Maxwell-Bloch-based dynamic modeling of quantum walk optical frequency combs

Often described as the quantum mechanical counterpart to the classical random walk, the quantum walk is characterized by a ballistic spread of the spatial particle probability distribution, with fundamental implications as well as practical relevance, e.g., for quantum algorithms. Recently, it has been shown that optical frequency combs can mimic the behavior of a quantum walk. This “quantum walk comb” is induced by the injection of a radio frequency (RF) signal into a ring-shaped, mid-infrared quantum cascade laser (QCL). Here, we report on a compact and accurate extension to the Maxwell-Bloch formalism to model RF injection into ring QCLs, including the dependence of the electronic system Hamiltonian on the RF bias field which co-propagates with the optical waveform. We present dynamical simulations of the quantum walk comb in good agreement with experiment, reproducing key features such as the ballistic buildup of the comb and the resulting Bessel-like spectra.