Spectra of coherent resonant light pulses interacting with a two-level atom in a waveguide

We present a theoretical analysis of the spectral features of coherent light pulses traveling in a one-dimensional waveguide with an embedded two-level quantum system. In particular, we clarify and explain the relevant physical mechanisms that lead to a rich variety of distinct features in the spectrum of the scattered light. This includes the phenomenon of discrete steps in the transmitted intensity as a function of the excitation amplitude, frequency mixing as a consequence of cascaded nonlinear processes, and the role of atom-photon bound states.

Figure 1

Schematic of a pulse propagating in our model waveguide. The TLS is coupled to the waveguide at site $x_0$ and the spectrum is detected at site $x_{\mathrm{test}}$.

Figure 2

Panels (a)–(c): Spectrum recorded at site $x_{\mathrm{test}}=x_0+1$ for on-resonant excitation using $k_{\mathrm{carr}}=0.5\pi$, $\sigma =50$, $\Omega =0J$, and $V=0.7J$. Panel (b) shows a vertical cut through (a), where the black vertical lines represent further rotations of the Bloch vector. Panel (c) displays a horizontal cut through (a) and the vertical lines correspond to the lines in panel (a). Panel (d) sketches a model for the analytic description of the black dashed lines in panels (a) and (c).

Figure 3

EF of the upper APBS for an incident light pulse on resonance. The values have been determined directly from the simulations [dotted lines, at $\sqrt{\mathcal{N}\left(t_0\right)}=0$ the vertical (gray) dots are in the same order as in the legend] and for each simulation and semianalytically (black lines). The inset depicts the spectral density for $k_{\mathrm{carr}}=0.75\pi$.