4 FIG. 5: (Color online) Time evolution (in units of ℏ /J ) of the impurity occupation 〈 n b 〉 for a system where two single- photon Gaussian wave packets of width s = 7 a with different intial positions ( x (1) c and x (2) c ) are launched from different sides towards the TLS. The corresponding system parameters are L = 199 a , x$_{0}$ = 100 a , Ω = √$_{2}$$_{J}$$_{, and}$ V = J . The photon parameters are x (1) c = 50 a , k (1) = 3 π/ 4 a = − k $^{(2)}$, and the initial position x (2) c = 150 a + Δ x is varied. FIG. 4: (Color online) Time evolution (in units of ℏ /J ) of the impurity occupation 〈 n b 〉 for initial two-photon states (see Fig. 1) where a broad-band loss waveguide has been intro- duced. The corresponding system parameters are (loss waveg- uide’s parameters are primed): L = L ′ = 399 a , x$_{0}$ = x ′ 0 = 200 a , Ω = √$_{2}$$_{J}$$_{,}$ V = J , and J ′ = 2 J . The strength of the coupling V ′ (in units of J ) to the loss channel is varied. The photon parameters are x c = 175 a , s = 6 a , and k = 3 π/ 4 a . that the excitation and control of the photon-atom bound states and associated effects will also occur in such situ- ations. channel. If we, for instance, interpret the coupling to the loss waveguide as a (admittedly crude) model for fabri- cation tolerances that in a quasi-one-dimensional system couple strictly guided modes to a continuum of radiative modes, we are led to speculate that the trapping effect would be observable in experimentally accessible systems. Finally, we have analyzed the possibility of tuning the trapped photon population at the TLS site. To do so, we have prepared two identical single-photon wave packets on different sides of the TLS and have launched them towards the TLS. By changing their initial relative sep- aration to the TLS, we can exert some control over the multi-particle processes in the Hamiltonian (2) (see Fig. 5). While the dynamcis is (expectedly) rather distinct for the different cases, we observe monotonic behavior of the trapped population: maximal trapping occurs for symmetrically launched pulses with zero relative initial distance. For increased distances the trapped population decreases to zero once there is no overlap of the pulses at the TLS site. Finally, we would like to emphasize the generality of our approach which is capable of treating systems with arbitrary dispersion relations and atom-field coupling strengths both in real and momentum space. Thus, the trapping of the photon population and its control sug- gest that such systems may be exploited for engineer- ing photon entanglement as well as for the realization of quantum logic circuits in a number of systems that range from silicon integrated optical elements all the way to su- perconducting quantum circuits for microwave photons. We acknowledge support by the Deutsche Forschungs- gemeinschaft (DFG) and the State of Baden- W¨ urttemberg through the DFG-Center for Functional Nanostructures (CFN) within subprojects A1.2 and B2.10. In conclusion, we have analyzed the dynamics of pho- ton transport in waveguiding systems in the presence of a TLS within the context of a quantum many-body frame- work. Our reformulation (2) allows us to identify strong multi-particle processes that may be utilized to excite and control photon-atom bound states. In turn, this fa- cilitates trapping of radiation at the TLS. In addition, we have shown that this trapping effect exhibits a cer- tain degree of robustness and can be found in a number of systems. Since few-photon (or low intensity) coherent states are superpositions of a few Fock states only (those that we have discussed in the present work), we expect [1] C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419 , 594 (2002). [2] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, Science 320 , 646 (2008). [3] M. Hofheinz, E.M. Weig, M. Ansmann, R.C. Bialczak, E. Lucero et al., Nature 454 , 310 (2008). [4] F. Xia, L. Sekaric, and Y. Vlasov, Nature Photon. 1 , 65 (2007). [5] M. Notomi, E. Kuramochi, and T. Tanabe, Nature Pho- ton. 2 , 741 (2008). [6] U. Fano, Nuovo Cimento 12 , 156 (1935); U. Fano Phys.