased density of waveguides in the squeezing PIC can result in more severe electron beam proximity effects and changes in the coupler dimensions. Stray light can propagate in the slab or insulator layer and be parasitically coupled to the circuit.
Data availability
The data sets generated during and/or analyzed during this study are available from the corresponding author on request.
References
Andersen, U. L., Gehring, T., Marquardt, C. & Leuchs, G. 30 years of squeezed light generation. Phys. Scr. 91, 053001 (2016).
Caves, C. M., Thorne, K. S., Drever, R. W., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum metrology. Phys. Rev. Lett. 96, 010401 (2006).
Goda, K. et al. A quantum-enhanced prototype gravitational-wave detector. Nat. Phys. 4, 472–476 (2008).
Aasi, J. et al. Enhanced sensitivity of the ligo gravitational wave detector by using squeezed states of light. Nat. Photonics 7, 613–619 (2013).
Guo, X. et al. Distributed quantum sensing in a continuous-variable entangled network. Nat. Phys. 16, 281–284 (2020).
Taylor, M. A. et al. Biological measurement beyond the quantum limit. Nat. Photonics 7, 229–233 (2013).
Casacio, C. A. et al. Quantum-enhanced nonlinear microscopy. Nature 594, 201–206 (2021).
Zhang, M., Wang, C., Cheng, R., Shams-Ansari, A. & Lončar, M. Monolithic ultra-high-q lithium niobate microring resonator. Optica 4, 1536–1537 (2017).
Wang, C. et al. Ultrahigh-efficiency wavelength conversion in nanophotonic periodically poled lithium niobate waveguides. Optica 5, 1438–1441 (2018).
Lu, J., Li, M., Zou, C.-L., Sayem, A. A. & Tang, H. X. Toward 1% single-photon anharmonicity with periodically poled lithium niobate microring resonators. Optica 7, 1654–1659 (2020).
Mishra, J. et al. Mid-infrared nonlinear optics in thin-film lithium niobate on sapphire. Optica 8, 921–924 (2021).
Park, T. et al. High-efficiency second harmonic generation of blue light on thin-film lithium niobate. Opt. Lett. 47, 2706–2709 (2022).
Lu, J. et al. Ultralow-threshold thin-film lithium niobate optical parametric oscillator. Optica 8, 539–544 (2021).
McKenna, T. P. et al. Ultra-low-power second-order nonlinear optics on a chip. Nat. Commun. 13, 4532 (2022).
Jankowski, M. et al. Ultrabroadband nonlinear optics in nanophotonic periodically poled lithium niobate waveguides. Optica 7, 40–46 (2020).
Jankowski, M., Mishra, J. & Fejer, M. M. Dispersion-engineered
χ (2) nanophotonics: a flexible tool for nonclassical light. J. Phys. Photonics 3, 042005 (2021).Mishra, J. et al. Ultra-broadband mid-infrared generation in dispersion-engineered thin-film lithium niobate. Opt. Express 30, 32752–32760 (2022).
Wang, C. et al. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 562, 101–104 (2018).
Celik, O. T. et al. High-bandwidth CMOS-voltage-level electro-optic modulation of 780 nm light in thin-film lithium niobate. Opt. Express 30, 23177–23186 (2022).
Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator. Nature 568, 373–377 (2019).
Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, 2008).
Wu, L.-A., Kimble, H. J., Hall, J. L. & Wu, H. Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520–2523 (1986).
Kaiser, F., Fedrici, B., Zavatta, A., d’Auria, V. & Tanzilli, S. A fully guided-wave squeezing experiment for fiber quantum networks. Optica 3, 362–365 (2016).
Kashiwazaki, T. et al. Continuous-wave 6-db-squeezed light with 2.5-thz-bandwidth from single-mode PPLN waveguide. APL Photonics 5, 036104 (2020).
Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013).
Dutt, A. et al. On-chip optical squeezing. Phys. Rev. Appl. 3, 044005 (2015).
Vaidya, V. D. et al. Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device. Sci. Adv. 6, eaba9186 (2020).
Zhang, Y. et al. Squeezed light from a nanophotonic molecule. Nat. Commun. 12, 2233 (2021).
Lenzini, F. et al. Integrated photonic platform for quantum information with continuous variables. Sci. Adv. 4, eaat9331 (2018).
