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Abstract
Parametric sources in quantum optics usually require some form of spectro-temporal control for conditional generation of high-purity single-photon states, but their properties have not yet been optimized using integrated microchips. Using external short-pulse lasers and separate devices for pump preparation and for photon generation, as is traditional, incurs many impediments such as reduced performance, increased loss, high cost, and limited scalability. To overcome these limitations, here we demonstrate a circuit including high-bandwidth, high-extinction ratio electro-optic modulators for pump-pulse preparation fully integrated with high-quality factor (Q) microresonators for efficient parametric nonlinearity, together with seamlessly interconnecting waveguides. The microchip uses different optical materials on a common platform and a multi-layer integrated photonic architecture. Using this, we control the joint spectrum of room-temperature biphoton generation for the first time on a single integrated microchip, and demonstrate that the theoretical purity bound can be achieved.
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1. Introduction
Quantum photonics requires source devices for a wide range of applications including communications, sensing, simulations, and computation [1]. Compared with atomic gas ensembles, cooled nonlinear fibers, and quantum dots, solid-state parametric optical devices have many advantages including compactness, room-temperature operation, and high collection efficiency of photons into waveguides. Such devices can be made from silicon (Si), a common semiconductor, which can improve manufacturing scalability and decrease cost [2,3].
A significant and important barrier is improving the purity of single photons generated by such devices, and one known approach is to develop the ability to dynamically tune light in a scalable and efficient way [4]. Specifically, the pump light must be shaped to ensure high purity and indistinguishability of conditionally prepared single photons [5]. (This approach is different from the spectral shearing and bandwidth manipulation of single photons after generation, shown using separate source and modulator devices [6].) As an example to guide the discussion, Fig. 1 shows two examples of a simulated joint spectral intensity (JSI) for a microring that is pumped with quasi-continuous-wave (CW) light [Fig. 1(a)] and with short pulses [Fig. 1(b)]; all JSI plots use a logarithmic scale (see the Supplement 1, Section 1). The former is a highly non-separable state with a long distribution of significant singular values in the Schmidt decomposition of the JSI (continuing past the ten largest values shown in the inset), whereas the latter is more approximately the desired state with only one dominant singular value.
Fig. 1. Simulated JSI (using a logarithmic color scale) for the biphoton state generated in a representative Si microring resonator using (a) continuous-wave pump laser light, and (b) the pump carved into short (80 ps) pulses. The insets show the distribution of singular values (first 10).
The current approach to pump preparation uses short-pulse laser systems. In some experiments, the pump was from a Ti:sapphire laser, which was shaped over a few terahertz of bandwidth [7,8]. In other experiments, a mode-locked fiber femtosecond laser was used as the pump [9,10]; such apparatus is very bulky and expensive. Our approach is to pump a third-order spontaneous parametric process in microresonators using shaped pulses generated by integrated electro-optic modulator (EOM) devices with adequately high modulation bandwidth, which then requires only a simple continuous-wave laser diode and a source of electrical signals (pulse generator). However, it is difficult to achieve the required modulation bandwidth (which is of the order of 1 nm, or approximately 100 GHz at 1550 nm wavelengths) and a high on–off extinction ratio (usually $> 100:1$, or 20 dB) using integrated EOM devices until recently. Here, a high-performance EOM is integrated with a bright and efficient pair source and we obtain a simple device architecture which can be fully implemented using microchip technology rather than today’s breadboard or table top experiments.
Our fabrication process is summarized in the Supplement 1, Section 2. The technical complexity of the fabrication is balanced by the scientific need to overcome mutually incompatible constraints in a simpler, single-material photonics platform, as explained in the “Discussion” section below. The complete photonic circuit has electro-optic, linear, and nonlinear components and uses several materials but the seamless interconnection between the devices avoids abrupt interfaces or junctions, and instead uses integrated photonic waveguides and multi-layer adiabatic transitions.
