Photon Conversion and Interaction on Chip

The conversion and interaction between quantum signals at a single-photon level are essential for scalable quantum photonic information technology. Using a fully-optimized, periodically-poled lithium niobate microring, we demonstrate ultra-efficient sum-frequency generation on chip. The external quantum efficiency reaches $(65\pm3)\%$ with only $(104\pm4)$ $\mu$W pump power, improving the state-of-the-art by over one order of magnitude. At the peak conversion, $3\times10^{-5}$ noise photon is created during the cavity lifetime, which meets the requirement of quantum applications using single-photon pulses. Using pump and signal in single-photon coherent states, we directly measure the conversion probability produced by a single pump photon to be $10^{-5}$ -- breaking the record by 100 times -- and the photon-photon coupling strength to be 9.1 MHz. Our results mark a new milestone toward quantum nonlinear optics at the ultimate single photon limit, creating new background in highly integrated photonics and quantum optical computing.

The conversion and interaction between quantum signals at a single-photon level are essential for scalable quantum photonic information technology. Using a fully-optimized, periodically-poled lithium niobate microring, we demonstrate ultra-efficient sum-frequency generation on chip. The external quantum efficiency reaches (65 ± 3)% with only (104 ± 4) µW pump power, improving the state-of-the-art by over one order of magnitude. At the peak conversion, 3 × 10 −5 noise photon is created during the cavity lifetime, which meets the requirement of quantum applications using single-photon pulses. Using pump and signal in single-photon coherent states, we directly measure the conversion probability produced by a single pump photon to be 10 −5 -breaking the record by 100 times-and the photon-photon coupling strength to be 9.1 MHz. Our results mark a new milestone toward quantum nonlinear optics at the ultimate single photon limit, creating new background in highly integrated photonics and quantum optical computing.
Unlike electrons, atoms, or any other material particles, photons do not interact with each other in vacuum. Even when mixed in optical media of the best known nonlinearities, their interaction is so weak that high optical intensities are needed to produce an appreciable effect. This inefficiency accounts for significant difficulties facing practical implementations of quantum transduction [1], faithful entanglement swapping [2,3], and heralded entanglement generation [4,5], to name a few. It also prohibits the construction of nonlinear photon-photon gates, thus forming a bottleneck for the development of scalable quantum computers at room temperature [6].
Here, we present a TFLN resonator that overcomes all aforementioned shortcomings and delivers its promised high efficiency for photon conversion and interaction. As illustrated in Fig.1(a), it is an overly coupled, triply resonant, periodically poled lithium niobate (PPLN) microring resonator for sum-frequency generation (SFG). All interacting light waves are in the low-loss fundamental modes with nearly perfect overlap and interact through TFLN's largest χ (2) susceptibility tensor element (e.g., d 33 ∼ 27 pm/V). It achieves an impressive photon-photon coupling strength of g = 9.1 MHz (angular frequency). Crucially, by strongly overcoupling the cavity to minimize the extraction loss of the sum-frequency (SF) photons, we demonstrate photon conversion at a record-high external efficiency of 65% with only about 100 µW pump power, marking orders of magnitude improvement over the state of the art across all existing photonic platforms; see Table I. At the peak conversion, the on-chip noise photon flux is only 3 × 10 −5 photons per 100-ps cavity lifetime, despite small-detuning pumping. This ultrahigh external efficiency yet low noise create new opportunities in various applications like quantum frequency conversion, optical squeezing, and phase sensitive amplification.
Beside the large coupling strength, our device's high cavity quality for all interacting waves provides extended interaction length to boost optical nonlinearities towards the single photon regime. To assess this prospect, we further perform photon interaction between two singlephoton signals in weak coherent states. Our measure-  (2) and χ (3) cavities. ηcon: conversion efficiency by photon number; FWM-BS: four-wave mixing Bragg scattering; DFWM: degenerate four-wave mixing. Q l lists the loaded quality factors for the pump, signal and SF waves in the case of FWM-BS, DFWM, and SFG, and the pump and second-harmonic waves in the case of SHG. This table only includes those whose conversion efficiency is over 10%. Note: a recent arxiv preprint reported SHG of ηcon = 33% [18]. According to its reported normalized efficiency of 602%/mW, the required pump power shall be Pp = 16 66% 602%/mW = 1.75 mW [14,15], which is over 16 times larger than its claimed value. We have not included it in this table due to this apparent inconsistence. ment directly shows that with only one pump photon in the microring, the external quantum efficiency for signal photon conversion is ∼ 10 −5 , while the best efficiency reported hitherto is 10 −7 [20]. The internal Rabi oscillation angle produced by the pump photon is 0.01, which can be improved to approach unity by further reducing the cavity loss.
