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Physical Review A

Transmission and correlation of a two-photon pulse in a one-dimensional waveguide coupled with quantum emitters

Qingmei Hu, Bingsuo Zou, Yongyou Zhang

Published Mar 26, 2018• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.97.033847

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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 \ensuremathδ\ensuremath{\delta}\ensuremathδ coupling between the 1DW and quantum emitter the transmission dips show a blueshift for the non-\ensuremathδ\ensuremath{\delta}\ensuremathδ 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-\ensuremathδ\ensuremath{\delta}\ensuremathδ coupling has potential for controlling the two-photon correlation.
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.
We study the dynamics of an ultrafast single photon pulse in a one-dimensional waveguide two-point coupled with a Jaynes-Cummings system. We find that for any single photon input the transmissivity depends periodically on the separation between the two coupling points. For a pulse containing many plane wave components it is almost impossible to suppress transmission, especially when the width of the pulse is less than 20 times the period. In contrast to plane wave input, the waveform of the pulse can be modified by controlling the coupling between the waveguide and Jaynes-Cummings system. Tailoring of the waveform is important for single photon manipulation in quantum informatics.
Scattering and correlation properties of a two-photon (TP) pulse are studied in a four-terminal waveguide system, i.e., two one-dimensional waveguides connected by a Jaynes-Cummings emitter (JCE). The wave function approach is utilized to exactly calculate the real-time dynamic evolution of the TP transport. When the width of the incident TP Gaussian pulse is much larger than the photon wavelength, the TP transmission spectra approach that of the corresponding single photon cases and are almost independent of the pulse width. On the contrary, as the pulse width is comparable to the photon wavelength, the TP transmission and correlation both show strong dependence on the pulse width. The resonant scattering due to the JCE and the photon interference together determine the TP correlation. When the distance between the TPs is small, the TP correlations between any two terminals for the scattered TP pulse are much different from those for the incident TP pulse and therefore, such a four-terminal waveguide system provides a way to control the TP correlation.
We develop a wavefunction approach to describe the scattering of two photons on a quantum emitter embedded in a one-dimensional waveguide. Our method allows us to calculate the exact dynamics of the complete system at all times, as well as the transmission properties of the emitter. We show that the nonlinearity of the emitter with respect to incoming photons depends strongly on the emitter excitation and the spectral shape of the incoming pulses, resulting in transmission of the photons which depends crucially on their separation and width. In addition, for counter-propagating pulses, we analyze the induced level of quantum correlations in the scattered state, and we show that the emitter behaves as a nonlinear beam-splitter when the spectral width of the photon pulses is similar to the emitter decay rate.
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.
We investigate the two-photon transport properties inside one-dimensional waveguide side coupled to a cavity. The cavity is doped with a four-level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field, the transmission and reflection of the correlated photons can be controlled.