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Bulletin of the American Physical Society

Simulating quantum dynamical phenomena using classical oscillators

O. V. Ivakhnenko, Sergey N Shevchenko, Franco Nori

Published Mar 17, 2021• 0 citations
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A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stückelberg-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.

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Artificial classical wave systems such as wave crystals and metamaterials have demonstrated promising capabilities in simulating a wide range of quantum mechanical phenomena. Yet some gaps between quantum and classical worlds are generally considered fundamental and difficult to bridge. Dynamics obeying special unitary groups, e.g., electronic spins described by SU(2), color symmetries of fundamental particles described by SU(3), are such examples. In this Letter, we present the experimental realization of universal SU(2) and SU(3) dynamic operations in classical mechanical oscillator systems with temporally modulated coupling terms. Our approach relies on the sequential execution of nonadiabatic holonomic evolutions, which are typically used in constructing quantum-logic gates. The method is swift and purely geometric and can be extended to realize more sophisticated dynamic operations. Our results open a new way for studying and simulating quantum phenomena in classical systems.

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A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stückelberg-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.
In a previous paper [J. S. Briggs and A. Eisfeld, Phys. Rev. A 85, 052111 (2012)] we showed that the time development of the complex amplitudes of NNN coupled quantum states can be mapped by the time development of positions and velocities of NNN coupled classical oscillators. Here we examine to what extent this mapping can be realized to simulate the ``quantum,'' properties of entanglement and qubit manipulation. By working through specific examples, e.g., of quantum gate operation, we seek to illuminate quantum and classical differences which hitherto have been treated more mathematically. In addition, we show that important quantum coupled phenomena, such as the Landau-Zener transition and the occurrence of Fano resonances can be simulated by classical oscillators.
Artificial classical wave systems such as wave crystals and metamaterials have demonstrated promising capabilities in simulating a wide range of quantum mechanical phenomena. Yet some gaps between quantum and classical worlds are generally considered fundamental and difficult to bridge. Dynamics obeying special unitary groups, e.g., electronic spins described by SU(2), color symmetries of fundamental particles described by SU(3), are such examples. In this Letter, we present the experimental realization of universal SU(2) and SU(3) dynamic operations in classical mechanical oscillator systems with temporally modulated coupling terms. Our approach relies on the sequential execution of nonadiabatic holonomic evolutions, which are typically used in constructing quantum-logic gates. The method is swift and purely geometric and can be extended to realize more sophisticated dynamic operations. Our results open a new way for studying and simulating quantum phenomena in classical systems.