As a whole, our results constitute a new milestone along the long pursuit of nonlinear optics in its ultimate quantum limit, where a single photon is enough to produce significant nonlinear effects. While there is still a good journey to take before hitting the finish line, the fact that we can attain the theoretical performance of this device is critical for us to take steps forward. By fur-ther improving the cavity quality, strong photon-photon interaction is within sight. Based on the current nonlinear parameters, a cavity qualify factor of 10 8 -which has been demonstrated in lithium niobate microdisks [18]will enable C-NOT gate between single photons. Meanwhile, the demonstrated photon conversion and interaction efficiency can already elevate the performance of nonlinear-optical devices for heralded entanglement generation, faithful entanglement swapping, and so on.
Device design: In χ (2) cavity, the effective Hamiltonian describing SFG between photons in their single modes isĤ where {â j } are the annihilation operators with j = p, s, f standing for the pump, signal and SF light, respectively, each with angular frequency ω j . g is the photon-photon coupling strength, which can be interpreted as the effective Rabi frequency produced by a pump photon (see Supplementary Material A). It is given by where d eff is the effective nonlinear susceptibility. ξ is the mode overlapping factor. V eff is the effective mode volume. m j is the azimuthal order of the cavity modes, and M is the azimuthal poling grating number, so that δ(m f − m p − m s − M ) accounts for quasi-phase matching (QPM) by periodic poling.
In this work, we use a microring with a radius of 80 µm and a cross-section of 600 nm in height and 1700 nm in top-width. The pump and signal are both in the telecom C-band and their SF is in the visible band, chosen so with repeater-based quantum communications in mind.
To maximize g, all three waves are in the fundamental quasi-transverse-magnetic (quasi-TM) modes and interact through TFLN's largest nonlinear tensor d 33 with over 90% mode overlap. As shown in Fig.1, concentric periodic poling is applied to the microring for QPM. To ensure triple resonances for all waves, fine temperature tuning (∼ 0.01 • C) is applied to compensate for any resonant mismatch due to any fabrication error.
For photon conversion and interaction, the device figure of merit is the external quantum efficiency (QE) defined as where N s is the number of input signal photons to the cavity and N f is that of converted SF photons at the cavity output (thus accounting for any internal cavity loss). This is in contrast to previous demonstrations, where critical coupling was adopted to maximize the intracavity optical power for high conversion efficiency [13,[15][16][17]. However, most of the input power and about half of the converted photons are lost inside the cavity, rendering a rather low QE while prohibiting cascaded operations. For practical applications, one instead needs to over-couple the cavity so that the photons can be extracted out before significantly lost in the cavity. Under QPM and triple resonance (see Supplementary Material A), the maximum QE is given by [21]: where Q j,o is the quality factor with o = c, l denoting the coupling and loaded Q, respectively. It is reached with an optimal pump power where η nor tran = P f /(P s P p ) is the normalized power transduction efficiency with P j the optical power of the j-th wave. In our case, η max QE ≈ 65% and η nor tran ≈ 4.5%/µW, so that the optimal power is around 115 µW.
We use a pulley coupler in optimized dimensions to achieve proper over-coupling for both the signal and SF modes. This is done by first determining its top width by requiring n p R p = n r R r [22], where n p,r are the effective refractive indices of the pulley waveguide and microring modes for the sum-frequency wave, and R p and R r denote their radii. For the SF wave, the waveguidemicroring coupling strength is proportional to the length of the pulley coupler, while inversely proportional to their gap. For the signal mode, in contrast, the coupling strength varies as sinc(∆Φ), where ∆Φ is the coupling phase mismatch. This allows to carefully design the dimensions to create the desirable over-coupling for both signal and sum-frequency waves.
