A two-level system coupled to a one-dimensional continuum is investigated. By using a real-space model Hamiltonian, we show that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties. The technique is applied to various related problems with different configurations, and analytical solutions are given. © Spontaneous emission is fundamental in the interactions of electromagnetic fields with atoms. Two regimes of spontaneous emission have been extensively explored. In a weak coupling regime, for instance, an excited atom in free space, the excited atom decays exponentially due to the ample photon phase space to which the atom couples. The spontaneous emission is generally treated as a loss, and a decoherence mechanism and is included as part of the absorption coefficient of the system. On the other hand, in the strong coupling regime, as is the case when an excited twolevel system is placed in a microcavity, 1,2 the atom undergoes Rabi oscillation, since the photonic mode spectrum is now discrete. Here we explore a different regime of spontaneous emission. We consider two-level atoms coupled to a one-dimensional continuum. Such a continuum can act as a line defect waveguide in a complete photonic bandgap crystal (Fig. 1). The atom can either be in the waveguide or side coupled to the waveguide. In this case, the excited two-level system will decay exponentially. However, in the reduced dimensionality, when a single photon is incident upon the two-level system with a frequency on resonance, the wave function of the spontaneously emitted photon inevitably interferes coherently with that of the incident wave, because the forward and backward directions are the only directions in phase space. Such interference can result in the photon's being completely reflected with no loss. This occurs in spite of the fact that the physical dimension of the two-level system is typically far smaller than the wavelength of light. Thus spontaneous emission can be exploited to influence the coherent transport properties of a single photon. Interesting transport properties result from this coherent interference and can be utilized in the design of various quantum optoelectronic devices, such as ultranarrow bandwidth filters and nanomirrors.The interaction between the photons and the twolevel atoms is described by a Dicke Hamiltonian 4 :where k is the frequency of the mode of the radiation field corresponding to wave vector k (i.e., the dispersion relation), a k † ͑a k ͒ is the creation (annihilation) operator of the photon, ⍀ is the resonance energy of the atom, V k = ͑2ប / k ͒ 1/2 ⍀D · e k is the coupling constant, D is the dipole moment of the atom, e k is the polarization unit vector of the photon, S + = a e † a g ͑S − = a g † a e ͒ is the creation (annihilation) operator of the atomic excited state, and a g † ͑a e † ͒ is the creation operator of the ground (excited) state of the electron.In one dimension, when the resonance energy of the atom is away from the cutoff frequ...

We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S-matrix is constructed using a generalized Bethe-Ansatz technique. 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.

A recent theoretical analysis and experimental results show that interesting transport properties of a single microwave photon emerge when a quantum bit in a cavity is coupled to a one-dimensional waveguide. Here we adopt a real-space model Hamiltonian to give a unified approach which accounts for the experimental results, and make new predictions on the properties of single photon transport, such as the general Fano line shape, symmetric vacuum Rabi splitting for a leaky cavity at resonance, and a one-photon switching capability.

We extend the input-output formalism of quantum optics to analyze few-photon transport in waveguides with an embedded qubit. We provide explicit analytical derivations for one and two-photon scattering matrix elements based on operator equations in the Heisenberg picture.

The single-photon transport in a single-mode waveguide, coupled to a cavity embedded with a two-leval atom is analyzed. The single-photon transmission and reflection amplitudes, as well as the cavity and the atom excitation amplitudes, are solved exactly via a real-space approach. It is shown that the dissipation of the cavity and of the atom respectively affects distinctively on the transport properties of the photons, and on the relative phase between the excitation amplitudes of the cavity mode and the atom.