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6CCVD Research

Hybrid quantum–classical chaotic NEMS

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2022-06-18
JournalPhysica D Nonlinear Phenomena
AuthorsAbhayveer Singh, L. Chotorlishvili, Z. Toklikishvili, I. Tralle, S. K. Mishra
InstitutionsBanaras Hindu University, Tbilisi State University
Citations5
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research presents an exactly solvable theoretical model for a Hybrid Nano-Electromechanical System (NEMS) consisting of a Nitrogen-Vacancy (NV) center spin coupled to a nonlinear, kicked nanocantilever.

  • Core Finding (Hybrid Chaos): Classical dynamical chaos (K > 1) in the nanocantilever successfully enforces stochastic dynamics onto the quantum NV spin subsystem.
  • Stochastic Signatures: This induced stochasticity is characterized by a significant broadening of the spin dynamics’ Fourier power spectrum and an abrupt loss of quantum coherence (measured via relative entropy).
  • Non-Conventional Quantum Chaos: The resulting spin dynamics are termed “hybrid quantum-classical chaos.” Crucially, this stochasticity does not manifest all traditional quantum chaos features; specifically, the nearest-neighbor level statistics remain Poissonian (for spin-1/2), rather than the expected Gaussian/Wigner-Dyson distribution.
  • Modeling Approach: The system dynamics are solved analytically using Floquet theory, where the classical cantilever motion is governed by a standard map derived from action-angle canonical variables.
  • Feedback Analysis: The effect of quantum feedback from the NV spin onto the classical cantilever dynamics was investigated and found to be negligible for small to moderate coupling strengths (g).
  • System Scale: The model uses parameters relevant to real NV centers (w0 ≈ 2.88 GHz) and microsecond time scales (T = 10 µs).

Technical Specifications

Section titled “Technical Specifications”

The following parameters were used in the analytical model and numerical simulations, representing a realistic NV-NEMS hybrid system.

ParameterValueUnitContext
NV Center Splitting Frequency (w0)2.88GHzBaseline spin transition frequency.
Cantilever Oscillation Frequency (wr)2π x 5 x 106 (5)Hz (MHz)Frequency of the mechanical oscillator.
Cantilever Mass (m)6 x 10-17kgMass of the nanocantilever.
Coupling Constant (g/2π)100kHzStrength of the spin-cantilever coupling.
Kicking Period (T)10µsPeriodicity of the external delta pulses driving the cantilever.
Zero Point Fluctuation (a0)5 x 10-3µmAmplitude of the zero point fluctuations.
Chaos Criterion (K)0.5DimensionlessRegular (quasi-periodic) classical regime (K < 1).
Chaos Criterion (K)10DimensionlessChaotic classical regime (K > 1).
Energy Scale (εV)≈ 10-9JDefined by w0 x amax.
Temperature Criterion (Tc)< 50nKTemperature required for quantum cantilever dynamics (T << 2πħwr/kB).

Key Methodologies

Section titled “Key Methodologies”

The study employed a rigorous analytical and numerical approach based on quantum and classical dynamics theory, specifically tailored for kicked hybrid systems.

  1. System Hamiltonian Formulation: The hybrid system was defined by a Hamiltonian combining the NV spin (quantum subsystem) and the nonlinear, kicked nanocantilever (classical subsystem).
  2. Classical Dynamics Mapping: The classical motion of the cantilever was simplified using action-angle canonical variables (I, θ). The dynamics under periodic kicking pulses were solved exactly using the Floquet map (a generalized standard map), which defines the transition between regular (K < 1) and chaotic (K > 1) motion.
  3. Quantum Evolution via Floquet Theory: The time evolution of the NV spin state was calculated analytically by solving the time-dependent Schrödinger equation using the Floquet operator (ÛN), which incorporates the time-dependent classical variables (In, θn) from the map.
  4. Chaos Quantification (Classical): Classical chaos was confirmed by plotting the cantilever’s phase space using Poincaré sections, showing the transition from elliptic/hyperbolic trajectories (regular) to a chaotic sea (K > 1).
  5. Chaos Quantification (Quantum): The effects of classical chaos on the quantum spin were analyzed using several metrics:
    • Fourier Power Spectrum: Used to observe the broadening of spectral peaks, indicating stochasticity.
    • Quantum Coherence: Quantified using relative entropy (D(ρ(t) | ρd(t))), showing abrupt loss in the chaotic regime.
    • Level Statistics: Nearest-neighbor spacing distribution (P(Sn)) was calculated to check for signatures of quantum chaos (Poissonian vs. Wigner-Dyson statistics).
  6. Statistical Averaging: To test robustness, spin dynamics were statistically averaged over multiple initial conditions (I0, θ0) of the classical cantilever.

Commercial Applications

Section titled “Commercial Applications”

The technology modeled—hybrid systems combining quantum spins and mechanical resonators—is foundational for several emerging fields in quantum engineering and high-precision sensing.

  • Quantum Information Processing:

    • Quantum Transducers: NEMS coupled to NV spins can act as efficient transducers, converting quantum information between microwave (spin) and mechanical (phonon) domains, critical for building scalable quantum networks.
    • Qubit Control: Utilizing mechanical motion to control and manipulate spin qubits in solid-state systems.

  • High-Precision Sensing (Quantum Sensing):

    • Nanoscale Magnetometry: NV centers are highly sensitive magnetic sensors. Coupling them to mechanical resonators enhances their sensitivity for detecting extremely weak magnetic fields or single-spin dynamics.
    • Mass Sensing: NEMS are used for ultra-sensitive mass detection (e.g., single-molecule mass spectrometry). Hybrid systems offer quantum-enhanced sensitivity in these applications.

  • Fundamental Physics Research:

    • Quantum Chaos Studies: Provides a controllable platform to study the fundamental transition between classical chaos and quantum stochasticity in hybrid systems, aiding in the design of robust quantum devices.

  • Advanced Materials Characterization:

    • Defect Engineering: Understanding the dynamics of NV centers (a point defect in diamond) under mechanical stress is crucial for optimizing diamond materials used in quantum technologies.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2007 - Deterministic quantum mechanics versus classical mechanical indeterminism
  2. 2019 - Physics without determinism: Alternative interpretations of classical physics
  3. 2019 - Selection of a stochastic Landau-Lifshitz equation and the stochastic persistence problem [Crossref]
  4. 1979 - A universal instability of many-dimensional oscillator systems [Crossref]
  5. 1979 - Stochastic behavior of a quantum pendulum under a periodic perturbation
  6. 1995 - Atom optics realization of the quantum δ-kicked rotor [Crossref]
  7. 2001 - Quantum enhancement of momentum diffusion in the delta-kicked rotor
  8. 1996 - Quantum mechanical entanglements with chaotic dynamics [Crossref]
  9. 1985 - Energy-level statistics of integrable quantum systems [Crossref]

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