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arXiv:0907.2776

Two-Photon Scattering in One Dimension by Localized Two-Level System

Tao Shi, C. P. Sun

Published Jul 16, 2009• 6 citations
arXivHTMLPDF

Abstract

We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The $S$-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the $S$-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.

DOI
10.48550/arxiv.0907.2776

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We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The SSS-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the SSS-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.
We present the model that two-level system (TLS) nonlocally interacts with one-dimensional coupled-resonator array (CRA). The coherent transport of single-photon inside CRA is well controlled by the state of TLS, which functions as quantum switch. Spin up and spin down correspond to switch on and switch off respectively, or vice versa, which originate from the constructive interference and the destructive interference of two coupling paths. We improve the fidelity of quantum switch by preadjusting the frequency of resonators which couple to TLS. Quantum switch realizes quantum beam splitter when TLS is in the superposition state. The single-photon wave packet would entangle with qubit and propagate to the remote resonators.
We use the generalized rotating-wave approximation approach [Irish, Phys. Rev. Lett. 99, 173601 (2007)] to study single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a one-dimensional (1D) coupled-resonator array. We obtain the scattering amplitudes by an analytical method, which works well in a broad parameter region, confirmed by independent numerical results. In particular, when the resonator mode is far off resonance with the TLS, our results appear more reasonable than the ones from the standard adiabatic approximation. The approach is further extended to cases with a 1D resonator array strongly coupled to more than one TLS.
We consider a one-dimensional (1D) coupled-resonator array (CRA), where a two-level quantum emitter (2LE) is electric-dipole coupled to the modes of two adjacent resonators. We investigate the energy spectrum, the photon probability distribution of the bound states, and the emission process of the 2LE into the CRA vacuum. A quantum phase transition is found which is characterized by the change of the number of the out-of-band discrete levels. The condition for this change is also presented. The photon wave functions of bound states are found to be asymmetry around the position of the 2LE when the coupling strengths between the 2LE and the resonator are not equal, and they have the same preferred directions which are primarily determined by the larger one among the coupling strengths. The presence of the atom-photon bound states is manifested in the form of a stationary oscillation or a non-vanishing constant in the long enough time.
Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multiphoton scattering process in a nanoarchitecture consisting of the coupled-resonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of a single photon for an elementary unit, the TTT-type CRA, and explicitly obtain its multiphoton scattering SSS matrix in various situations. We also use this method to calculate the multiphoton SSS matrices for the more complex quantum network constructed with main TTT-type CRAs, such as a HHH-type CRA waveguide.
We give exact solutions for correlated two-photon transport in one-dimensional waveguide coupled to a two-level system, using a Bethe-Ansatz-like approach. The S-matrix is explicitly constructed to account for the transport properties of the photons. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.