Chen, P.-K., Briggs, I., Hou, S. & Fan, L. Ultra-broadband quadrature squeezing with thin-film lithium niobate nanophotonics. Opt. Lett. 47, 1506–1509 (2022).
Nehra, R. et al. Few-cycle vacuum squeezing in nanophotonics. Science 377, 1333–1337 (2022).
de Beeck, C. O. et al. III/V-on-lithium niobate amplifiers and lasers. Optica 8, 1288–1289 (2021).
Li, M. et al. Integrated pockels laser. Nat. Commun. 13, 5344 (2022).
Tasker, J. F. et al. Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light. Nat. Photonics 15, 11–15 (2021).
Kuo, P. S. Noncritical phasematching behavior in thin-film lithium niobate frequency converters. Opt. Lett. 47, 54–57 (2021).
Zhu, D. et al. Integrated photonics on thin-film lithium niobate. Adv. Opt. Photonics 13, 242–352 (2021).
Wang, M. et al. Thin-film lithium-niobate modulator with a combined passive bias and thermo-optic bias. Opt. Express 30, 39706–39715 (2022).
He, L. et al. Low-loss fiber-to-chip interface for lithium niobate photonic integrated circuits. Opt. Lett. 44, 2314–2317 (2019).
Hu, C. et al. High-efficient coupler for thin-film lithium niobate waveguide devices. Opt. Express 29, 5397–5406 (2021).
Ying, P. et al. Low-loss edge-coupling thin-film lithium niobate modulator with an efficient phase shifter. Opt. Lett. 46, 1478–1481 (2021).
Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nat. Photonics 6, 768–772 (2012).
Hanay, M. S. et al. Single-protein nanomechanical mass spectrometry in real time. Nat. Nanotechnol. 7, 602–608 (2012).
Gehring, T. et al. Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks. Nat. Commun. 6, 8795 (2015).
Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460–1463 (2020).
Zhong, H.-S. et al. Phase-programmable gaussian boson sampling using stimulated squeezed light. Phys. Rev. Lett. 127, 180502 (2021).
Nagy, J. T. & Reano, R. M. Reducing leakage current during periodic poling of ion-sliced x-cut MgO doped lithium niobate thin films. Opt. Mater. Express 9, 3146–3155 (2019).
Shams-Ansari, A. et al. Reduced material loss in thin-film lithium niobate waveguides. APL Photonics 7, 081301 (2022).
Acknowledgements
This work was supported in part by the Defense Advanced Research Projects Agency (DARPA) LUMOS program (Grant No. HR0011-20-2-0046, received by A.H.S.-N.) and the DARPA Young Faculty Award (YFA, Grant No. D19AP00040, received by A.H.S.-N.). We also thank NTT Research for their financial and technical support, and the US Department of Energy for their support through Grant No. DE-AC02-76SF00515, received by A.H.S.-N. In addition, the US Air Force Office of Scientific Research provided a MURI grant (Grant No. FA9550-17-1-0002, received by A.H.S.-N.) that supported this research. H.S.S. acknowledges support from the Urbanek Family Fellowship, and V.A. was partially supported by the Stanford Q-Farm Bloch Fellowship Program. This work was also performed at the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-2026822. We also acknowledge the Q-NEXT DOE NQI Center and the David and Lucille Packard Fellowship for their support. D.D. acknowledges support from the NSF GRFP (No. DGE-1656518). H.S.S. and V.A. thank Kevin Multani, Christopher Sarabalis, and Michael Stefszky for discussions and technical support.
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H.S.S. designed the device. H.S.S., T.P., and A.Y.H. fabricated the device. H.S.S., V.A., T.P.M., and O.T.C. developed the fabrication process. M.M.F. and A.H.S.-N. provided experimental and theoretical support. H.S.S., V.A., T.P., and D.J.D. performed the experiments and analyzed the data. H.S.S., V.A., and A.H.S.-N. wrote the manuscript. H.S.S., V.A., T.P.M., and A.H.S.-N. conceived the experiment, and A.H.S.-N. supervised all efforts.
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Stokowski, H.S., McKenna, T.P., Park, T. et al. Integrated quantum optical phase sensor in thin film lithium niobate. Nat Commun 14, 3355 (2023). https://doi.org/10.1038/s41467-023-38246-6
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DOI: https://doi.org/10.1038/s41467-023-38246-6
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