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Physical Review A

Effects of non- δ coupling between one-dimensional waveguides and side optical cavities

Yongyou Zhang, Bingsuo Zou

Published Jun 17, 2014• 13 citations
Publisher

Abstract

We study the effects of the non-$\ensuremath{\delta}$ coupling between a one-dimensional waveguide (1DW) and a side optical cavity (SOC), which is a development of previous well-studied $\ensuremath{\delta}$-coupling situations. We first find the real-space Hamiltonian of the non-$\ensuremath{\delta}$ coupling system of the 1DW and SOC, and then derive out an equation determining the energy of the hybridization state between the 1DW and SOC modes and an analytic formula for the single-photon transmission. Through them, we recognize that the single-photon transmission-dip position can be changed by adjusting the SOC size and the coupling strength between the 1DW and the SOC. The transmission spectrum strongly depends on the coupling types between the 1DW and the SOC and holds an asymmetric line shape. At last, we simulate the asymmetry of the single-photon transmission by a gold-based waveguide coupled with a rectangular SOC.

DOI
10.1103/physreva.89.063815

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We study the effects of the non-\ensuremathδ\ensuremath{\delta}\ensuremathδ coupling between a one-dimensional waveguide (1DW) and a side optical cavity (SOC), which is a development of previous well-studied \ensuremathδ\ensuremath{\delta}\ensuremathδ-coupling situations. We first find the real-space Hamiltonian of the non-\ensuremathδ\ensuremath{\delta}\ensuremathδ coupling system of the 1DW and SOC, and then derive out an equation determining the energy of the hybridization state between the 1DW and SOC modes and an analytic formula for the single-photon transmission. Through them, we recognize that the single-photon transmission-dip position can be changed by adjusting the SOC size and the coupling strength between the 1DW and the SOC. The transmission spectrum strongly depends on the coupling types between the 1DW and the SOC and holds an asymmetric line shape. At last, we simulate the asymmetry of the single-photon transmission by a gold-based waveguide coupled with a rectangular SOC.
Transmission and correlation properties of a two-photon pulse are studied in a one-dimensional waveguide (1DW) in the presence of three types of quantum emitters: two-level atom (TLA), side optical cavity (SOC), and Jaynes-Cummings model (JCM). Since there are many plane-wave components for a two-photon pulse, a nonlinear waveguide dispersion is used instead of the linearized one. The two-photon transmission spectra become flatter with decreasing the pulse width. With respect to the $\ensuremath{\delta}$ coupling between the 1DW and quantum emitter the transmission dips show a blueshift for the non-$\ensuremath{\delta}$ one and the blueshift first increases and then decreases with increasing the width of the coupling. The TLA and JCM can induce an effective photon-photon interaction that depends on the distance between the two photons, while the SOC cannot. We show that the 1DW coupled with the TLA or JCM is able to evaluate the overlap of the two photons and that the non-$\ensuremath{\delta}$ coupling has potential for controlling the two-photon correlation.
Photon scattering properties in one-dimensional waveguide side coupled to a nanocavity embedded in two atoms with dipole-dipole interaction (DDI) are investigated theoretically. The analytical expressions of the transmission and reflection amplitudes are deduced by using the real-space Hamiltonian. A method to determine the coupling strength of DDI is proposed. Realization of single photon switching by modulation the DDI is investigated. The influence of dissipations on the performance of the single photon switching are exhibited. An asymmetric Fano-type resonance, which can be controlled by the DDI, appears in the transmission spectrum.
We study the transmission and reflection properties of a single-photon pulse in a one-dimensional waveguide side coupled with a Jaynes-Cummings system, namely, a multi-cavity with an embedded Rydberg atom. A Single-photon pulse is applied to tune the atoms energy spectrum, and varying it can bring the atomic qubit transition on or off-resonance for the cavity. The transmission and reflection behavior are systematically explored by a real-space model Hamiltonian and we find that the coupling strength between the waveguide and the side optical cavity exerts a tremendous impact on it. The influence of cavity and atomic dissipations and the incident pulse width on the transport properties of the single-photon is also investigated simultaneously. Based on these phenomena, we point out the possibility of utilizing this system as a single-photon transport in practice and has potential applications in quantum information.
Starting with one-cavity side-coupled with waveguide system, we theoretically study on transmission spectrum for a two-cavity side-coupled with waveguide system based on coupled mode theory by using light-tracing method. Interesting effects called all-optical analog to EIT appear in some cases. 3D finite-difference time-domain (FDTD) method provides optical modes distributions at different wavelengths, including the EIT-like wavelength. Influences of different parameters on the narrow EIT-like peak such as cavity quality factors Q, frequency difference detuning Δω, and phase difference detuning between cavities ΔΦ are discussed. Compared with previous studies, this method is easier to understand and can be used as a model for both standing cavities like line-defect photonic crystal cavities and whispering gallery modes cavities like microring cavities.
We investigate theoretically single photon transport in one-dimensional waveguide coupled to a pair of cavities, which are denoted by the first cavity and the auxiliary cavity. Two cases with no atom and one atom embedded in the first cavity are discussed. The Fano dips in the transmission spectrum and locations of transparency window are calculated. When no atom is embedded in the first cavity, there exists a transparency window under the condition that the first cavity and the auxiliary cavity are not resonant. The locations of the transparency window and Fano line type depend strongly on the eigen frequency of the auxiliary cavity and the coupling strength between the auxiliary cavity and the waveguide. When one atom is embedded in the first cavity, we show that the transparency window exists even though the first cavity, the atom and the auxiliary cavity are resonant. The Fano line type is strongly dependent on the eigen frequency of the auxiliary cavity and the coupling strength. Our results have potential applications in design of quantum devices at the level of single photon, such as single photon switch and single photon routers.
Single-photon scattering properties in a coupled-resonator waveguide (CRW) coupled to a nanocavity embedded with a two-level system are investigated theoretically. Two cases are considered: when the nanocavity is locally coupled to one resonator and when it is nonlocally coupled to two resonators of the CRW. The transmission and reflection amplitudes are obtained for the two cases, respectively. The results show that the position of perfect transmission remains unchanged, while the position of perfect reflection is shifted due to the nonlocal coupling. An asymmetric Fano resonance appears in the transmission spectrum and can be controlled by adjusting the coupling strengths in the nonlocal coupling case. The effects of the coupling strengths and dissipation on the transport properties are also analyzed for the two cases.