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arXiv:2607.07340

Time domain Stokes mechanism of pair correlated k gap solitons in nonlinear photonic time crystal slabs

J F Sun, Guowei Chen, Liang Zhang, Yiming Pan

Published Jul 8, 2026• 0 citations
arXivHTMLPDF

Abstract

Pair generation in time-varying media is commonly attributed to time reflection at temporal boundaries or to amplification inside momentum k gaps. Here we show that these two processes are connected by the time domain Stokes phenomenon. A finite duration photonic time crystal (PTC) slab provides the necessary Stokes connection between the incident vacuum mode, transient k gap amplification, and time boundary scattering. With Kerr nonlinearity, the otherwise unbounded amplification is arrested, spawning Kerr stabilized k gap solitons. When these solitons cross the exit boundary of the time slab, Stokes induced mode conversion produces a secondary pair generation process, yielding four spatially separated and entangled pulse branches. Detection of a backward propagating light pulse therefore heralds its forward propagating partner. We further propose combined Hanbury Brown Twiss and Hong Ou Mandel measurements to test their nonclassical correlations. These results reveal a link between asymptotic Stokes physics and quantum temporal scattering in PTCs, and suggest a route toward ultrafast heralded quantum light sources.

DOI
10.48550/arxiv.2607.07340

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Pair generation in time-varying media is commonly attributed to time reflection at temporal boundaries or to amplification inside momentum k gaps. Here we show that these two processes are connected by the time domain Stokes phenomenon. A finite duration photonic time crystal (PTC) slab provides the necessary Stokes connection between the incident vacuum mode, transient k gap amplification, and time boundary scattering. With Kerr nonlinearity, the otherwise unbounded amplification is arrested, spawning Kerr stabilized k gap solitons. When these solitons cross the exit boundary of the time slab, Stokes induced mode conversion produces a secondary pair generation process, yielding four spatially separated and entangled pulse branches. Detection of a backward propagating light pulse therefore heralds its forward propagating partner. We further propose combined Hanbury Brown Twiss and Hong Ou Mandel measurements to test their nonclassical correlations. These results reveal a link between asymptotic Stokes physics and quantum temporal scattering in PTCs, and suggest a route toward ultrafast heralded quantum light sources.
Nonlinear photonic time crystals (PTCs) can support solitons inside momentum k gaps, where the amplification of k gap modes is saturated by Kerr nonlinearity, forming spatially homogeneous but temporally localized excitations. Yet their quantum nature remains unclear. Here we quantize nonlinear k gap dynamics of PTCs and show that k gap solitons are represented by biphoton Fock ladder states. K gap amplification drives two-mode squeezing of the biphoton, while Kerr nonlinearity generates an anharmonic potential along the biphoton Fock ladder that balances this squeezing process, creating a finite biphoton number turning point and giving rise to quantum collapse and revival dynamics and nonclassical phase space interference. We further analyze how photon loss and dephasing reshape the biphoton statistics of quantized k gap solitons. Our results establish a biphoton Fock space description of k gap soliton quantization and provide a framework for studying quantum nonlinear excitations and entangled light generation in photonic time crystals.
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Controllable generation of photon pairs is essential for the utilization of quantum pair states for quantum applications such as quantum communication, quantum cryptography, teleportation, and linear optics quantum computing. Raman scattering is one of the most fundamental light-matter interactions and can be used to generate photon pairs. Using the spontaneous Stokes Raman interaction, a photon from a strong pump laser pulse is annihilated, and a Stokes photon and Raman-mediated collective excitation are created. This excitation can then be read out deterministically as an anti-Stokes photon with the application of a second laser pulse within the excitation lifetime, creating a photon pair. The heralding capability of the Stokes photon and lifetime of the excitation makes this source quasi-deterministic, where the anti-Stokes photon can be created at a later time than the Stokes. This gives additional advantages and uses over traditional photon-pair sources using nonlinear interactions of light in a transparent medium, which generate the pair of photons simultaneously. In this thesis, we study the correlations of photon pairs generated via spontaneous Raman interactions and demonstrate how these interactions can be used for quantum applications. First, we develop a model to study the spectral correlations between the Raman generated Stokes and anti-Stokes photons. This model is used to calculate the spectral single-photon purity of the photons in a generic material system ignoring the effects of material dispersion. We calculate how various parameters effect the purity including pump spectral bandwidth, excitation linewidth, and time delay between pump pulses. We then introduced an experimental realization of a Raman-mediated photon-pair source in an integrated quantum photonic circuit platform. Interstitial N2 molecules inherently trapped in silicon nitride thin films during the deposition process possess a sharp Raman mission corresponding to the vibrational mode of the molecules, which can be used as a Raman-mediated photon-pair source. We present evidence of N2 defects in silicon nitride thin films and estimate the defect density and excitation lifetime. By patterning the films into waveguide structures, the photon-matter interaction is enhanced. We perform finite-element simulation of light propagation in our fabricated waveguides and use the results to examine effects from the waveguide on ultrafast optical pulses and phase-matching requirements for efficient photon-pair generation. We then present experimental progress towards detecting Stokes and anti-Stokes photon-pair generation from N2 defects in silicon nitride waveguides. We show results from degenerate and non-degenerate wavelength optical pump pulses. We discuss limitations of the experimental methods and study in detail the sources of noise arising from the silicon nitride waveguide, and conclude by discussing future extensions on the results presented here.
If a boundary between two static media is moving with a constant superluminal velocity, or there is a sudden change of the refractive index with time, this yields generation of entangled pairs of photons out of vacuum propagating in the opposite directions. Here we show that during this process, entanglement of Minkowski vacuum is transferred to the entanglement of the generated photon pairs. If initially an electromagnetic pulse is present in the medium the photon generation is stimulated into the pulse mode, and since photons are created as entangled pairs the counter-propagating photon partners produce a pulse moving in the opposite direction, which is known as time reflection. Thus, time reflection occurs due to stimulated generation of the entangled photon pairs out of entangled vacuum and no photons in the original pulse are in fact being reflected. This is different from the mechanism of light reflection from spatial inhomogeneities for which no photons are generated.
Using a hydrogen-filled hollow-core photonic crystal fiber as a nonlinear optical gas cell, we study amplification of ns-laser pulses by backward rotational Raman scattering. We find that the amplification process has two characteristic stages. Initially, the pulse energy grows and its duration shortens due to gain saturation at the trailing edge of the pulse. This phase is followed by formation of a symmetric pulse with a duration significantly shorter than the phase relaxation time of the Raman transition. Stabilization of the Stokes pulse profile to a solitonlike hyperbolic secant shape occurs as a result of nonlinear amplification at its front edge and nonlinear absorption at its trailing edge (caused by energy conversion back to the pump field), leading to a reshaped pulse envelope that travels at superluminal velocity.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.