Simulating quantum dynamical phenomena using classical oscillators: Landau-Zener-Stuckelberg-Majorana interferometry, latching modulation, and motional averaging

Abstract

A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging, respectively. We demonstrate that these pronounced and interesting effects are also inherent in the dynamics of classical two-state systems. We discuss how such classical systems are realized using either mechanical, electrical, or optical resonators. In addition to the fundamental interest of such dynamical phenomena linking classical and quantum physics, we believe that these are attractive for the classical analogue simulation of quantum systems.

12 pages, 6 figures

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• Mirror, mirror: Landau-Zener-Stuckelberg-Majorana interferometry of a superconducting qubit in front of a mirror
• Quantum interferometry with a g-factor-tunable spin qubit
• Two-level systems with periodic $N$-step driving fields: Exact dynamics and quantum state manipulations
• Driving-induced resonance narrowing in a strongly coupled cavity-qubit system
• Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials
• Single spin Landau-Zener-Stückelberg-Majorana interferometry of Zeeman-split states with strong spin-orbit interaction in a double quantum dot
• Probabilistic motional averaging
• Controllable single spin evolution at sub-harmonics of electric dipole spin resonance enhanced by four-level Landau-Zener-St{ü}ckelberg-Majorana interference
• Coulomb coupling between two nanospheres trapped in a bichromatic optical tweezer
• Landau-Zener without a Qubit: Unveiling Multiphoton Interference, Synthetic Floquet Dimensions, and Dissipative Quantum Chaos
• Supercomputer simulations of transmon quantum computers
• Visualized Wave Mechanics by Coupled Macroscopic Pendula: Classical Analogue to Driven Quantum Bits
• Fluctuating parametric drive of coupled classical oscillators can simulate dissipative qubits
• Energy Transfer and Coherence in Coupled Oscillators with Delayed Coupling: A Classical Picture for Two-Level Systems
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Photon-assisted Landau Zener transitions in a tunable driven Rabi dimer coupled to a micromechanical resonator
• Tunable frequency conversion and comb generation with a superconducting artificial atom