Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the elementary physical mechanism of stimulation by individual photons has remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by an ultra-weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we access the regime in which the single-photon component of the seed can stimulate the emission of a photon pair, giving rise to a temporally correlated three-photon event. We observe a clear enhancement that cannot be explained by spontaneous processes or accidental coincidences alone, providing time-domain evidence of the fundamental stimulation mechanism at the single-photon level. Beyond its fundamental significance, these results suggest new ways to characterize seed–PDC mode overlap, phase matching, and weak nonlinear coupling in regimes where bright stimulated-emission measurements are not appropriate. Multimode and interferometric extensions could enable correlation-based imaging and phase-sensitive spectroscopy.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the elementary physical mechanism of stimulation by individual photons has remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by an ultra-weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we access the regime in which the single-photon component of the seed can stimulate the emission of a photon pair, giving rise to a temporally correlated three-photon event. We observe a clear enhancement that cannot be explained by spontaneous processes or accidental coincidences alone, providing time-domain evidence of the fundamental stimulation mechanism at the single-photon level. Beyond its fundamental significance, these results suggest new ways to characterize seed–PDC mode overlap, phase matching, and weak nonlinear coupling in regimes where bright stimulated-emission measurements are not appropriate. Multimode and interferometric extensions could enable correlation-based imaging and phase-sensitive spectroscopy.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the regime in which stimulation occurs at the single-photon level has hitherto remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by a weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we observe a clear enhancement that cannot be accounted for by spontaneous processes or accidental coincidences alone, and is consistent with stimulation involving the seed and the generated photon pair. These results provide time-domain evidence of seed-induced three-photon correlations and suggest new ways to engineer and probe multi-photon states for quantum imaging, sensing, and information processing.
Stimulated parametric down-conversion (StimPDC) is the seeded version of the process that underlies much of photonic quantum information. Replacing the vacuum at one input port with a coherent seed leaves the interaction Hamiltonian, the phase-matching function and the two-photon amplitude unchanged, while raising the output to levels accessible with ordinary classical detectors. This review treats the transverse spatial physics of that process. We show that a single relation, in which the idler amplitude is the pointwise product of the pump field with the complex conjugate of the seed, organizes results usually presented separately: the image and coherence transfer experiments of the 1990s; phase conjugation and its use for wavefront correction; the conservation and conjugation of orbital angular momentum, together with the generation of radial modes and geometric intensity patterns; and the processing of vector vortex beams carrying spatially varying polarization. We then consider StimPDC as an instrument rather than as an object of study, covering stimulated emission tomography, the experimental realization of Klyshko's advanced-wave picture, and the transfer of partial coherence, including the conservation of the twist phase of twisted Gaussian Schell-model beams. We close with the quantum regime, reached when the seed approaches the single-photon level or the idler is used as a herald, and with an assessment of open problems and prospective applications.
We study the process of seeded or stimulated third-order parametric down-conversion as an extension of our previous work on spontaneous parametric down-conversion (TOSPDC). We present general expressions for the spectra and throughputs expected for the cases where the seed field or fields overlap either only one or two of the TOSPDC modes and allow for both pump and seed to be either monochromatic or pulsed. We present a numerical study for a particular source design, showing that doubly overlapped seeding can lead to a considerably greater generated flux as compared with singly overlapped seeding. We, furthermore, show that doubly overlapped seeding permits stimulated emission tomography for the reconstruction of the three-photon TOSPDC joint spectral intensity. We hope that our paper will guide future experimental efforts based on the process of third-order parametric down-conversion.
Stimulated parametric down-conversion (StimPDC) can act as a phase-conjugating nonlinear process when one of the down-converted modes is driven by a bright classical field. In this regime, the stimulated contribution to the nonlinear interaction dominates over the spontaneous background and the generated idler reproduces the conjugated phase of the seed with high fidelity. This behaviour has enabled classical turbulence-mitigation schemes in free-space optical channels, where a probe beam acquires a distorted wavefront that is deterministically conjugated in a nonlinear crystal and corrected upon reverse propagation. This thesis examines whether the same mechanism can be extended to the single-photon regime. The analysis begins by reviewing the spatial-mode structure of classical StimPDC using a Laguerre–Gaussian description of the nonlinear interaction. The turbulence-mitigation protocol is then summarized to clarify why high-fidelity phase conjugation is central to its operation. The main theoretical development introduces the single-photon–seeded version of the process, referred to as SPS-PDC. Using the full biphoton amplitude of SPS-PDC, the idler mean photon number is derived and shown to contain coherent spontaneous and stimulated contributions of comparable magnitude when only one photon occupies the seeded mode. Because the stimulated term no longer overwhelms the spontaneous background, the generated idler does not reproduce a unique conjugated wavefront. This result identifies a fundamental limit: perfect phase conjugation cannot be achieved with a single-photon seed in a second-order nonlinear interaction of this type. The implications of this scaling behaviour are examined in the context of turbulence mitigation and quantum key distribution. Although a single-photon version of the classical protocol would offer intrinsic security, the absence of deterministic conjugation prevents reliable wavefront correction. The thesis concludes by outlining an experimental approach for resolving the joint spatial structure of the two idler photons produced in a cascaded parametric down-conversion process. Such measurements would directly test the predicted division between spontaneous and stimulated contributions and further clarify the boundary between classical and quantum phase-conjugation regimes.
Quantum correlations, where two or more parties exhibit strong correlations in a particular degree of freedom are important resources for fundamental science [1], such as the exploration of non-locality and entanglement, as well as non-classical technologies including quantum computation, quantum key distribution and quantum metrology. One typical way to generate correlated photon pairs is to use the spontaneous four-wave mixing process, with demonstrations on various platforms [2]. So far, single-photon stimulated four-wave mixing (FWM) has been demonstrated in optical fibers [3]. Here we show induced correlation by single photon seeded FWM through exploiting the orthogonal polarization modes in an integrated ring resonator [4]. We allow two different four-wave mixing processes to occur simultaneously with the same signal frequency mode but different idler frequency modes (see Fig.1(a)). The single-photon induced FWM process, named here seeded FWM, was created through the link of type-0 SFWM and type-2 SFWM. In the type-0 process, two excitation photons from the same field are converted into two new photons, signal and idler, with the same polarization as the pump field. While in the type-2 FWM, two annihilated photons, each one from a different polarized pump field, namely TE and TM, generate an orthogonal-polarized photon pair. More importantly, spatial and temporal overlapping of two processes and their sharing of one common resonance lead to correlation between the other two signal photons, one from each process. For example, an idler photon created in type-0 FWM seeds the type-2 FWM process or vice versa, i.e. the TM idler photon in Fig. 1, induces correlation between the signal TM and TE photons. This is proven by the observation of a clear coincidence peak for both signal photons in Fig.1(b). Furthermore, we confirmed our observation via power-dependent correlation measurements (see Fig.1 (c)). We summarized the true coincidence count (C) and its coincidence to accidental ratio (CAR) when only the TE pump power is increased while maintaining the TM mode pump power (black squares), and both pump powers are increased with a constant ratio (blue dots). We found that the seeded FWM scales with the square of both pump powers (C ∝ PjePtm) and that the CAR reach its maxima of 1.5 at the available pump power, indicating thermal statistics. Our findings are relevant to the fundamental understanding of spontaneous parametric effects as well as single-photon induced processes and single photon cloning.
We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.