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arXiv:1404.4513 · Physical Review A

One-photon wave packet interacting with two separated atoms in a one-dimensional waveguide: Influence of virtual photons

S. Derouault, M. A. Bouchène

Published Aug 15, 2014• 12 citations
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Abstract

We present a theoretical study of a one-photon wave packet scattered by two atoms in a one-dimensional waveguide. We investigate the role of terms beyond the rotating-wave approximation to correctly take into account the effects of the virtual photons that are exchanged between the atoms. These terms are shown to drastically influence the reflected and the transmitted fields, imposing strict constraints on their temporal envelopes.

DOI
10.1103/physreva.90.023828

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We present a theoretical study of a one-photon wave packet scattered by two atoms in a one-dimensional waveguide. We investigate the role of terms beyond the rotating-wave approximation to correctly take into account the effects of the virtual photons that are exchanged between the atoms. These terms are shown to drastically influence the reflected and the transmitted fields, imposing strict constraints on their temporal envelopes.
We present a theoretical study of one photon wave-packet scattered by two atoms in one dimensional waveguide, stressing on both the spectral and the temporal behavior. Rotating wave approximation is not done to take into account the effects of the virtual photons that are exchanged between the atoms. These photons are shown to influence drastically the spectrum of both the reflected and the transmitted fields. In the temporal domain, the envelopes of these fields are shown to obey strict constraints on their shape.
We present a time-dependent quantum calculation of the scattering of a few-photon pulse on a single atom. The photon wave packet is assumed to propagate in a transversely strongly confined geometry, which ensures strong atom-light coupling and allows a quasi-one-dimensional treatment. The amplitude and phase of the transmitted, reflected, and transversely scattered part of the wave packet strongly depend on the pulse length (bandwidth) and energy. For a transverse mode size of the order of ${\ensuremath{\lambda}}^{2},$ we find nonlinear behavior for a few photons already, or even for a single photon. In a second step we study the collision of two such wave packets at the atomic site and find striking differences between the Fock state and coherent state wave packets of the same photon number.
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 the paper, we employ a wave-function approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave packet scattered from the JC system experience transformation for nonzero atom-cavity couplings. Moreover, using Schmidt decomposition, we show that the scattered photons feature frequency entanglement contrary to the incident ones which are not entangled.
Single-photon transport properties in a one-dimensional coupled resonator waveguide, coupled to a whispering-gallery resonator interacting with two separated two-level atoms, are theoretically investigated. Based on the real-space approach, the transmission and reflection amplitudes of the single photon are deduced. Numerical results demonstrate that the transmission and reflection depend on the resonator–atom coupling, the intermode backscattering, and especially the phase difference between these two separated atoms. Effects of dissipation on single-photon transport properties are also discussed.
We consider the interaction of one- and two-photon pulses in a waveguide with two two-level systems (TLSs) that are also able to interact directly either through an exchange- or a dipole-type interaction. We focus on the system's transport properties and show how the presence of a second TLS increases the control options, especially when direct interactions are also allowed. We also obtain, within a Markov (long-pulse) approximation, exact results for the nonlinear or entangled terms that arise in the two-photon case and discuss both their potential applications and ways to minimize their effects.