Correlated two-photon transport in a one-dimensional waveguide side-coupled to a nonlinear cavity

We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present analytic solution of quantum states of the transmitted and reflected two photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerge after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in the relative coordinates, which is a feature that may be interpreted as a two-photon bound state in this waveguide-cavity system.Comment: 9 pages, 5 figure

Parametric generation of quadrature squeezing of mirrors in cavity optomechanics

We propose a method to generate quadrature squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment.Comment: 4 pages, 2 figure

Spectrum of single-photon emission and scattering in cavity optomechanics

We present an analytic solution describing the quantum state of a single photon after interacting with a moving mirror in a cavity. This includes situations when the photon is initially stored in a cavity mode as well as when the photon is injected into the cavity. In addition, we obtain the spectrum of the output photon in the resolved-sideband limit, which reveals spectral features of the single-photon strong-coupling regime in this system. We also clarify the conditions under which the phonon sidebands are visible and the photon-state frequency shift can be resolved.Comment: 5 pages, 5 figure

Correlated two-photon scattering in cavity optomechanics

We present an exact analytical solution of the two-photon scattering in a cavity optomechanical system. This is achieved by solving the quantum dynamics of the total system, including the optomechanical cavity and the cavity-field environment, with the Laplace transform method. The long-time solution reveals detailed physical processes involved as well as the corresponding resonant photon frequencies. We characterize the photon correlation induced in the scattering process by calculating the two-photon joint spectrum of the long-time state. Clear evidence for photon frequency anti-correlation can be observed in the joint spectrum. In addition, we calculate the equal-time second-order correlation function of the cavity photons. The results show that the radiation pressure coupling can induce photon blockade effect, which is strongly modulated by the phonon sideband resonance. In particular, we obtain an explicit expression of optomechanical coupling strength determining these sideband modulation peaks based on the two-photon resonance condition.Comment: 10 pages, 6 figure

Majorana Fermion Induced Non-local Current Correlations in Spin-orbit Coupled Superconducting Wires

Recent observation of zero bias conductance peaks in semiconductor wire/superconductor heterostructures has generated great interest, and there is a hot debate on whether the observation is associated with Majorana fermions (MFs). Here we study the local and crossed Andreev reflections in a junction of two normal leads and a sandwiched superconductor-semiconductor wire with two spatially separated but strongly coupled MF end states. The conductance and Fano factors of such a device are sharply different from the topologically trivial case even in the presence of disorder, and can hence be used to identify MFs unambiguously.Comment: 7+ pages, 10 figure