Generation of coherence in an exactly solvable nonlinear nanomechanical system

Singh, A. K.; Chotorlishvili, L.; Srivastava, S.K.; Tralle, I.; Toklikishvili, Z.; Berakdar, Jamal; Mishra, S. K.

doi:10.1103/physrevb.101.104311

Cited by 16 publications

(9 citation statements)

References 66 publications

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“…Having considered two-level systems, it is important to extend the study to possible multilevel systems, with multiple avoided-level crossings. These may relate to such diverse systems as a chain of interacting spins-1/2 (Larson, 2014;Ostrovsky and Volkov, 2006), a spin or multiple spins coupled to a resonator (O'Keeffe et al, 2013;Singh et al, 2020), molecular nanomagnets (Földi et al, 2007;Garanin et al, 2008;Pavlyukh, 2020), interacting bosons in optical lattices (Tschischik et al, 2012), broad periodic photonic waveguide (Benisty et al, 2011), or a NV center coupled with a substitutional nitrogen center in diamond (Band and Japha, 2022;Zangara et al, 2019), to name a few.…”

Section: G Multilevel Systemsmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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H. Comparison of different methods IV. Interferometry A. Superconducting circuits B. Semiconductor quantum dots C. Donors and impurities (atomic qubits) D. Graphene E. Microscopic systems F. Other systems G. Multilevel systems V. Quantum control A. Coherent control of microscopic and mesoscopic structures B. Universal single-and two-qubit control C. Shortcuts to adiabaticity D. Adiabatic quantum computation VI. Related classical coherent phenomena VII. Conclusion 1. With near-adiabatic limit (Landau) 2. With parabolic cylinder functions (Zener) 3. With contour integrals (Majorana) 4. With WKB approximation and phase integral method (Stückelberg) 5. Duration of the LZSM transition B. Description of a periodically driven two-level system 1. Adiabatic-impulse model a. Adiabatic evolution b. Multiple-passage evolution 2. Rotating-wave approximation (RWA) 3. Floquet theory 4. Rate equation and white noise approach a. Transition rate b. Rate equation c. From Bessel to Airy d. Double-passage regime ReferencesAbbreviations and most-often-used symbols Because this review article is quite long, for the readers' convenience, we present the main abbreviations used. This list also includes some of the topics covered.

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Section: G Multilevel Systemsmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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“…On the other hand, spins are not coupled directly and the correlation between NV spins may arise only through the quantum feedback exerted from the first NV spin to the first oscillator and transferred from the first oscillator to the second oscillator via the direct coupling. The Hamiltonian of the two NV spins coupled to the nonlinear oscillators reads: [58]…”

Section: Modelmentioning

confidence: 99%

Scrambling and quantum feedback in a nanomechanical system

Singh,

Sachan,

Chotorlishvili

et al. 2022

Preprint

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The question of how swiftly entanglement spreads over a system has attracted vital interest. In this regard, the out-of-time ordered correlator (OTOC) is a quantitative measure of the entanglement spreading process. Particular interest concerns the propagation of quantum correlations in the lattice systems, e.g., spin chains. In a seminal paper D. A. Roberts, D. Stanford and L. Susskind, J. High Energy Phys. 03, 051, (2015) the concept of the OTOC's radius was introduced. The radius of the OTOC defines the front line reached by the spread of entanglement. Beyond this radius operators commute. In the present work, we propose a model of two nanomechanical systems coupled with two Nitrogen-vacancy (NV) center spins. Oscillators are coupled to each other directly while NV spins are not. Therefore, the correlation between the NV spins may arise only through the quantum feedback exerted from the first NV spin to the first oscillator and transferred from the first oscillator to the second oscillator via the direct coupling. Thus nonzero OTOC between NV spins quantifies the strength of the quantum feedback. We show that NV spins cannot exert quantum feedback on classical nonlinear oscillators. We also discuss inherently quantum case with a linear quantum harmonic oscillator indirectly coupling the two spins and verify that in the classical limit of the oscillator, the OTOC vanishes.

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“…For this purpose we employ two different proper measures of coherence [2]. Namely we use (i) the relative entropy as an entropic measure of coherence and (ii) the l 1 norm of coherence [55,56]: Hereˆ d (t) is the diagonal part ofˆ (t) in the flavor basis (3), i.e.,ˆ d = diag(ρ d11 , ρ d22 , ρ d33 , ρ d44 ). Further, we use mixedness [57,58]…”

Section: Neutrino Oscillations' Probability Coherence and Mixednessmentioning

confidence: 99%

Coherence and mixedness of neutrino oscillations in a magnetic field

et al. 2021

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The radical departure from classical physics implies quantum coherence, i.e., coherent superposition of eigenstates of Hermitian operators. In resource theory, quantum coherence is a resource for quantum operations. Typically the stochastic phenomenon induces decoherence effects. However, in the present work, we prove that nonunitary evolution leads to the generation of quantum coherence in some cases. Specifically, we consider the neutrino propagation in the dissipative environment, namely in a magnetic field with a stochastic component, and focus on neutrino flavour, spin and spin-flavour oscillations. We present exact analytical results for quantum coherence in neutrino oscillations quantified in terms of the relative entropy. Starting from an initial zero coherence state, we observe persistent oscillations of coherence during the dissipative evolution of an ultra-high energy neutrino in a random interstellar magnetic field. We found that after dissipative evolution, the initial spin-polarized state entirely “thermalizes”, and in the final steady state, the spin-up/down states have the same probabilities. On the other hand, neutrino flavour states also “thermalize”, but the populations of two flavour states do not equate to each other. The initial flavour still dominates in the final steady state.

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Generation of coherence in an exactly solvable nonlinear nanomechanical system

Cited by 16 publications

References 66 publications

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Scrambling and quantum feedback in a nanomechanical system

Coherence and mixedness of neutrino oscillations in a magnetic field

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