Abstract
Spontaneous two-photon emission (STPE) is a second-order quantum radiation process with implications in astrophysics1, atomic physics2 and quantum technology3. In particular, on-demand STPE from single quantum emitters has long been predicted to revolutionize photonic quantum science and technology4,5. Here we report STPE with brightness comparable to that of competing single-photon radiation from a single semiconductor quantum dot deterministically coupled to a high-quality micropillar cavity. This is because of strong vacuum fluctuations in the microcavity, which drive a biexciton directly to the ground state. We show the quantum nature associated with STPE in the cavity quantum electrodynamics regime using photon statistics measurements. Furthermore, STPE is exploited to build unconventional entangled quantum light sources that can simultaneously achieve near-unity entanglement fidelity for spontaneous parametric down-conversion sources and on-demand photon emission for atomic quantum emitters. Our work provides insights into the two-photon process in the quantum regime, which could empower photonic quantum technology with nonlinear quantum radiation.
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Data availability
The data that support the plots in this paper and other findings of this study are available at Figshare64 (https://doi.org/10.6084/m9.figshare.29155466.v1). All other data used in this study are available from the corresponding author upon request.
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All codes produced during this research are available from the corresponding author upon request.
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Acknowledgements
J.L. thanks X. Zhou, X. Ren, R. Jin and C. Zou for discussions. This research was supported by the National Natural Science Foundation of China (12494600, 12494602, 62035017, 12361141824 and 12304409); the National Key Research and Development Program of China (2021YFA1400800); the Natural Science Foundation of Guangdong Province (2023B1515120070 and 2024B1515040013); the Guangdong Provincial Quantum Science Strategic Initiative (GDZX2206001 and GDZX2306003); the Chinese Academy of Sciences Project for Young Scientists in Basic Research (YSBR-112) and the National Super-Computer Center in Guangzhou. Y.S. and M.C. acknowledge funding by the Return Program of the State of North Rhine-Westphalia.
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J.L. conceived the project; S.L., J.L. and H.L. designed the epitaxial structure and the devices; H.L., Y.Y., C.-A.Y. and H.N. grew the QD wafers; S.L., J.Y. and X.L. fabricated the devices; S.L. and Y.W. built the setup and performed the optical measurements; Y.S. and M.C. developed the theory model to calculate spectra and correlations; Y.M. and X.H. provided the SNSPD for lifetime and correlation measurement; S.L. and J.L. analysed the data; J.L. and S.L. prepared the paper with input from all authors; J.L., M.C., Z.N. and X.W. supervised the project.
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Extended data figures and tables
Extended Data Fig. 1 Polarization characteristics of the QD and micropillar cavity investigated in this study.
(a) Polarization-resolved spectra of the cQED system under CW above-band excitation. Under above-band excitation, X and XX are not equally populated and the non-resonant coupling effect is more pronounced than that of the resonant excitation used in the maintext. (b) Polarization dependence of the energy difference between X and XX, from which a fine-structure splitting (FSS) of 8.1 μeV is extracted. (c) Polarization dependence of the energy shift of the cavity mode, showing a cavity splitting of 3.4 μeV between horizontally (H) and vertically (V) polarized modes. The angle between the main polarization axes of the QD and the cavity is 0.23°. (d) The reflection spectrum of the cavity in H-polarization. The data is fitted with a Lorentzian function, leading to a FWHM of 0.0338 nm corresponding to a Q-factor of 26,911(5).
Extended Data Fig. 2 Schematic of the setup for optical characterizations.
(a) A pulse shaper in a 4f configuration is used to shape the femtosecond (fs) pulses to picosecond (ps) pulses with a pulse duration of 79.95 ps. (b) Controlling the power of the laser by rotating a polarizer between two fixed polarizers with the same polarization axis, the laser power is monitored and measured by a power meter. (c) Cryogenic optical system for excitation and collection. The QD is housed in a cryostat at 1.67 K. Lasers are delivered to the optical path via an optical fiber to excite the QD and the emitted photons are collected by a single-mode fiber for further analysis. To characterize the two-photon nature of the emission, the QD is pumped under two-photon resonant excitation in a cross-polarization configuration with an extinction ratio as high as 106 in which the excitation laser is V-polarized while only H-polarized emission is collected. Pairs of polarizers and half-wave plates are inserted into the excitation and collection optical paths for polarization control. The photons collected in the fiber are sent either to a spectrometer for spectral analysis or through a grating filter to select specific spectral components. To characterize the entanglement fidelity, a CW laser and a pulsed laser with energies resonant with XX and X are used to excite the QD. The half-wave plate and polarizer in the collection path are removed, and the photons are sent to a tomography measurement setup for correlation measurements in different polarization basis. (d) A home-made grating filter with an FWHM of 0.061 nm and an efficiency of ~70%. (e) The spectrometer is equipped with 1800 lines per millimeter grating, a focal length of 750 mm, and a spectral resolution of ~4 GHz at 900 nm. (f) Correlation measurement unit. (g) Tomography measurement setup for XX-X cascaded emission, the HWP, QWP, and polarizer are used to set the polarization basis. (h) Tomography measurement setup for STPE. BS: beam splitter, Pol: polarizer, HWP: half-wave plate, QWP: quarter-wave plate, EMCCD: electron-multiplying charge-coupled device, SNSPD: superconducting nanowire single-photon detector (time jitter: 24.68 ps, quantum efficiency: 10%), APD: avalanche photon diode (time jitter: 250 ps, quantum efficiency: 25%).
