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6CCVD Research

Dynamical decoupling for realization of topological frequency conversion

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-11-06
JournalPhysical review. A/Physical review, A
AuthorsQianqian Chen, Haibin Liu, Min Yu, Shaoliang Zhang, Jianming Cai
InstitutionsEast China Normal University, Wuhan National Laboratory for Optoelectronics
Citations5
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research investigates the robust realization of topological frequency conversion using a solid-state spin system, specifically the Nitrogen-Vacancy (NV) center in diamond, under realistic noise conditions.

  • Core Achievement: Demonstrated the feasibility of realizing a two-dimensional (2D) Floquet lattice, which simulates the synthetic quantum Hall effect, using a single NV electron spin driven by two incommensurate microwave frequencies.
  • Challenge Addressed: The primary limitation in solid-state spin systems—dephasing caused by longitudinal magnetic field fluctuation (noise)—was analyzed and mitigated.
  • Mitigation Strategy: A Dynamical Decoupling (DD) scheme, based on periodic π-pulses (similar to CPMG), was proposed and integrated with the two-frequency driving Hamiltonian.
  • Robustness Demonstrated: Numerical simulations show that the DD scheme successfully sustains the quantized energy pumping (topological frequency conversion) and the associated topological phase transition features.
  • Critical Performance: The topological features remain unambiguously observable even when the NV center spin coherence time (T2*) is severely degraded, down to 0.1 µs.
  • Mechanism: The DD sequence effectively averages the noisy Hamiltonian elements over the short inter-pulse period (Δt), mitigating the influence of the Ornstein-Uhlenbeck noise model.
  • Value Proposition: Establishes the NV center in diamond as a highly controllable, versatile platform for investigating robust topological phenomena induced by periodic driving.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
NV Zero-Splitting (D)(2π)2870MHzElectronic ground state Hamiltonian (S=1)
NV Gyromagnetic Ratio (γ)(2π)2.8MHz/GElectronic ground state Hamiltonian
Microwave Drive Amplitude (2η)(2π)2MHzOverall energy scale of the two-tone drive
Modulation Frequency (ω1)(2π)50kHzFirst frequency component of the drive
Modulation Frequency (ω2)(2π)80.9kHzSecond frequency component (incommensurate ratio)
Minimum Energy Gap (Δ)η min (m
Simulated Coherence Time (T2*)0.1 to 2µsRange tested under magnetic noise
Noise Correlation Time (τ)1msTypical nuclear spin bath noise model
Time Discretization Step (dt)5nsUsed for numerical simulation of propagator
DD Inter-Pulse Period (Δt)50nsTime between π-pulses in the decoupling sequence
Topological Invariant (C)-1, 0, 1DimensionlessChern number characterizing the Floquet bands

Key Methodologies

Section titled “Key Methodologies”

The realization and simulation of the Floquet lattice and topological frequency conversion rely on precise control and modeling of the NV center spin system:

  1. System Preparation: The NV center electron spin is initialized into a two-level qubit subspace (|ms = 0> and |ms = -1>) by applying an external static magnetic field (B) parallel to the NV symmetry axis.
  2. Hamiltonian Engineering: The target BHZ model Hamiltonian (Hrot) is realized by applying microwave (MW) driving fields perpendicular to the NV axis. These MW fields are modulated with time-dependent amplitude and phase at two incommensurate frequencies (ω1 and ω2).
  3. Noise Modeling: Realistic dephasing noise (longitudinal magnetic field fluctuation, δ(t)σz) is incorporated. This noise is modeled as a classical Gaussian Ornstein-Uhlenbeck (OU) process, characterized by coherence time (T2*) and correlation time (τ).
  4. Dynamical Decoupling (DD) Strategy: A CPMG-like DD sequence is implemented, consisting of repetitive, equally distant π-pulses applied during the evolution.
    • The DD sequence alternates between the original noisy Hamiltonian (H1) and a toggled Hamiltonian (H’1 = σxH1σx) during the short inter-pulse period (Δt = 50 ns).
    • This strategy effectively averages the noise term δ(t)σz to zero, mitigating dephasing and restoring the effective Hamiltonian (Heff).
  5. Numerical Simulation: The system evolution operator U(t) is calculated using time discretization (dt = 5 ns). Results are averaged over 1000 random instances of the OU noise to simulate experimental conditions.
  6. Topological Measurement: The topological phase transition is characterized by:
    • Energy Pumping Rate (Pk): Calculated from the time-averaged total work (Ek) done by the frequency modes. Quantized pumping (P1 = -P2) confirms the topological phase (Chern number C).
    • State Fidelity (F): Measured between the evolving state and the instantaneous eigenstate of the Hamiltonian. Fidelity deterioration marks the closing of the energy gap (critical phase transition points).

Commercial Applications

Section titled “Commercial Applications”

The robust control and simulation techniques developed for topological frequency conversion in solid-state spin systems are highly relevant to several emerging high-tech fields:

  • Quantum Computing and Simulation: NV centers are leading candidates for solid-state qubits. This work provides a robust method for engineering complex, high-dimensional synthetic lattices (Floquet lattices) for quantum simulation, potentially exploring quasi-crystals and exotic topological phases.
  • Quantum Sensing and Metrology: The ability to maintain coherence and control spin dynamics under high noise conditions (via DD) is fundamental to high-precision NV-based magnetometry and thermometry.
  • Topological Quantum Devices: The realization of robust, quantized frequency conversion suggests applications in novel signal processing and quantum electronics, where the topological protection ensures stability against environmental fluctuations.
  • Spintronics: The principles of controlling pseudo-spin degrees of freedom using microwave fields contribute directly to the development of next-generation spintronic devices and memory elements.
  • Arbitrary Waveform Generation (AWG): The experimental implementation relies on high-precision AWGs to generate the complex, time-dependent amplitude and phase modulation required for the two-tone drive and the integrated DD pulses.
View Original Abstract

The features of topological physics can manifest in a variety of physical systems in distinct ways. Periodically driven systems, with the advantage of high flexibility and controllability, provide a versatile platform to simulate many topological phenomena and may lead to novel phenomena that can not be observed in the absence of driving. Here we investigate the influence of realistic experimental noise on the realization of a two-level system under a two-frequency drive that induces topologically nontrivial band structure in the two-dimensional Floquet space. We propose a dynamical decoupling scheme that sustains the topological phase transition overcoming the influence of dephasing. Therefore, the proposal would facilitate the observation of topological frequency conversion in the solid state spin system, e.g. NV center in diamond.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - Topological Insulators and Topological Superconductors [Crossref]

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