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.
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.
Stimulated parametric down-conversion (StimPDC) produces an idler beam that exhibits a phase conjugate of the spatial structure of the classical seed beam. Extending this effect to the single-photon regime can, in principle, enable the control of the orbital angular momentum of single photons. However, its experimental implementation remains challenging due to the lower photon flux of realistic single-photon sources compared to a classical pump beam, which causes the StimPDC process to occur less frequently compared to its spontaneous counterpart. To overcome this, we propose a cascaded parametric down-conversion scheme, in which the signal photon from a spontaneously down-converted pair seeds the StimPDC process, while the idler photon heralds the seed's presence. This configuration uses coincidence detection to effectively post-select for stimulated events among the background of spontaneous contributions. We show that phase conjugation at the single-photon level manifests as a bias towards equal orbital angular momentum between the heralding idler and the stimulated idler. Our results offer a practical route to manipulate single-photon correlations in the orbital angular momentum degree of freedom and could have implications for applications such as free-space quantum communication and quantum-enhanced sensing.
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.
The ability to manipulate the orbital angular momentum (OAM) of a single photon is of vital importance to photonic quantum technologies. A particularly relevant operation is the phase conjugation of OAM. One can in principle achieve this using stimulated parametric down-conversion (StimPDC), which produces an idler beam that exhibits a phase conjugate of the seed beam’s spatial structure. However, implementing StimPDC for single-photon OAM phase conjugation remains challenging. This is because the photon flux of realistic single-photon sources is low compared to that of a classical pump beam, which causes the StimPDC process to occur less frequently compared to its spontaneous counterpart. To overcome this, we propose a cascaded parametric down-conversion scheme, in which the signal photon from a spontaneously down-converted pair seeds the StimPDC process, while the idler photon heralds the seed’s presence. This configuration uses coincidence detection to effectively post-select for stimulated events among the background of spontaneous contributions. We show that single-photon OAM phase conjugation manifests as a bias toward equal OAM between the heralding idler and the stimulated idler. Our results offer a practical route to manipulate single-photon correlations in the OAM degree of freedom and could have implications for applications such as free-space quantum communication and quantum-enhanced sensing.
In this work, we propose and demonstrate a turbulence-resilient scheme for free-space quantum communication. By leveraging the phase conjugation property of stimulated parametric down-conversion, our scheme enables all-optical dynamic correction of spatial-mode distortion induced by atmospheric turbulence, thereby enhancing the secure key rate in high-dimensional quantum key distribution. We develop a theoretical model that provides detailed guidelines for selecting the optimal basis and spatial properties needed to maximize the efficiency of the proposed scheme. Both numerical simulations and experimental results show that, even under strong turbulence, our scheme can reduce the quantum error rates well below the security threshold. These results highlight the potential of nonlinear optical approaches as powerful tools for robust quantum communication in realistic free-space environments. Our work could have important implications for the practical implementation of secure quantum channels over long free-space distances.
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.
Free-space quantum communications offers a promising route for securely transmitting information over long distances. However, a major challenge for these systems is atmospheric turbulence, which distorts the spatial structure of light and can severely limit the amount of information that can be reliably transmitted. In this work, we propose and demonstrate a turbulence-resilient scheme for free-space quantum communication. By leveraging the phase conjugation property of stimulated parametric down-conversion, our scheme enables all-optical dynamic correction of spatial-mode distortion induced by atmospheric turbulence, thereby enhancing the secure key rate in high-dimensional quantum key distribution. We develop a theoretical model that provides detailed guidelines for selecting the optimal basis and spatial properties needed to maximize the efficiency of the proposed scheme. Both numerical simulations and experimental results show that, even under strong turbulence, our scheme can reduce the quantum error rates well below the security threshold. These results highlight the potential of nonlinear optical approaches as powerful tools for robust quantum communication in realistic free-space environments.