Extended Data Fig. 3 Convoluted spectra under CW resonant excitation.
(a) Calculated power-dependent spectra under CW resonant excitation after convoluting with the IRF of the spectrometer, with a resolution of 4 GHz. (b) The calculated spectrum with a driving strength of 2 GHz (Fig. 2(b)) without the convolution of the IRF. (c) Calculated spectrum with the convolution of the IRF. (d) Experimental spectrum for the corresponding excitation power (Fig. 2(a)).
Extended Data Fig. 4 Effective decay process via cavity coupling.
(a) The full three-level system dynamics. The biexciton state (\(| XX\rangle \)) and exciton state (\(| Y\rangle \)) are coupled to the cavity mode via interaction strength g, with cavity losses denoted by κ. (b) The effective two-photon decay channel after applying the Schrieffer-Wolff transformation and adiabatic elimination. The cavity coupling leads to additional effective decay rates: the STPE rate γ2p, the effective rate from the biexciton to the exciton γXX and the effective rate from exciton to ground state γX. See Methods section for the derivation of the effective rates.
Extended Data Fig. 5 Evaluation of the single-photon contribution via the phonon-assisted process to STPE.
(a) Schematics of the emission from the cQED system. Cavity photons are predominantly emitted from the top of the micropillar, while the direct QD emission can be probed from the side [Phys. Rev. B 93 115308 (2016)]. (b) Simulated emission spectra with and without accounting for QD-phonon interaction for the direct QD emission to the side (based on the first-order coherence for QD transition operators \(\langle {\sigma }_{Y}^{+}(t+\tau ){\sigma }_{Y}^{-}(t)\rangle \)). (c) Simulated emission spectra with and without accounting for QD-phonon interaction for the cavity emission to the top (based on the first-order coherence for cavity operators \(\langle {b}^{\dagger }(t+\tau )b(t)\rangle \), and consistent with what is measured in the experimental spectra). While the direct emission from the QD features sizable phonon side bands, the cavity effectively filters the emission, leading to a strong suppression of phonon sidebands, in agreement with literature [Nature Photon. 11, 521 (2017)]. (d) Simulated decay of an initially prepared biexciton state. Single-photon emission from the biexciton state occurs by a process involving only virtual occupations of the cavity. I.e. the slight mixing between state \(| XX,0\rangle \) and \(| Y,1\rangle \) enables emission via cavity losses towards the state \(| Y,0\rangle \) (see methods section on derivation of γXX). The photon energy corresponds to the difference between energies of the initial and final states, \(| XX,0\rangle \) and \(| Y,0\rangle \), respectively. This is opposed to a sequential process, which would involve significant occupations of the state \(| Y,1\rangle \), where the photon-emission to state \(| Y,0\rangle \) would contribute with a cavity photon energy resonant with the TPE transition. This is seen in panel (d) by the fact that the coherence between \(| XX,0\rangle \) and \(| Y,1\rangle \) are much larger than the occupations of \(| Y,1\rangle \). Furthermore, phonons do not significantly affect the dynamics of these observables. In particular, no significant phonon-assisted cavity feeding is found that would result in sizable real occupations of the state \(| Y,1\rangle \).
Extended Data Fig. 6 Simulation of \({{\boldsymbol{g}}}_{{\boldsymbol{X}}}^{({\bf{2}})}({\boldsymbol{\tau }})\) and \({{\boldsymbol{g}}}_{{\boldsymbol{X}}{\boldsymbol{X}}}^{({\bf{2}})}({\boldsymbol{\tau }})\).
