Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.30508

Quantization and Biphoton Statistics of k-Gap Solitons in Nonlinear Photonic Time Crystals

Liang Zhang, Chenhao Pan, Yiming Pan

physics.opticsnlin.PSquant-phSubmitted Jun 29, 2026• Announced Jun 30, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

Comments
34pages

Related papers

Optical Exciton Molecules in Three-Dimensional Kerr-Nonlinear Photonic Crystals

Ze Cheng

Three-dimensional Kerr-nonlinear photonic crystals support a new kind of quantum gap solitons. Such 3D-quantum gap solitons are described by an approximate Bethe-ansatz solution of the quantized nonlinear-field Hamiltonian under the effective mass approximation. Their main manifestations are predicted: (i) a series of discrete transmission peaks in the band gap, which progresses linearly with the diphoton number; (ii) Bessel-function dependence of the intensity correlation function on the detector separation.

Communications in Theoretical Physics•Dec 15, 1998•1 citation

Phase-space dynamics of a quantum dissipative Kerr nonlinear oscillator

Karjula, Matias

Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.

•Oct 24, 2025•0 citations

Quantum optics in photonic crystals

Gershon Kurizki, Tomáš Opatrný, David Petrosyan +1 more

We survey basic quantum optical processes that undergo modifications in photonic crystals doped with resonant atoms: (a) Solitons and multi-dimensional localized 'bullets' propagating at photonic band gap frequencies. These novel entities differ substantially from solitons in Kerr-nonlinear photonic crystals. (b) Giant photon-photon cross-coupling that can give rise to fully entangled two-photon states. We conclude that doped photonic crystals have the capacity to form efficient networks for high-fidelity classical and quantum optical communications.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 26, 2002•0 citations

Classical and quantum nonlinear optics in confined photonic structures

Mohamadreza Ghafari Banaee

Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.

•Jan 1, 2008•0 citations

Multimode squeezing in soliton crystal microcombs

Melissa A. Guidry, Daniil M. Lukin, Ki Youl Yang +1 more

Soliton microcombs are self-organized pulses of light sustained in driven Kerr microresonators, intensively studied for applications in integrated photonic technologies and for their rich nonlinear dynamics. In this work, we theoretically study the collective dynamics of the quantum fluctuations of soliton microcombs. We find that the mean field of a dissipative Kerr soliton crystal is accompanied by pulses of squeezed multimode vacuum and derives its operational stability from the strong detuning of the below-threshold parametric process. We present a photonic architecture that enables independent control of the above- and below-threshold states and achieves a high degree of squeezing (>15dB) in the output waveguide with realistic losses. Our work elucidates the quantum dynamics of formation and annihilation in dissipative Kerr soliton systems, and establishes a pathway for the realization of a practical integrated source of multimode squeezed light.

Optica•May 5, 2023•36 citations

Quantum electrodynamics of photonic time crystals

Junhyeon Bae, Kyungmin Lee, Bumki Min +1 more

Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.

arXiv:2501.03106•Nature Communications•Dec 19, 2025•7 citations
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.
Three-dimensional Kerr-nonlinear photonic crystals support a new kind of quantum gap solitons. Such 3D-quantum gap solitons are described by an approximate Bethe-ansatz solution of the quantized nonlinear-field Hamiltonian under the effective mass approximation. Their main manifestations are predicted: (i) a series of discrete transmission peaks in the band gap, which progresses linearly with the diphoton number; (ii) Bessel-function dependence of the intensity correlation function on the detector separation.
Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
We survey basic quantum optical processes that undergo modifications in photonic crystals doped with resonant atoms: (a) Solitons and multi-dimensional localized 'bullets' propagating at photonic band gap frequencies. These novel entities differ substantially from solitons in Kerr-nonlinear photonic crystals. (b) Giant photon-photon cross-coupling that can give rise to fully entangled two-photon states. We conclude that doped photonic crystals have the capacity to form efficient networks for high-fidelity classical and quantum optical communications.
Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.
Soliton microcombs are self-organized pulses of light sustained in driven Kerr microresonators, intensively studied for applications in integrated photonic technologies and for their rich nonlinear dynamics. In this work, we theoretically study the collective dynamics of the quantum fluctuations of soliton microcombs. We find that the mean field of a dissipative Kerr soliton crystal is accompanied by pulses of squeezed multimode vacuum and derives its operational stability from the strong detuning of the below-threshold parametric process. We present a photonic architecture that enables independent control of the above- and below-threshold states and achieves a high degree of squeezing (>15dB) in the output waveguide with realistic losses. Our work elucidates the quantum dynamics of formation and annihilation in dissipative Kerr soliton systems, and establishes a pathway for the realization of a practical integrated source of multimode squeezed light.
Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.