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Control of one-photon wavepacket interacting with two separated atoms in a one-dimensional waveguide: Influence of real and virtual photons

S. Derouault, M. A. Bouchène

Published Apr 17, 2014• 0 citations
OpenAlex

Abstract

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.

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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.
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.
Controlling the interaction between photons is one of the important technologies applied to quantum information processing at the few-photon level. We investigate the two-photon interaction via a Ξ-type atom, where one atomic transition is coupled to a one-dimensional waveguide, and the other transition is coupled to a cavity field. Whether the cavity is initially in the vacuum state or not, determines the effective configuration of the quantum emitter. When the cavity is in the vacuum state, only one bound state appears. We further found that the joint probability of transmitted photons oscillates with their spatial separation due to the coexistence of two bound states, if the cavity is in fock state |n〉 (n ≠ 0). With the incoming wave function consists entirely of plane waves, we present the exact out-state function that exhibit the bunching and antibunching behaviors. And, we discuss in detail with the behaviors of varying both the photon pair energy(E) and the energy difference between the two photons (Δ). Moreover, the spatial attraction and repulsion between the two transmitted photons can be controlled by the parameters of the cavity.
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.
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.