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arXiv:1603.07130 · Physical Review A

One- and two-photon scattering from generalized V-type atoms

Eduardo Sánchez-Burillo, Luis Martín-Moreno, David Zueco, Juan José García‐Ripoll

Published Nov 30, 2016• 10 citations
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Abstract

The one- and two-photon scattering matrix $S$ is obtained analytically for a one-dimensional waveguide and a pointlike scatterer with $N$ excited levels (generalized $\mathsf{\text{V}}\text{-type}$ atom). We argue that the two-photon scattering matrix contains sufficient information to distinguish between different level structures which are equivalent for single-photon scattering, such as a $\mathsf{\text{V}}$ atom with $N=2$ excited levels and two two-level systems. In particular, we show that the scattering with the $\mathsf{\text{V}}\text{-type}$ atom exhibits a destructive interference effect leading to two-photon coupled-resonator-induced transparency, where the nonlinear part of the two-photon scattering matrix vanishes when each incident photon fulfills a single-photon condition for transparency.

DOI
10.1103/physreva.94.053857

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The one- and two-photon scattering matrix SSS is obtained analytically for a one-dimensional waveguide and a pointlike scatterer with NNN excited levels (generalized V-type\mathsf{\text{V}}\text{-type}V-type atom). We argue that the two-photon scattering matrix contains sufficient information to distinguish between different level structures which are equivalent for single-photon scattering, such as a V\mathsf{\text{V}}V atom with N=2N=2N=2 excited levels and two two-level systems. In particular, we show that the scattering with the V-type\mathsf{\text{V}}\text{-type}V-type atom exhibits a destructive interference effect leading to two-photon coupled-resonator-induced transparency, where the nonlinear part of the two-photon scattering matrix vanishes when each incident photon fulfills a single-photon condition for transparency.
We study two-photon scattering of a tightly focused weak light beam from a small atomic ensemble of two-level atoms (2LAs). This is similar to the scattering of photons from an atomic ensemble in a one-dimensional waveguide. The scaling of two-photon nonlinearity at single-photon resonance shows a nonmonotonic behavior with an increasing number of few identical 2LAs. The two-photon nonlinearity decays monotonically with an increasing number of atoms for incident photons detuned from single-photon resonance. Single-photon transport in two 2LAs is similar to that in a single VVV-type three-level atom (3LA). However, two-photon transport in these two systems shows very different line shapes. When single-photon transmission is zero in these systems, two transmitted photons are bunched together in a VVV-type 3LA, while their correlation is zero in two 2LAs. The difference in the two-photon line shape persists for few 2LAs and 3LAs. Therefore, the two-photon scattering of a tightly focused weak light beam can be used as a probe to detect atomic level structures of different atoms with similar transition energies.
We consider the coherent propagation of nnn photons in a one-dimensional coupled-resonator waveguide for n=2,3,4….n=2,3,4\dots{}.n=2,3,4…. The scattering by a three-level atom, which resides in one of the resonators of the waveguide and gives rise to only two-photon transitions, results in a perfect quantum switch that allows either total reflection or total transmission. This is to be contrasted to the case of a single photon inside a one-dimensional resonant waveguide scattered by a two-level system with single-photon transitions where only total reflection can be accomplished; viz. the system behaves only as a perfect mirror but not as an ideal, transparent medium.
We investigate the quantum scattering involving a single photon and a chain of NNN polarized $\ensuremath{\Lambda}$-type three-level atoms inside a one-dimensional waveguide. By using a transfer matrix method, we obtain analytic expressions of eigenvectors of the Hamiltonian, which determine the polarization dependent transmission and reflection spectra for a single photon. We show that the scattering is most significant when the interatomic distance equals an integer multiple plus a quarter of the resonance wavelength. In such a configuration, an incident photon with an unknown polarization can be converted into a specified polarization with a transmission probability higher than that in polarizers obeying Malus's law.
Abstract We study two-photon scattering by a two-level giant atom in a waveguide. We first study the case that the giant atom is coupled to the waveguide via two coupling points, and obtain Bethe ansatz (BA) eigenstates and eigenvalues in the Hilbert space of two-excitation. Then we derive bound states by subtracting the states corresponding to BA solutions from the entire two-excitation Hilbert space, and construct the two-photon scattering matrix ( S -matrix) by using BA eigenstates and bound states. We further study the properties of output states, which include both the scattering and bound states, for arbitrarily incident two-photon states by using a concrete example. We find that the oscillation period of the scattering states and decay rates of the bound states strongly depend on the distance between two coupling points. Moreover, we find that the two-photon correlation in the bound states can be enhanced by changing such distance when the total energy of two incident photons equals to two times of single photon resonance energy. We also generalize our study to the case that the giant atom is coupled to the waveguide via N coupling points. We obtain all the eigenstates and eigenvalues of the S -matrix and construct the S -matrix. Comparing with the case of the two coupling points, we find the photon correlation can be further enhanced by increasing the number of the coupling points for the same incident states when the distance of any two nearest neighbor coupling points is half of the wavelength.
We investigate theoretically quantum scattering of two distinguishable photon wave packets from a $\ensuremath{\Xi}$-type three-level atom in a one-dimensional waveguide. The quantum state of scattered photons is solved analytically, and the solution indicates how the two photons become strongly correlated after the scattering. We determine the two-photon reflection and transmission properties, and analyze the quantum entanglement between the scattered photons. In particular, we show that the degree of entanglement can be enhanced by decreasing the spectral width of the incident photon wave packets.
In this paper, we investigate the single-photon scattering and bound states in a one-dimensional coupled-resonator waveguide which couples to a single artificial giant atom with two or more coupling points. When the atom couples to the waveguide via two resonators, the single-photon reflection rate is characterized by either Breit-Wigner or Fano lineshapes. When the atom couples to the waveguide via multiple resonators, we show numerically how the destructive interference effect leads to a complete single-photon reflection. We also find a phase-transition phenomena for the multiresonator coupling case, which reveals that the upper bound state only exists when the atom-waveguide coupling strength is above a critical value.