Two-photon self-Kerr nonlinearities for quantum computing and quantum optics

Abstract

The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here, we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon S matrices for fields propagating in this medium. From these scattering matrices we show that our proposal leads to a high fidelity photon-photon gate. In the limit where the number of nodes in the network tends to infinity, the medium approximates a perfect self-Kerr interaction in the one- and two-photon regime.

V2: published version; with new section with a qualitative description and new appendix comparing to probabilistic gates. V1: also see arXiv:1604.04278 and arXiv:1604.03914

References in corpus (7)

• Chiral Quantum Optics
• Input-Output Formalism For Few-Photon Transport in One-Dimensional Nanophotonic Waveguides Coupled to a Qubit
• From three-photon GHZ states to ballistic universal quantum computation
• Quantum Feedback Networks: Hamiltonian Formulation
• Scattering of massless particles in one-dimensional chiral channel
• Deterministic Quantum Network for Distributed Entanglement and Quantum Computation
• Induced cavities for photonic quantum gates

Cited by in corpus (14)

• Exact Markovian and non-Markovian time dynamics in waveguide QED: collective interactions, bound states in continuum, superradiance and subradiance
• Non-Markovian super-superradiance in a linear chain of up to 100 qubits
• Multiphoton pulses interacting with multiple emitters in a one-dimensional waveguide
• Nonlinear Optical Properties and Self-Kerr Effect of Rydberg Excitons in Cu${}_2$O
• Generation of quantum states with nonlinear squeezing by Kerr nonlinearity
• Quantum Correlations in the Kerr Ising Model
• Diagrammatic approach for analytical non-Markovian time-evolution: Fermi's two atom problem and causality in waveguide quantum electrodynamics
• Nonlinear quantum logic with colliding graphene plasmons
• Multidimensional super- and subradiance in waveguide quantum electrodynamics
• Solution of Cross-Kerr Interaction Combined with Parametric Amplification
• Genuine non-Gaussian entanglement of light and quantum coherence for an atom from noisy multiphoton spin-boson interactions
• Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum
• Joint estimation of noise and nonlinearity in Kerr systems
• Generation of large Fock states from coherent states using Kerr interaction and displacement