Device characterization: The details of our device fabrication and experiment setup are presented in Method and Supplementary B. The fiber-chip-fiber coupling losses are measured to be 8 ± 0.15 dB at 1556 nm and 9.5 ± 0.2 dB at 778 nm, respectively. To find phase matching, we first search for strong SHG across the C-band by sweeping an infrared laser while optimizing the chip's temperature. This gives several cavity modes around 1556 nm, based on which we select a set of cavity modes at 1560.15 nm, 1551.85 nm, and 778.00 nm, considering the over-coupling requirement and limited by our visible band-pass filter (BPF, bandwidth ∼3 nm, 760 to 780 nm). To reduce the Raman background, we designate the 1560.15 nm mode to the pump. For this set, m p = 602, m s = 606, m f = 1357, so that M = 149. The loaded quality factors Q j,l are measured for each modes, while the coupling Q j,c and intrinsic Q j,0 factors are calculated by fitting the resonance spectra, as shown in Fig. 2 (a). Those Q's, according to Eq. (2), give the highest possibl external quantum efficiency of η max QE ≈ 65%. For an even higher efficiency, the cavity needs to be further overcoupled.
Low-noise Frequency Conversion: We perform SFG using the setup detailed in Fig. S1. We first couple a strong pump at 1560 nm and a weak signal at 1552 nm into the microring, and fine tune the microring temperature and the laser wavelengths to verify QPM and triple resonance. The resulting spectrum, measured without any filtering thus manifesting all possible nonlinear processes, is shown in Fig. 2(c). It exhibits a clean profile with low baseline, except for a residual second-harmonic peak at ∼780 nm by the strong pump. This peak is significant only in the high conversion regime (i.e.,>50%) and can be conveniently filtered out. In this experiment, we reject it using a ∼3 nm bandpass filter centered at 778 nm. The otherwise low background over the entire spectral range shows that all other competing processes are well suppressed, as desirable for quantum applications.
In this experiment, the signal power is fixed to be about 37 nW on chip, while the pump power is grad- ually increased. During the measurement, we only need to slightly optimize the temperature within 45 ± 0.3 • C and tune the wavelengths of both lasers within ± 20 pm to compensate for slight phase mismatch and resonance drift caused by thermo-optical and photorefractive effects [14]. The quantum efficiency as a function of the on-chip pump power is shown in Fig. 3. Thanks to the overcoupling and nearly ideal poling, (65 ± 3)% quantum efficiency is achieved with at (104 ± 4) µW pump power. Taking into account all insertion losses both on and off chip, this corresponds to about 9% total efficiency. In the low conversion region, the normalized power transduction efficiency is fitted to be about 4.5% µW −1 . By fitting the experimental data with the steady-state solution to Eqs.(S1-S3), as shown in Fig. 3, the photon-photon coupling coefficient g is determined to be 8.2 MHz.
The above results speaks to the ultrahigh efficiency. For quantum frequency conversion, it is critical that no significant in-band noise is injected during the conversion. As illustrated in Fig. 2(b), there are multiple processes that can produce in-band noise, such as Raman scattering from strong classical pump to the signal band followed by SFG, Raman scattering by the pump's residue SH light, and spontaneous parametric down-conversion (SPDC) followed by SHG and SFG. To quantify their total contributions, we measure the noise photon flux generated in the SF band when only the pump is applied. To ensure total rejection of any outband noise, the SF photons are passed through additional free-space filters (see Supplementary Material B), before detected by a silicon-based single-photon detector (Si-SPD, quantum efficiency: 50%, dark count: 250 Hz). The results are plotted in Fig. 3, where the increase of the noise photon flux is between quadratic and cubic with the pump power. This result indicates that besides Raman scattering, the cascaded SPDC and SFG process also presents, similar to what we observed in a PPLN nanowaveguide [23]. At the 65% peak QE, the onchip noise photon flux is 0.3 MHz under continuous-wave pumping. If using ∼100 ps pulses that match the cavity lifetime, the noise photon per pulse is 3 × 10 −5 , which is low especially given the small detuning between the pump and signal that are both in the telecom C-band. This noise level can be substantially lowered by, for example, further detuning the pump from the signal [24].
Interaction Between Photon-level Coherent States: Strong interaction between single photons is of great values for both fundamental optics studies and quantum applications such as faithful quantum entanglement swapping [2,3], heralded entanglement source [4,5], and device-independent quantum key distribution [25]. Here, we characterize the device responses in the single To maximize the detection efficiency for the SF photons, we remove the free-space filtering system-used in the last section to reject background noise created by the strong pump-and directly couple the SF photons from the chip to the Si-SPD via a lensed fiber. To ensure that the pump photons do not generate background counts (that could contribute to the over-estimation of the single-photon nonlinearity), we block the signal and verify that even at the highest on-chip flux (∼ 5 GHz), the photon counts remain at its dark count level (∼ 250 Hz). Here, the total detection efficiency for the sumfrequency photons is η = η d η c ≈ 17%, with detector efficiency η d ∼ 50% and coupling efficiency η c ∼ 33.5%.