2. Integrated Device Concept and Design
Figure 2(a) shows a top-view schematic diagram and Fig. 2(b) shows the vertical cross section. A Si waveguide layer runs continuously throughout the chip, and a thin-film lithium niobate (TFLN) layer is used (only) in the EOM portion of the device. The first part of the circuit implements a push–pull Mach–Zehnder EOM device, which was designed using a feeder mode [cross section “A” in Fig. 2(b) and mode “A” in Fig. 2(d)] transitioning to hybrid modes [cross sections and modes labeled “B” and “C”], in which light is partially localized in Si and partly in TFLN. The wide Si rib waveguide concentrates most of the light in the Si region, with a small amount of light in the cladding [as shown in Fig. 2(d)]. This allows a low-loss transition to mode “B” where TFLN is bonded, and then to mode “C” which is used in the voltage-driven phase shift section. The mode-fraction in lithium niobate (LN), the electro-optic material, can be varied over a wide range (from less than 20% to over 80%) and is controlled solely by the Si rib waveguide width. Etching or patterning of TFLN is not required [11], which simplifies the fabrication process and results in stable devices which retain their performance over several years [12].
Fig. 2. (a) Schematic layout of the microchip (not to scale). (b) Cross sectional diagram showing the various layers (not to scale). (c) Photograph of the microchip. (d) Simulated optical modes in regions “A”, “B”, and “C” indicated in panel (b).
Outside of the EOM section is the all-optical portion, where light routing, splitting, filtering, and parametric generation of photons using spontaneous four-wave mixing (SFWM) is performed using Si waveguides, spline bends, racetracks, and directional couplers. The Supplement 1, Section 3 gives further details about the passive components and their performance. The width and bend radius were chosen to achieve a high-$Q$ and a clean, single-mode family of resonances [13]. We also designed adiabatic waveguide transitions in the Si layer, whose width adiabatically changes between 275 nm and 650 nm in the different parts of the photonic circuit (see the Supplement 1, Section 4). The smooth connection avoids abrupt transitions and butt-coupled interfaces which can cause back-reflections, potentially changing the biphoton spectrum.
3. Results
Some test chips were diced into individual sections and tested. Light was coupled to the chip using optical fibers and micro-positioning stages, and electrical signals generated using a radio-frequency (RF) signal generator were applied as shown in Fig. 3(a) [14].
Fig. 3. (a) Schematic diagram of the measurement of the modulator electro-optic response. (b) Half-wave voltage times phase-shifter length product ($V_\pi L$) and optical extinction ratio at 1550 nm. (c) Measured electro-optic response (blue dots) with the modeled behavior based on vector network analyzer data (red line). The dashed line shows the $-3$ dB roll-off level. (d) Schematic diagram of the measurement of biphoton generation. (e) Transmission measurement of the Si microring. (f) Coincidences-to-accidentals ratio (CAR) versus raw measured singles rate, without loss scaling. The inset shows the second-order autocorrelation trace even when the CAR is at its lowest value.
By performing cut-back measurements on diced segments of test chips, an optical insertion loss of 0.4 dB was measured for the phase-shifter section, a loss of 1.8 dB was measured for the complete EOM including the two 3 dB coupler sections. The total loss of the passive optical waveguides is only approximately 0.3 dB based on their length and the measured propagation loss (0.8 dB/cm at 1550 nm) by comparing the transmission through waveguides of different lengths on a test chip (see the Supplement 1, Section 2). The main sources of overall loss are the waveguide-to-fiber losses at each chip edge facet (approximately 6 dB per facet); these losses can be improved with better fiber coupler designs, or alternatively, not incurred if the photons are entirely processed on the chip, as in certain applications [15].
The laser was tuned away from the microring resonance to isolate the characteristics of the modulator. The electro-optic (EO) response of the modulator as the modulating RF frequency was stepped is shown using blue dots in Fig. 3(c), and shows a 3 dB electro-optic bandwidth from near direct current (DC) to beyond 100 GHz. The data trend also matches simulations based on the electrical $S$-parameter measurements of the high-bandwidth coplanar waveguide electrode structure using a vector network analyzer, shown by the solid red line. The oscillations in the EO response data are likely due to the fabricated microwave impedance not being exactly $50\,\Omega$. Further details about the EOM design are presented in the Supplement 1, Section 5. Additional low-frequency tests were performed to determine the extinction ratio and $V_\pi L$ figure-of-merit (see the Supplement 1, Section 6). The voltage-controlled optical extinction ratio was approximately 26 dB (on–off ratio of $400:1$) as shown in Fig. 3(b) and $V_\pi L$ was measured to be 3.5 V cm at 1550 nm.
