Abstract
We study the dynamics of single-photon absorption by a single emitter coupled to a one-dimensional waveguide that simultaneously provides channels for spontaneous emission (SE) decay and a channel for the input photon. We have developed a time-dependent theory that allows us to specify any input single-photon wavepacket guided by the waveguide as the initial condition, and calculate the excitation probability of the emitter, as well as the time evolution of the transmitted and reflected fields. For single-photon wavepackets with a Gaussian spectrum and temporal shape, we obtain analytical solutions for the dynamics of absorption, with maximum atomic excitation . We furthermore propose a terminated waveguide to aid the single-photon absorption. We found that for an emitter placed at an optimal distance from the termination, the maximum atomic excitation due to an incident single-photon wavepacket can exceed 70%. This high value is a direct consequence of the high SE β-factor for emission into the waveguide. Finally, we have also explored whether waveguide dispersion could aid single-photon absorption by pulse shaping. For a Gaussian input wavepacket, we found that the absorption efficiency can be improved by a further 4% by engineering the dispersion. Efficient single-photon absorption by a single emitter has potential applications in quantum communication and quantum computation.
Highlights
Absorption of single photons by light emitters is an attractive option that may be realized using recent advances in the engineering of complex photonic environments [13, 16,17,18,19,20,21,22,23]
We explore the possibility of maximizing the single-photon absorption by the emitter via engineering the photonic environment of the emitter and by shaping the pulse of the input single-photon wavepacket through waveguide dispersion
We apply the theoretical model to quasi-1D waveguides coupled to a single emitter
Summary
The result obtained from the time-dependent theory [46, 49] explicitly describes the atomic excitation as a function of time. As shown in [44], stationary theory [22, 39] can be extended to obtain the time-dependent C0e(t) via the calculation of the stationary interacting eigenstates, projection of the initial state and application of the time evolution operator. Alternative route to obtain C0e(t), that likewise includes the initial condition and does not require eigenstates to be calculated first, is the Laplace transform method developed by one of us (see Wubs et al [52]). The derivation of |C0e(t)|2 based on the Laplace transform method is briefly outlined in appendix A
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