The measurement results are shown in Fig. 4, where we observe linear dependency of the quantum efficiency on the intracavity pump photon number. The on-chip quantum efficiency is about 10 −5 when there is one pump photon on average in the cavity, after correcting for the coupling loss and finite detector efficiency. By fitting with the coupling-mode equations, we extract the photonphoton coupling coefficient g to be 9.1 MHz, compared to 8.2 MHz as from the classical measurement. This slightly higher value may come from better QPM or triple resonance for single-photon light waves, due to the absence of thermo-optical and photorefrative effects.
The above quantum efficiency gives the probability of a signal photon at the cavity input being converted to its SF and appear at the cavity output. It has accounted for the signal coupling loss and the SF extraction loss, thus constituting a direct measure of the device figure of merit that dictates its performance in quantum applications. Another measure, of less practical relevance but nonetheless describing an intrinsic property, is the internal Rabi rotation angle θ = 2gQ p,i /ω p . That's, Eq. (1) can be interpreted as the pump induced Rabi oscillation between signal and SF photons. θ then gives how much Rabi rotation can a pump photon induce during it is lost in the cavity. In our case, g = 9.1 × 10 6 and Q p,i = 7.1 × 10 5 , so that θ = 0.01, which is already appreciable from a fundamental standpoint. Increasing θ to π/2 would require improving Q p,i to 10 8 , which has been demonstrated in polished TFLN microdisks [18].
Heralded Entanglement Generation: The demonstrated photon-level nonlinearity implies unprecedented performance in quantum information science and technology. In particular, because of lithium niobate's exceptional optical properties in multiple aspects, the demonstrated photon conversion and interaction are ready to be integrated with other passive and active elements on the same chip, such as PPLN wavegudies [26,27], electrooptical modulators [28], frequency comb sources [29][30][31][32], and microring filters [33], to create functional quantum devices of practical impacts [34]. Compared with the existing table-top or assembled systems, the detrimental insertion loss will be eliminated, and the mechanical and optical stabilities are expected to be exceptional.
As an example, in Fig. 5 we present the design of an integrated chip for heralded entanglement generation, following the scheme in [2]. It consists of a PPLN nanowaveguide to create photon pairs by SPDC, a series of thermally-tuned microrings for optical filtering, directional couplers for photon combination, and a PPLN microring for photon conversion. The process starts with passing a visible pump through a PPLN nanowaveguide to generate via SPDC photon pairs simultaneously over multiple wavelength channels, ω s1 +ω i1 , ω s2 +ω i2 ,..., and ω sn + ω in [26,27]. The signal and idler photons will each be picked and separated into different arms by using coupled add-drop filters for high extinction while eliminating free spectrum ambiguity. In each arm, amorphous-silicon over-cladding will be applied to further reject any residue pump in the visible band. The signal photons will be recombined via cascaded directional couplers and sent into a PPLN microring, where they are interact to create a SF photon. The existence of a photon pair in the idler channels will be heralded upon the detection of the SF photon. To create entanglement in time bins, the SF photon needs to pass through a Franson interferometer and be detected in a superposition time-bin state [2]. Unlike schemes using SPDC and linear optical Bell state measurement, where the success probability is fundamentally capped at 50% [35], this scheme is deterministic in that upon heralding, the entangled photon pair exists with nearly certainty. In this design, with 12 pm net filtering bandwidth and 100 ps pump pulses, one can drive the SPDC at 1% photon pair production rate per pulse for each channel. The heralding rate can approach 10 Hz for the demonstrated 10 −5 photon conversion, which would correspond to orders of magnitude improvement over previous demonstrations [4,5]· Discussion: We have demonstrated photon conversion and interaction with record high efficiency and low noise in a Z-cut, periodically poled microring on thin-film lithium niobate. Combining nearly perfect QPM, tight mode confinement, high cavity quality, and efficient photon extraction, we achieved 65% wavelength transduction with only about 100 microwatt pump power, advancing the state of the art by large. Despite a small detuning between the signal and pump, at the peak conversion only 3 × 10 −5 noise photons are created over the cavity lifetime, thanks to the deep single-mode condition and suppression of side processes. The same device allowed nonlinear interaction between two single-photon level coherent states, where the photon-photon coupling strength reaches 9.1 MHz, and a single photon can produce 0.01 internal Rabi rotation angle. The external quantum efficiency is directly measured to be about 10 −5 , compared with the best reported efficiency of 10 −7 . Our results mark new milestones towards quantum nonlinear optics in the single photon regime, with broad implications in areas of fundamental studies and applied quantum information technology. Combining with other favorable optical proprieties of thin film lithium niobate, a superior platform of photonic integrated circuits is within sight for scalable quantum applications.