Figure 3(d) shows the test setup for parametric pair generation and measurement of the CAR. Figure 3(e) shows the transmission measurement showing a loaded $Q$ for the microring of approximately 120 000 near 1550 nm, resulting in a photon lifetime of approximately 80 ps, which is similar to stand-alone devices [16]. We achieved the design target, and higher $Q$ values may not improve the pair generation rate in Si microrings due to nonlinear impairments at higher intra-cavity optical intensities [17]. (Note that very high-$Q$ Si microrings which use wide, multimode waveguides are not suitable for generating a high-purity state.) The measured free spectral range (FSR) of the microring was 7.6 nm which was near the design target (7.5 nm). Values of the FSR that are too small (radius too large) makes it difficult to separate the signal and idler photons using standard wavelength-division multiplexing (WDM) components, whereas FSR values that are too large (radius too small) make it difficult to optimize the waveguide-resonator coupling over a large range of wavelengths. Under optical pumping, the signal and idler photons generated by SFWM were separated using off-chip filter components and detected by superconducting nanowire single photon detectors and time-tagging, as shown schematically in the lower portion of Fig. 3(d). The measured CAR is shown in Fig. 3(f) with a clean, background-free second-order autocorrelation trace even at the highest pump rates as shown in the inset. This is typical of pair-generation in high-quality Si microrings where only low, milliwatt-scale pump powers are needed, which does not cause significant spontaneous scattering noise in the feeder waveguides. No correction was performed to the CAR calculation for the loss of the unused EOM device on the test chip. We estimate an on-chip brightness of $1.4 \times 10^8$ cp GHz$^{-1}$ mW$^2$ which improves upon our previous work using stand-alone microresonators [16].
Sequential measurements were performed on the combined circuit to demonstrate electronic tuning of the biphoton JSI by shaping the pump pulses and improvement of the purity, with a reduction in the participation of higher-order singular values. Purity estimated from the JSI is an upper-bound which is sufficient for the present purpose; more refined estimates for higher values of purity that approach unity can be obtained by measuring the joint spectral phase in various ways as discussed elsewhere [10,18,19]. Input CW light from a laser diode at 1550.51 nm was shaped using the integrated EOM and subsequently, the parametric process occurred in the high-$Q$ microresonator, and light was routed to the output ports using passive integrated waveguides. Measuring JSIs over a narrow spectral range is challenging and these results required approximately six orders of magnitude higher two-dimensional spectral resolution than for typical JSI in spontaneous parametric down conversion (SPDC) waveguides [20]. As shown in Fig. 4(a), the JSI was measured using stimulated emission tomography using probe light from a second, tunable laser and detecting the parametric mixing products at the output on a high-resolution optical spectrum analyzer [21–23]. Both the signal and pump are pulsed if they are injected into the same waveguide that is fed into the EOM, and we did not include secondary input ports and pathways to access the ring. The off-line signal processing performed using computer software on the raw data is based on the maximum-likelihood estimation procedure, and is described in the Supplement 1, Section 7.
Fig. 4. (a) Schematic diagram of the measurement of the JSI using the seeded method. (b) Open circles and connecting line segments are the expected trend of single-photon purity versus the ratio of the resonator photon lifetime $\tau _Q$ to the pump pulse full-width at half-maximum $\tau _\mathrm {pulse}$, reaching the theoretical limit around $\tau _Q/\tau _\mathrm {pulse} = 1$. The blue dots are the experimental results based on the measured JSIs shown in panel (c). (c) Measured JSIs after data processing for (1) continuous-wave pump, (2) pulsed pump width $\tau _\mathrm {pulse} =$ 540 ps, (3) 320 ps, and (4) 80 ps, which matches the photon lifetime in the cavity ($\tau _Q$). (d) Corresponding distributions of singular values (first 10).
The JSI without pump modulation, i.e., with CW pumping, is shown in Fig. 4(c1), where the $x$ and $y$ axis are the wavelength deviations in nanometers around the center of the signal and idler wavelength bands, which were 1543.02 nm and 1558.07 nm, respectively. As expected, the JSI under these conditions shows strong signal-idler correlations. A Schmidt decomposition was performed computationally, and the Schmidt number $K$ takes a high value for this state, approximately 32, and the associated purity $P = K^{-1}$ is low. Next, the modulator was driven with electrical waveforms generated by an arbitrary waveform generator (AWG) to carve optical pulses of widths of 560 ps, 320 ps, and 80 ps. While the AWG can accurately define the pulse shape, with 10 bits of vertical resolution and low spurious tones (which are key advantages over simpler methods of short-pulse generation that we have used earlier [24]), it has certain constraints. In these experiments, we were constrained to pick pulse widths in multiples of 40 ps by the AWG instrument but customized driver electronic circuits will not have this limitation. Also, the optimal operating wavelength, bias voltages, and optimized pulse waveform were optimized manually, but since the resulting purity trend is monotonic, we believe it should be simple to optimize under automatic control in the future. The resulting JSIs are shown in Figs. 4(c2)–4(c4), respectively. All these JSI plots are on a decibel scale, and the colormap ranges from 0 dB to $-13$ dB in Figs. 4(c1) and 4(c4), and from 0 dB to $-24$ dB in Figs. 4(c2) and 4(c3). No optical amplifier was used in the CW case, and among the pulsed-pump experiments, the lowest average optical power was necessarily obtained for the shortest-pulse case. These causes result in a compressed dynamic range for Figs. 4(c1) and 4(c4), compared with the intermediate cases in Figs. 4(c2) and 4(c3), but there is adequate signal-to-background ratio, with the latter not exceeding 5% of the former, to show the JSIs in all cases. The distribution of the first 10 singular values ($\kappa _k$, $k=1, 2, \ldots, 10$) of each JSI (i.e., the occurrence ratio, normalized to unity) are shown in Figs. 4(d1)–4(d4), respectively, and the Schmidt numbers are 2.31, 1.65, and 1.09, respectively.
The purity ($P$) is plotted versus the pulse width in Fig. 4(b): the experimental values are shown using blue filled circles (0.031, 0.43, 0.61, and 0.92, respectively), and the small open circles, connected by a trend line, show the expected behavior using simulations of the SFWM process for different pump pulse widths. Here $P$ increases monotonically but nonlinearly as the ratio of the pulse width to the cavity photon lifetime approaches unity. The experimental results for the shortest pulse is close to the theoretical bound $P \approx 0.93$ for this type of single bus-waveguide-coupled microring structure [23]. Higher values of $P$ can be achieved using different microresonator designs [25], which could also benefit from electro-optic pump pulse shaping using an integrated EOM. Alternatively, more complex manipulation of the pump spectrum can be attempted [26,27], but this strategy requires higher bandwidth than is available at present (the AWG only allows sample rates up to 50 giga-samples per second).
4. Discussion
As mentioned earlier, the technical complexity of the fabrication is balanced by the scientific need to overcome mutually incompatible constraints in simpler approaches, as explained below, and overcoming the limitations of a single-material photonics platform.
Crystalline Si uses the third-order ($\chi ^{(3)}$) parametric nonlinearity of SFWM in which the pump, signal, and idler wavelengths are near each other, and are conveniently positioned in the telecommunications band where pump laser diodes, filters, and detectors are common. The source brightness is greatly enhanced using high-$Q$ microresonators (e.g., ring resonators) which also narrows the bandwidth without using post-selection filters [16,28,29]. Poling is not required for SFWM in Si microresonators. Also, the SFWM process is quadratic in the pump and is less demanding in the EOM extinction ratio than SPDC; a $10:1$ on–off contrast ratio in the pump translates to a $100:1$ ratio in the rate of SFWM pairs generated from the “on" and “off" portions of the modulated pump (the latter being considered noise). However, pump pulse shaping cannot be adequately performed using integrated EOMs in Si photonics, which are fundamentally limited by strong trade-offs between speed, on–off ratio, chirp, and loss, due to the intrinsic carrier properties of Si [30,31].
LN and TFLN, can be used for photon pair generation using the second-order ($\chi ^{(2)}$) nonlinear SPDC process [32–34]. However, SPDC requires very widely separated pump and biphoton wavelengths (separated by an octave), which complicates the design of waveguides, couplers, and microresonator structures. Efficient SPDC in TFLN uses multi-mode waveguides and/or short-period periodic poling (PP), which requires specialized processing steps and depends on materials properties [35–37]. Because of the wide phase-matching bandwidth in TFLN waveguides, which typically exceeds tens of nanometers, photons generated using SPDC have broad bandwidths [36], and optimizing SPDC without losing brightness by pump pulse shaping would require an EOM bandwidth greater than 10 THz. This far exceeds what is feasible in integrated TFLN modulators currently [38]. Alternatively, SPDC in TFLN microresonators could achieve a narrower bandwidth, but potentially suffer from the trade-offs between brightness, purity, and heralding efficiency [39]. Thus, the generation of high-purity photons in TFLN continues to rely on off-chip short-pulse lasers and diffraction gratings and bulk-optics transmission filters for pump shaping [40] as with traditional PPLN waveguides.
We have overcome these mutually incompatible trade-offs, by jointly designing across two materials platforms, Si and TFLN, which are heterogeneously integrated on the same chip, selecting from the positive attributes of each platform. The complete photonic circuit has electro-optic, linear, and nonlinear components and the seamless interconnection between the devices avoids abrupt interfaces or junctions, and instead uses integrated photonic waveguides and multi-layer adiabatic transitions. Such an approach is also amenable to cost-effective, high-volume production using silicon-on-insulator wafers. Note that TFLN is not patterned, etched, or poled, and no precise alignment was needed for the bonding, which is an advantage over other integration strategies, such as chip-to-chip packaging or transfer printing. As such, this integrated architecture is more powerful than assemblies of different types of microchips that use flip-chip or butt-coupling techniques which can result in abrupt interfaces, higher failure rates, and difficulties in scaling-up to larger circuits.
In summary, we have reported a new approach to optimization of photon-pair generation. We control and optimize the parametric SFWM process without using mode-locked laser pump pulses or off-chip spectral shaping, and only a simple commercial CW laser diode is needed. We used external modulation, rather than direct modulation of the laser, because it offers higher bandwidths, higher extinction ratio, and chirp-free modulation among other potential benefits. We fabricated a photonic microchip which integrates a high-bandwidth (110 GHz), high extinction ratio (26 dB, or approximately $400:1$ contrast ratio) EOM for pump pulse shaping and a high-$Q$ ($1.2 \times 10^5$) Si microring resonator for biphoton generation. Though not shown here, simple CW lasers can also be fully integrated on a Si chip and have suitable properties for pumping pair generation in Si microrings [41]. The EOM device uses a stable and reliable Pockels material, LN, with a high electro-optic coefficient to overcome the inherent limitations of Si EOMs, and uses the efficient SFWM process in the Si microrings to avoid the inherent limitations such as wideband dispersion and periodic poling of parametric downconversion using LN waveguides. We incorporated LN with Si photonics without etching, patterning, or poling of TFLN, and therefore, no precise alignment is needed in the bonding step. The EOM device seamlessly connects to the Si microring on the same chip. There are low optical losses of approximately 1.8 dB for the EOM device and 0.7 dB additional on-chip loss in the various feeder and bus waveguides. When pump pulses are generated with a (short) lifetime that matches the photon lifetime in the microresonator, the purity saturates the theoretical maximum bound for this device. Similar devices could be used for more complex pulse shaping [26,27,42], or for generating short pump pulses that are needed for quantum dots [43]. While these experiments were carried out at 1550 nm using a hybrid LN–Si photonics platform, integrated EOMs with similarly high bandwidth and high extinction ratio also now exist at shorter wavelengths (e.g., below $1\,\mathrm{\mu}$m wavelength) using thin-film LN with silicon nitride (SiN) waveguides [44] and such integrated modulators may be useful for photon-pair generation using SiN microresonators [45,46]. Many quantum photonics applications will benefit from the heterogeneous integration of electro-optic, linear, and nonlinear optical functionality on the same microchip, as described here.
Funding
U.S. Government; Defense Advanced Research Projects Agency (HR001120S0008); Office of Naval Research (N00014-21-1-2805); National Science Foundation (ECCS-2025752).
Acknowledgments
The authors thank: M. Rüsing, P.O. Weigel, and J. Zhao (formerly of UC San Diego); A. Lentine (formerly of Sandia National Laboratories); N. Boynton and T A. Friedman (Sandia National Laboratories); C. Coleman, R. Scott, and G. Lee (Keysight Technologies) for discussions and assistance. The silicon wafer was fabricated at Sandia National Laboratories. Sandia National Laboratories is a multi mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The rest of the fabrication was performed at the San Diego Nanotechnology Infrastructure (SDNI) of UCSD, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the National Science Foundation (grant ECCS-2025752). This research was developed in part with funding from the Defense Advanced Research Projects Agency (DARPA) and the U.S. Government. This paper describes objective technical results and analysis. The views, opinions and/or findings expressed are those of the authors alone and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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