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.
Terahertz (THz) quantum cascade lasers (QCL) may operate as harmonic frequency combs, exhibiting a mode-separation of multiple times the round trip frequency. This work aims to shed light on the coupled field-electron dynamics that lead to harmonic mode-locking in defect-engineered THz QCLs. Therefore, we use the Maxwell-Bloch equations describing a medium of two-level quantum systems interacting with the electric field in the laser cavity. We find that both the amplitude and phase of the electric field are coupled to the introduced defects, and the system quickly reaches a locked state. Despite the presence of the reflectors, spatial hole burning is necessary to enable multimode operation.
Mid-infrared optical solitons may be a powerful tool for applications in on-chip integrated photonics and spectroscopy, as they provide broadband, phase-locked frequency combs. Quantum cascade lasers (QCLs) embedded in a ring cavity have been found to enable self-starting optical soliton generation. In order to study these phenomena numerically, we use a model based on coupled Maxwell-density matrix equations. The introduction of backscattering in our model stabilizes self-assembled soliton field solutions, which is in very good agreement with experimental data. In this contribution, we present our model and discuss the mechanisms that lead to soliton operation in ring QCLs.
Passive mode-locking of lasers enables a compact way of stable optical pulse generation and is thus of high interest in research and application. Quantum cascade lasers (QCLs) emit radiation in the mid-infrared or terahertz (THz) spectral region and exhibit gain recovery on picosecond timescales. As the cavity round trip time is typically some tens of picoseconds, passively mode-locked operation of QCLs is undoubtedly challenging to achieve. However, short pulses from a THz QCL were recently observed by embedding a graphene saturable absorber into the top contact of the cavity. This contribution presents a model of the dynamic interplay between electric field, gain, and absorber, revealing that pulse formation and stability are possible in a narrow bias range, enhanced by spatial hole burning.
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