To reproduce the shape and width of the delay time dependence of the second-order coherence under weak CW driving (Ω = 2.5 GHz) filtered at the single-photon emission frequencies, we employ the quantum regression theorem. The left panel (a) shows the time evolution of Y exciton occupations when the system is prepared in the ground state at time t = 0. This is proportional to \({g}_{X}^{(2)}(\tau )\), where the signal arises from Y occupations, where upon the first photon detection the system wave function collapses to the ground state. The right panel (b) show the XX occupation, given the state of the system is collapsed to the Y exciton state at time t = 0, which is proportional to \({g}_{XX}^{(2)}(\tau )\). The results are similar in shape and timescales as the measured g(2)(τ) in Fig. 2(d,e), respectively. Comparison of simulations with and without including phonons further shows that, after normalization, phonons hardly affect the second-order coherence.
Extended Data Fig. 7 Dressed state picture of the energy levels under CW two-photon resonant excitation.
(a) Energy level diagram of the bare QD states. (b) Dressed energy level diagram and allowed H-polarized transitions in the rotating frame of the excitation laser, ωL with XX binding energy \({E}_{B}^{XX}\) obtained by analytically diagonalizing Hamiltonian H4l for constant driving Ω. V-polarized driving does not affect the H-polarized exicton state \(| {D}_{H}\rangle =| X-H\rangle \) with energy \({E}_{{D}_{H}}=(1/2){E}_{B}^{XX}\). The three remaining states consist of the antisymmetric combination of ground and biexciton state \(| {D}_{0}\rangle =(1/\sqrt{2})[| 0\rangle -| XX\rangle ]\), whose energy remains \({E}_{{D}_{0}}=0\), and two states \(| {D}_{\pm }\rangle =(1/{N}_{\pm })[| 0\rangle +(2E\,{/}_{\pm }\hbar \varOmega )+| XX\rangle ]\) with driving dependent energy \({E}_{\pm }=(1/4){E}_{B}^{XX}\pm (1/4)\sqrt{8{\hbar }^{2}{\varOmega }^{2}+{({E}_{B}^{XX})}^{2}}\). N± are normalization constants. Thus, the driving-induced gap between \(| {D}_{0}\rangle \) and \(| {D}_{-}\rangle \) as well as between \(| {D}_{H}\rangle \) and \(| {D}_{+}\rangle \) is \(\Delta =-\,(1/4){E}_{B}^{XX}+(1/4)\sqrt{8{\hbar }^{2}{\varOmega }^{2}+{({E}_{B}^{XX})}^{2}}\). (c) Calculated spectrum under driving strength of Ω, and showing the location of peaks which are well described the dressed-level picture in (b).
Extended Data Fig. 8 Calibration of the setup efficiency and calculation of the photon conversion efficiency.
(a) All the optical elements used in the collection path. (b) Transmissions of the optical elements in the setup with a total efficiency of 0.034. We detect 496.58 K photon pairs per second under two-photon resonant excitation at π-pulse, with an excitation rate of 80 MHz. Taking into account our setup’s overall efficiency of 0.034 and an extraction efficiency of 0.8 for a typical micropillar device, we can deduce that 18.25 million photon pairs per second are generated in the cavity, corresponding to a generation efficiency of 18.25/80 = 0.228. By measuring the laser power of 0.77 nW at π-pulse, we estimate that approximately 26 photons were coupled into the cavity per single pulse. The photon conversion efficiency-defined as the probability of converting a single input photon from the laser pulse into a spontaneously emitted photon pair-is calculated as 0.228/26 = 0.877%.
Extended Data Fig. 9 Characteristics of the STPE under cascaded resonant excitation.
(a) Spectrum under cascaded excitation. (b) Relation between the STPE intensity and pulsed laser power, with the CW laser power fixed at 4.7 μW, demonstrating clear Rabi oscillations. (c) Relation between the STPE intensity and CW laser power, with the pulsed laser power fixed at π-pulse. (d) Typical lifetimes of STPE measured at different CW laser powers. The oscillation originates from the coherent interaction between the QD and the resonant CW laser. The driving strength(ΩXX) of 1.78 GHz at a power of 4.7 μW is extracted. (e) Power-dependent entanglement fidelity under cascaded resonant excitation. The fidelity remains above 0.99 even at a power of 26 μW, where the QD is far beyond the saturation power.
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Liu, S., Wang, Y., Saleem, Y. et al. Quantum correlations of spontaneous two-photon emission from a quantum dot. Nature 643, 1234–1239 (2025). https://doi.org/10.1038/s41586-025-09267-6
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DOI: https://doi.org/10.1038/s41586-025-09267-6
