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Semiconductor Lasers and Laser Dynamics

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

Michael A. Schreiber, Lukas Seitner, Johannes Stowasser, Ina Heckelmann, Michael Haider, Jérôme Faist, Christian Jirauschek

Published Jun 20, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.3017587

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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.
We present a full-wave Maxwell-density matrix simulation tool including c-number stochastic noise terms for the modeling of the spatiotemporal dynamics in active photonic devices, such as quantum cascade lasers and quantum dot structures. The coherent light–matter interaction in such devices plays an important role in the generation of frequency combs and other nonlinear and non-classical optical phenomena. Since the emergence of nonlinear and non-classical features is directly linked to the noise properties, detailed simulations of the noise characteristics are required for the development of low-noise quantum optoelectronic sources. Our semiclassical simulation framework is based on the Lindblad equation for the electron dynamics, coupled with Maxwell’s equations for optical propagation in the laser waveguide. Fluctuations arising from the interactions of the optical field and quantum system with their reservoirs are treated within the quantum Langevin theory. Here, the fluctuations are included by adding stochastic c-number terms to the Maxwell-density matrix equations. The implementation in the mbsolve dynamic simulation framework is publicly available.
Abstract Dual-comb spectroscopy in the mid-infrared provides an unparalleled combination of wide optical bandwidth and high resolution with fast acquisition times. In addition, the absence of moving mechanical parts makes it especially suitable for portable sensors, offering the availability of compact and controllable dual-comb sources. In this work, we demonstrate a quantum walk comb source with an optical bandwidth of 78 cm -1 near 1330 cm -1 wavenumber (440 nm and 7.5 μm wavelength, respectively), and use it to report a dual quantum walk comb demonstration over a bandwidth of 34 cm -1 (192 nm). Analysis of the dual-comb signal demonstrates that in the quantum walk comb, the repetition frequency is fully locked to the external RF source, whose power also determines the comb bandwidth, allowing a high control of the power-per-line distribution. In addition, a multi-heterodyne signal is collected from the RF feed of the device, providing a dual-comb reference signal and avoiding the need to split the optical beam and use a second photodetector. The proof-of-concept spectroscopy of a plastic film reported shows the great potential of quantum walk combs for the realization of high-performance and cost-effective spectroscopy systems consisting of only a dual-comb source, an interaction cell and a photodetector, thus having a major impact on a plethora of sensing applications.
Quantum walks are the quantum mechanical analog to classical random walks. However, due to the wavelike nature of quantum particles, they reveal drastically different dynamics compared to their classical counterpart. These unique properties make quantum walks a new promising platform for quantum algorithms and a powerful tool to understand complex transport phenomena. This thesis presents three experiments specifically designed to send photons on a quantum walk. The experiments are based on a fiber network spreading the photonic wave packets over discrete time bins. With these Quantum Walks in Time we simulate the propagation of quantum particles in various different environments, revealing diverse dynamics such as a fast ballistic spread and an Anderson-like localization effect. Furthermore we use our concept to implement the first quantum walk on a two-dimensional lattice. The underlying topology allows for investigations of the intriguing dynamics of two strongly interacting quantum particles, which reveals unique effects such as the creation of bound states.
Quantum optical frequency combs are of great significance in the fields of quantum computing, quantum information, and high precision quantum measurement, which can be produced by using a degenerate type-I synchronously pumped optical parametric oscillator (SPOPO). When anisotropic crystal is used as a nonlinear medium in the SPOPO, the spatial walk-off effect will occur due to the birefringence effect, which cannot be ignored and will adversely affect the generation of squeezed state. In this work, we investigate the influence of spatial walk-off effect on the squeezing level of quantum optical frequency combs both theoretically and experimentally. A Ti∶sapphire mode-locked femtosecond pulsed laser which produces 130 fs pulse trains at 815 nm with a repetition rate of 76 MHz is utilized as a fundamental source. Its second harmonic at 407.5 nm is used to pump the collinear BiB3O6 (BIBO) crystal for generating the squeezed vacuum frequency comb. It is indicated that as the crystal length increases, the area of interaction between pump light and signal light decreases gradually. Thus the enhancement of squeezing is eventually limited by the spatial walk-off effect. According to the simulations, the squeezing level reaches a maximum value when the crystal length is 1.49 mm. The quantum properties of squeezed vacuum optical frequency combs obtained for four crystal lengths (0.5, 1.0, 1.5 and 2.0 mm) are subsequently measured experimentally. When the length of BIBO is 1.5 mm, the maximum vacuum squeezing of (3.6±0.2) dB is obtained, which is (7.0±0.2) dB after being corrected for detection loss. The experimental results are consistent with the numerical simulations. This study demonstrates that the spatial walk-off effect in nonlinear crystal is a significant factor affecting the quantum optical frequency comb, and the theoretical model presented in this paper can be used to provide a guideline for optimizing the experimental implementation.
We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior expressed in the form of a limit probability distribution of a double horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes-Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin-field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behavior of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental setup that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.