Experimental emulator of pulse dynamics in fractional nonlinear Schrödinger equation

• URL: http://arxiv.org/abs/2311.15150v2
• Date: Thu, 02 Jan 2025 17:17:51 GMT
• Title: Experimental emulator of pulse dynamics in fractional nonlinear Schrödinger equation
• Authors: Shilong Liu, Yingwen Zhang, Stéphane Virally, Ebrahim Karimi, Boris A. Malomed, Denis V. Seletskiy,
• Abstract summary: We present a nonlinear optical platform that supports the pulse propagation governed by a generalized fractional nonlinear Schr"odinger equation (FNLSE)<n>Our approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity.<n>These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.
• Score: 6.084996921308185
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a nonlinear optical platform to emulate a nonlinear \textit{L\'{e}vy waveguide} that supports the pulse propagation governed by a generalized fractional nonlinear Schr\"{o}dinger equation (FNLSE). Our approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity. In the intra-cavity configuration, we observe stable \textit{fractional solitons} enabled by an engineered combination of the fractional and regular dispersions in the fiber cavity. The soliton pulses exhibit their specific characteristics, \textit{viz.}, "heavy tails" and a "spectral valley" in the temporal and frequency domain, respectively, highlighting the effective nonlocality introduced by FGVD. Further investigation in the extra-cavity regime reveals the generation of spectral valleys with multiple lobes, offering potential applications to the design of high-dimensional data encoding. To elucidate the spectral valleys arising from the interplay of FGVD and nonlinearity, we have developed an innovative "force" model supported by comprehensive numerical analysis. These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.

Related papers

• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems. We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors. We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Nonlinear squeezing generation via multimode PDC and single photon measurement [0.5999777817331317]
  nonlinear squeezing is a property of non-Gaussian states of light. We study the generation of nonlinear squeezing in multimode systems produced by the photon-added coherent state technique.
  arXiv  Detail & Related papers  (2024-11-14T11:44:49Z)
• Nonlinear semiclassical spectroscopy of ultrafast molecular polariton dynamics [0.0]
  We introduce a theoretical framework that allows for the systematic and efficient description of the ultrafast nonlinear response of molecular polaritons. Our approach is based on a semiclassical, mean-field evolution of the molecular Hamiltonian and the cavity field. We show how, by storing the pulses, the cavity facilitates additional excitation pathways which are not possible in free space.
  arXiv  Detail & Related papers  (2024-10-22T02:19:13Z)
• Diffraction and pseudospectra in non-Hermitian quasiperiodic lattices [0.0]
  spatial distributions of gain and loss elements are physically possible in the context of integrated photonic waveguide arrays. We systematically study the non-Hermitian quasiperiodic Aubry-Andr'e-Harper model with on-site gain and loss distribution (NHAAH)
  arXiv  Detail & Related papers  (2024-10-11T18:38:30Z)
• Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-Lévy-index fractional Kerr media [13.082347639610987]
  Modulation instability of continuous waves is investigated in the two-L'evy-index system too. We produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.
  arXiv  Detail & Related papers  (2024-09-02T10:16:53Z)
• Josephson bifurcation readout: beyond the monochromatic approximation [49.1574468325115]
  We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits. This circuit can serve as an efficient detector of the quantum state of superconducting qubits.
  arXiv  Detail & Related papers  (2024-05-25T22:22:37Z)
• Weak Kerr Nonlinearity Boosts the Performance of Frequency-Multiplexed Photonic Extreme Learning Machines: A Multifaceted Approach [49.1574468325115]
  We investigate the Kerr nonlinearity impact on the performance of a frequency-multiplexed Extreme Learning Machine (ELM) The Kerr nonlinearity facilitates the randomized neuron connections allowing for efficient information mixing. We introduce a model to show that, in frequency-multiplexed ELMs, the Kerr nonlinearity mixes information via four-wave mixing, rather than via self- or cross-phase modulation.
  arXiv  Detail & Related papers  (2023-12-19T16:18:59Z)
• Quantum noise dynamics in nonlinear pulse propagation [0.0]
  We numerically study quantum noise dynamics and multimode entanglement in several ultrafast systems. We show that our model exhibits nonlinear dynamics in both the mean field and the quantum correlations.
  arXiv  Detail & Related papers  (2023-07-11T17:50:33Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling [5.249388938927588]
  We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model. We find a class of discrete breathers that aggregate to one boundary, here named as it skin discrete breathers (SDBs) The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.
  arXiv  Detail & Related papers  (2022-12-28T09:55:58Z)
• Microscopic theory of nonlinear phase space filling in polaritonic lattices [16.34646723046073]
  We develop a full microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. We go beyond the existing theoretical description and discover the broad scope of regimes where NPSF crucially modifies the optical response. Our findings can help describing recent observations of strong nonlinearity in heterobilayers of transition metal dichalcogenides.
  arXiv  Detail & Related papers  (2022-12-15T17:02:33Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Fast quantum state discrimination with nonlinear PTP channels [0.0]
  We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution equations. PTP channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states. We argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault-tolerant nonlinear state discriminator.
  arXiv  Detail & Related papers  (2021-11-10T22:42:37Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics [49.41640137945938]
  We propose a neural dynamic mode decomposition for estimating a lift function based on neural networks. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
  arXiv  Detail & Related papers  (2020-12-11T08:34:26Z)
• General analytic theory of classical collinear three wave mixing in a monolithic cavity [0.0]
  We present the analytic theory for a general, classical three wave mixing process in a cavity with arbitrary finesse and non-zero propagation losses. We demonstrate remarkable agreement between the presented model and the experimentally obtained highly complex second-harmonic spectrum of a titanium-diffused lithium niobate waveguide cavity.
  arXiv  Detail & Related papers  (2020-10-13T12:02:52Z)
• Frequency-resolved photon correlations in cavity optomechanics [58.720142291102135]
  We analyze the frequency-resolved correlations of the photons being emitted from an optomechanical system. We discuss how the time-delayed correlations can reveal information about the dynamics of the system. This enriched understanding of the system can trigger new experiments to probe nonlinear phenomena in optomechanics.
  arXiv  Detail & Related papers  (2020-09-14T06:17:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.