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Floquet dynamical quantum phase transitions in periodically quenched systems

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2021-06-15
JournalJournal of Physics Condensed Matter
AuthorsLongwen Zhou, Qianqian Du, Longwen Zhou, Qianqian Du
InstitutionsOcean University of China
Citations24
AnalysisFull AI Review Included

Technical Analysis and Documentation: Floquet Dynamical Quantum Phase Transitions in Periodically Quenched Systems

Section titled “Technical Analysis and Documentation: Floquet Dynamical Quantum Phase Transitions in Periodically Quenched Systems”

Executive Summary

Section titled “Executive Summary”

This research establishes a robust theoretical framework for observing and controlling Floquet Dynamical Quantum Phase Transitions (DQPTs) in periodically quenched systems, with direct implications for quantum simulation platforms.

  • Quantum Platform Validation: The Piecewise Quenched Lattice (PQL) model used to demonstrate the theory is explicitly cited as “readily realizable in quantum simulators like the nitrogen-vacancy (NV) center in diamonds.”
  • Floquet Engineering Control: The study confirms that tuning quench amplitudes (Jx, Jy) allows for flexible control over the number and timing of Floquet DQPTs within a single driving period.
  • Topological Detection: A Dynamical Topological Order Parameter (DTOP) is introduced, which exhibits quantized jumps (Δw = 1 or 2) at critical times, serving as an efficient, non-decaying probe for topological phase transitions.
  • Material Requirement: Successful experimental realization, particularly in NV-diamond setups, necessitates ultra-high purity, low-strain Single Crystal Diamond (SCD) substrates to maintain long coherence times.
  • 6CCVD Value Proposition: 6CCVD specializes in the production of Quantum Grade MPCVD SCD wafers, offering the precise material specifications (Ra < 1 nm polishing, custom thickness, and orientation) required to replicate and advance this cutting-edge research.
  • Scalability: The framework provides a pathway for observing DQPTs over extended time windows (multiple driving periods), requiring stable, high-quality diamond platforms for sustained quantum evolution.

Technical Specifications

Section titled “Technical Specifications”

The following hard data points and parameters were extracted from the theoretical and numerical analysis of the periodically quenched system (PQL model).

ParameterValueUnitContext
Driving Period (T)2DimensionlessPeriodicity of the time-dependent Hamiltonian H(k, t)
Planck Constant (ħ)1DimensionlessSet for theoretical calculations
Quasimomentum Range (k)[-π, π)Radian/Length-1Defined in the first Brillouin Zone
Quench Amplitudes (Jx, Jy)Up to 4.1πDimensionlessNumerical examples demonstrating multiple DQPTs
Experimental Coupling StrengthUp to 3DimensionlessAchievable in existing NV center setups (Ref. [61])
Numerical Integration Grid (N)300GridsUsed for k-space integration to ensure convergence
DTOP Quantized Jump (Δw)1 or 2IntegerChange in the Dynamical Topological Order Parameter at critical time
Critical Time SymmetrySymmetric around t = 1DimensionlessObserved when Jx = Jy (equal quench amplitudes)
Surface Roughness (Inferred)Ra < 1 nmnmRequired for high-fidelity optical readout in NV centers

Key Methodologies

Section titled “Key Methodologies”

The theoretical framework and numerical demonstration rely on the following sequence of steps applied to the Piecewise Quenched Lattice (PQL) model:

  1. Hamiltonian Definition: The time-dependent Hamiltonian H(k, t) is defined as piecewise quenched, possessing chiral (sublattice) symmetry.
  2. Floquet Dynamics Calculation: The Floquet operator U(k) is derived, representing the evolution operator over a complete driving period (T=2).
  3. Floquet Eigenstate Initialization: The system is initialized in a uniformly filled Floquet band, characterized by the Floquet eigenstate |ψv(k)⟩.
  4. Return Amplitude Calculation: The return amplitude Gv(k, t) is computed, which is the central object for identifying DQPTs.
  5. Rate Function Analysis: The rate function of return probability, f(t), is calculated by integrating the logarithm of the return probability over the quasimomentum k. Nonanalytic cusps in f(t) signal a Floquet DQPT.
  6. Geometric Phase Determination: The noncyclic geometric phase φGv(k, t) is calculated by taking the difference between the total phase and the dynamical phase of the return amplitude.
  7. DTOP Quantification: The Dynamical Topological Order Parameter (DTOP), wv(t), is determined by calculating the winding number of the geometric phase in k-space. Quantized jumps in wv(t) confirm the topological nature of the transition.

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

The successful experimental realization of Floquet DQPTs using NV centers hinges entirely on the quality and precision of the diamond substrate. 6CCVD is uniquely positioned to supply the necessary materials and engineering support for this advanced quantum research.

Applicable Materials

Section titled “Applicable Materials”

To replicate or extend the quantum simulation experiments referenced in this paper (Refs. [35, 60, 61]), researchers require:

  • Material: Quantum Grade Single Crystal Diamond (SCD).
  • Purity: Ultra-low nitrogen concentration (below 1 ppb) to ensure minimal native defects and maximize the coherence time (T2) of the implanted NV centers.
  • Orientation: Standard [100] or [111] oriented SCD wafers, depending on the specific magnetic field alignment and NV axis requirements of the experimental setup.

Customization Potential

Section titled “Customization Potential”

6CCVD’s advanced MPCVD growth and post-processing capabilities directly address the stringent requirements of NV center quantum platforms:

Requirement from Research6CCVD CapabilityTechnical Specification
Substrate SizeCustom dimensions availablePlates/wafers up to 125 mm (PCD), custom SCD sizes
Thickness ControlPrecision SCD thickness controlSCD wafers from 0.1 ”m up to 500 ”m
Surface QualityUltra-low roughness polishingRa < 1 nm (Optical Grade SCD)
Defect EngineeringLow-strain, high-purity growthOptimized MPCVD growth for long T2 coherence
Integration/ReadoutCustom Metalization ServicesInternal capability for Au, Pt, