Biphoton Generation in Microring Resonators

• Biphoton generation in microring resonators is the on-chip creation of quantum-correlated photon pairs via resonantly enhanced nonlinear optical processes.
• The process exploits χ² and χ³ nonlinearities, modal phase matching, and dispersion engineering in high-Q cavities to ensure efficient conversion.
• These devices enable high-purity and high-brightness quantum light sources vital for applications in quantum communication, computing, and sensing.

Biphoton generation in microring resonators refers to the on-chip creation of quantum-correlated photon pairs via resonantly enhanced nonlinear optical processes in ring-shaped, high-Q photonic cavities. These devices exploit the strong optical confinement, dispersion engineering, and spectral selectivity afforded by microrings integrated in a wide range of material platforms, including silicon, thin-film lithium niobate, III–V semiconductors, and AlGaAs. The generated biphotons are critical resources for quantum information, communication, and photonic sensing.

1. Nonlinear Mechanisms for Biphoton Generation

Biphoton generation in microrings is mediated by either second-order (χ^2: spontaneous parametric down-conversion, SPDC) or third-order (χ^3: spontaneous four-wave mixing, SFWM) nonlinear interactions. The effective interaction Hamiltonians are:

• For χ^2 SPDC:

$$H_{\text{int}} = \varepsilon_0 \int dV\,\chi^{(2)}(\mathbf{r})\,E_p^{(+)}(\mathbf{r},t)\,E_s^{(-)}(\mathbf{r},t)\,E_i^{(-)}(\mathbf{r},t) + \text{h.c.}$$

A classical pump field $E_p$ drives creation of signal ($E_s$) and idler ($E_i$) photon pairs under phase-matching ($\Delta k = k_p - k_s - k_i = 0$) (Chen et al., 8 Aug 2025, Fontaine et al., 12 Sep 2024).

• For χ^3 SFWM:

$$H_{\text{int}} = \hbar\,\kappa\,a_p a_p a_s^\dagger a_i^\dagger + \text{h.c.}$$

Here, two pump photons ($a_p$) are annihilated to create a signal–idler pair ($a_s^\dagger$, $a_i^\dagger$) when energy and momentum are conserved ($2\omega_p = \omega_s + \omega_i$) (Grassani et al., 2016, Steiner et al., 2020).

The nonlinear spatial overlap integral and phase-matching conditions (modal or quasi-phase-matching) dictate efficiency, as does the ability to resonantly enhance the relevant interacting fields.

2. Principles of Resonant Enhancement and Phase Matching

In microrings, field enhancement by cavity resonance is quantified via the buildup factor $F_j \sim Q_j/\pi$ for mode $j$, where $Q_j$ is the loaded quality factor. The photon-pair generation rate scales strongly with the product of these enhancements:

$R \propto F_p\,F_s\,F_i\,|d_{\text{eff}}|^2\,P_p$

for χ^2 SPDC (Chen et al., 8 Aug 2025), or with $Q^3$ for degenerate SFWM (Savanier et al., 2015). The mode volumes $V_{\text{eff}}$ and spatial overlap integrals further determine the effective nonlinearity.

Phase matching is achieved by:

• Quasi-phase matching (e.g., periodic poling in TFLN, but challenging to scale (Chen et al., 8 Aug 2025)),
• Modal phase matching (engineering waveguide dispersion so, e.g., TM20 pump and TE00 signal/idler have $$n_\text{eff,TM20}(\lambda_p) = n_\text{eff,TE00}(\lambda_{s,i})$$),
• Intrinsic phase-matching in rings by mode-selective resonance (integer $m$ mode selection) (Steiner et al., 2020, Fontaine et al., 12 Sep 2024).

High-Q micro-rings thus serve as compact, efficient sources by exploiting long photon storage times and high circulating powers.

3. Modal Engineering and Dispersion Control

The modal structure and engineered dispersion are central for both high conversion efficiency and spectral properties of the generated biphotons. Techniques include:

• Using high-order transverse modes for pumps and fundamental modes for signal/idler to satisfy modal phase matching in TFLN (Chen et al., 8 Aug 2025).
• Engineering group-velocity dispersion ($\beta_2$) via waveguide cross-section to broaden phase-matching bandwidth and relax phase requirements in silicon and AlGaAs microrings (Savanier et al., 2015, Steiner et al., 2020).
• Fine-tuning free spectral range (FSR) and coupling constants to control mode selectivity and resonance alignment.

Mode converters and asymmetric mode-couplers provide high-efficiency conversion between pump and desired higher-order modes, as in TFLN (Chen et al., 8 Aug 2025). The overlap integral of the field profiles is calculated numerically for accurate determination of $d_{\text{eff}}$ and pair generation rates.

4. Biphoton State, Spectral Properties, and Purity

The output biphoton state is formally written as

$$|\psi\rangle \simeq |0\rangle + \iint d\omega_s d\omega_i\,\Phi(\omega_s,\omega_i)\,a_s^\dagger(\omega_s) a_i^\dagger(\omega_i)|0\rangle$$

where the joint spectral amplitude (JSA) $\Phi(\omega_s,\omega_i)$ encodes the frequency correlations. The JSA is shaped by the cavity Lorentzian transfer functions and the effective pump envelope, determined by the resonance widths and pumping regime:

• In CW pumping with narrow resonance, strong time-energy entanglement appears (high Schmidt number $K \gg 1$) (Grassani et al., 2016).
• In broadband (short-pulse) pumping or with increased cavity linewidth, spectral factorability ($K\sim1$) and nearly pure heralded single-photon states can be achieved (1808.04435, 1711.02401, Vernon et al., 2017, Ye et al., 24 Aug 2024).

Spectral engineering techniques, such as dual-pulse pump shaping (1711.02401) or resonance-splitting-induced ADP/TDSI control (Ye et al., 24 Aug 2024), enable direct control of the joint spectral intensity and entanglement structure.

Purity is quantified via the Schmidt decomposition of $\Phi(\omega_s,\omega_i)$, with heralded single-photon purities $P = 1/K > 0.99$ attainable in engineered platforms. Dual-bus or multi-resonator schemes provide independent tuning of $Q$ factors to further optimize purity and efficiency (Vernon et al., 2017, 1808.04435).

5. Material Platforms and Device Performance

Biphoton generation in microrings is established across various platforms:

Platform	Nonlinearity	Best Demo. Results	Reference
TFLN (thin-film LiNbO$_3$)	$\chi^{(2)}$	40.2 MHz/mW, CAR>1200, modal phase matching	(Chen et al., 8 Aug 2025)
Si (crystalline)	$\chi^{(3)}$	123 MHz, CAR≳600, reverse-bias free-carrier sweep-out	(Engin et al., 2012)
Si (amorphous)	$\chi^{(3)}$	$n_2$ ≈ $4\times$ crystalline, best for moderate Q	(Hemsley et al., 2016)
AlGaAs-on-insulator	$\chi^{(3)}$	$2\times10^{10}$ pairs/s/mW$^2$, $Q>1$M	(Steiner et al., 2020)
III–V (SPDC)	$\chi^{(2)}$	39 MHz/μW, $\eta\sim10^{-5}$, modal QPM	(Fontaine et al., 12 Sep 2024)

Key performance metrics are the photon pair rate (brightness), coincidence-to-accidental ratio (CAR), heralding efficiency, and spectral purity. Advances in device architecture (reverse-biased p-i-n diodes in silicon (Engin et al., 2012), modal phase matching in TFLN (Chen et al., 8 Aug 2025), and integration of mode converters) directly impact these figures.

6. Experimental Protocols and Characterization

Experimental setups involve:

• Pumping the ring with either CW or pulsed lasers (electronic step-recovery diodes for GHz-rate pulsed operation (Savanier et al., 2016)).
• Monitoring transmission and resonance splitting for parameter extraction via linear response fits (Ye et al., 24 Aug 2024).
• Measuring coincidence rates and CAR with superconducting nanowire detectors.
• Stimulated emission tomography (stimulated FWM) to reconstruct joint spectral intensities with high spectral resolution (Grassani et al., 2016).

Parameter extraction uses cavity transfer matrix models and TCMT, informed by direct transmission measurements. Integration with on-chip filtering, detection (SNSPDs), and active elements facilitates scalable quantum photonic circuits.

7. Design Trade-offs, Scalability, and Outlook

Optimization of biphoton sources in microrings involves trade-offs between coupling regime (critical vs overcoupling), $Q$ factor, pump regime (CW vs pulsed), entanglement (purity vs brightness), phase-matching bandwidth, and fabrication yield (Lukens et al., 11 Nov 2025, 1808.04435).

• Critical coupling maximizes single-photon extraction; overcoupling can maximize two-photon rates but at the cost of spectral purity.
• Modal phase matching removes need for periodic poling in TFLN, simplifying lithographic scalability (Chen et al., 8 Aug 2025).
• Advanced coupling architectures (dual-bus MZI, SCISSOR arrays) enable tailored biphoton statistics and superradiant scaling ($N^2$ enhancement with multiple rings) (Onodera et al., 2015).
• Emerging techniques (resonance splitting, on-chip differentiators) provide multi-axis programmability of the biphoton frequency-time wavefunction (Ye et al., 24 Aug 2024).

These advances support the development of high-rate, high-purity, and application-optimized on-chip biphoton sources for quantum communications, quantum computing (heralded single photons), and integrated quantum sensing, with ongoing research targeting $Q > 10^6$, deterministic multiplexing, and further monolithic integration (Chen et al., 8 Aug 2025, Steiner et al., 2020, Ye et al., 24 Aug 2024).