METHODS
The entire device is fabricated on a magnesium-doped Z-cut LNOI wafer (NANOLN Inc.), with a 600-nm thick LN thin film bonded on 2 µm silicon dioxide layer above a silicon substrate. First, the microring and waveguide structure are defined using hydrogen silsesquioxane (HSQ, Fox-16) by electron beam lithography. The top width and the radius of the microring are 1.7 µm and 80 µm, respectively. Then, ICP Argon milling is applied to shallowly etch the structures, where 430-nm thick LN is etched with 170-nm LN remaining, and the sidewall angle is approximately 64 • . The optimized pulley coupler, shown in Fig. 1(b) with the pulley top width of w pulley = 400 nm, the gap of g pulley = 650 nm, and the length of L pulley = 40 µm, is created to increase the ringbus waveguide coupling to attain simultaneously overcoupling condition for both the visible and IR lightwaves. Then, a concentric periodically-poled region with period of Λ = 3.37 µm given by Λ = 2πR/M , M = 149 and near 50% duty cycle (see Fig. 1(c)) is created via several 1-ms and 450-V electrical pulses using a similar process described in [27]. After removing the poling electrodes, the chip is coated with 1.5 µm silicon dioxide. Finally the chip is diced and polished.  TABLE S1. Simulation parameters used in coupled-mode equations models for sum-frequency generation. a : used in Fig.3, b : used in Fig.4. The fitted g a and g b are 8.2 MHz and 9.1 MHz, respectively.

B. Experimental setup
We use the setup shown in Fig.S1 to characterize the device and perform the photon conversion and interaction experiment. The whole chip is placed on a thermoelectric cooler and the temperature is set at about 45 • C. For linear characterization, as shown in Fig.S1(a), we use two polarized tunable continuous-wave (CW) lasers (Santec 550 and Newport TLB-6712) and tapered fibers (OZ OPTICS) to independently characterize the fiber-chip-fiber coupling, whose losses are measured to be (8 ± 0.15) dB around 1556 nm and (9.5 ± 0.2) dB around 778 nm, respectively. For its nonlinear optical properties, we sweep the infrared laser across the whole C-band while optimizing the chip's temperature to achieve strong second-harmonic generation (SHG).
Once identifying the quasi-phase matching resonances, we switch to the setup in Fig.S1(b) for sum-frequency generation. Additional tunable CW laser (Coherent, MTP-1000) is used to serve as the signal. We will further optimize the system around its optimum SHG condition to maximize the SFG.
• For classical measurement, optical spectrum analyzer (OSA, Yokogawa AQ6370D) is used to collect the data.
• For quantum noise measurement, a silicon-based single-photon detector (Excelitas, efficiency 50%, dark count 250 Hz) and a free-space filtering system are introduced. It consist of two fiber collimators (insertion loss, IL∼ 2 dB), one short-pass filter ( IL∼0.5 dB, extinction ratio, ER ∼50 dB) and one band-pass filter (10nm, 780 nm, IL∼0.5 dB, ER ∼50 dB) rejecting pump and signal in C-band while passing through visible light, and three narrow band-pass filters (Alluxa, 3 nm, IL∼1 dB, ER>120 dB) rejecting residue second-harmonic light of 780 nm while passing through the target light of 778 nm.
• For interaction between single-photon coherent states, superconducting nanowire single-photon detector (ID Quantique, ID281, efficiency 85%, dark count 100 Hz) are used to monitor the input photon flux. Due to limited photon-count saturation rate (∼20 MHz) of SNSPDs, each monitor channel has about 50 dB attenuation. Meanwhile, the free-space filtering system will be removed to reduce the insertion loss (IL∼4 dB). The SF photons will be directly measured by silicon-based single-photon detector via a lensed fiber.