Vibrational resonance in a driven two-level quantum system, linear and nonlinear response

A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Section: Logical Vibrational Resonancementioning

confidence: 99%

Construction of logic gates exploiting resonance phenomena in nonlinear systems

Murali

Rajasekar

Aravind

et al. 2021

“…From the physical applications point of view, Shibashis & Ray [28] consider the response of a two-level quantum system interacting with two deterministic time-periodic electromagnetic fields. By examining the linear, second-harmonic and Stokes and anti-Stokes Raman responses of the dressed two-level quantum systems whose dynamics are governed by loss-free Bloch equations, the authors opine that quantum optics can offer a stimulating direction for future research on VR.…”

Section: General Content Of the Issuementioning

confidence: 99%

“…On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon by Sorokin & Demidov [27]. Vibrational resonance in a driven two-level quantum system; linear and nonlinear response by Shibashis & Ray [28]. The effect of high-frequency stochastic actions on the low-frequency behaviour of dynamic systems by Kremer [29].…”

Section: General Content Of the Issuementioning

confidence: 99%

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Vibrational and stochastic resonances in driven nonlinear systems

Vincent

McClintock

Khovanov

et al. 2021

Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties—one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances—addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

“…The general content of the theme issue has been described explicitly in part 1 [ 18 ] and organized with papers in three broad domains: theory, methods and analysis; complex networks and experimental applications. While a few articles in part 1 presented analysis on position-dependent mass systems [ 21 ], delayed feedback-induced resonances in deformable potential system [ 22 ] and Duffing oscillator [ 23 ], and driven two-level quantum systems [ 24 ], part 2 assembles state-of-the-art, original contributions on VR and SR in some systems not covered by part 1. These include a Brownian particle confined in a structural cavity [ 25 , 26 ], coupled neuron-astrocyte [ 27 ] systems and neural networks [ 28 , 29 ].…”

Section: General Content Of Partmentioning

confidence: 99%

Vibrational and stochastic resonances in driven nonlinear systems: part 2

Vincent

McClintock

Khovanov

et al. 2021

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.