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arXiv:1611.09743 · Physical Review A

Photonic Kondo-like model

Mikhail Pletyukhov, Niclas Müller, Vladimir Gritsev

Published Apr 20, 2017• 0 citations
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Abstract

We introduce and study a photonic analog of the Kondo model. The model is defined as a far-detuned regime of photonic scattering off a three-level emitter in a $\mathrm{\ensuremath{\Lambda}}$-type configuration coupled to a one-dimensional waveguide with linear dispersion. We study dynamics of this local emitter driven by a coherent field pulse as well as the first- and second-order correlation functions of a scattered light. Various polarization-dependent correlation effects and an entanglement between the emitter and transmitted photons are quantified by the purity of an emitter's state. We also show that statistical properties of the scattered light are very sensitive to a polarization of the incoming coherent pulse.

DOI
10.1103/physreva.95.043829

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We introduce and study a photonic analog of the Kondo model. The model is defined as a far-detuned regime of photonic scattering off a three-level emitter in a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type configuration coupled to a one-dimensional waveguide with linear dispersion. We study dynamics of this local emitter driven by a coherent field pulse as well as the first- and second-order correlation functions of a scattered light. Various polarization-dependent correlation effects and an entanglement between the emitter and transmitted photons are quantified by the purity of an emitter's state. We also show that statistical properties of the scattered light are very sensitive to a polarization of the incoming coherent pulse.
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.
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We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multimode transmission line coupled to a two-level emitter. Using a recently developed scattering approach, we discuss transmission properties, the power spectrum, the full counting statistics, and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe the time evolution of the power spectrum and observe deviations from the Poissonian statistics for reflected and transmitted fields. In particular, the statistics of reflected photons can change from sub-Poissonian to super-Poissonian for increasing values of the detuning, while the statistics of transmitted photons is strictly super-Poissonian in all parametric regimes. We study the entanglement entropy of some spatial part of the scattered pulse and observe that it obeys the area laws and that it is bounded by the maximal entropy of the effective four-level system.
We study two-photon transport in a one-dimensional waveguide with a side-coupled two-level system. Depending on the momentum of the incoming photons, we find that the nature of the scattering process changes considerably. We further show that bunching behavior can be found in the scattered light. As a result, we find that the waveguide dispersion has a strong influence on the photon correlations. By modifying the momentum of the pulse, the nature of the correlations can therefore be altered or optimized.
For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation L. We study the correlations by calculating the second-order correlation function in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation L could be readily explored with our approach.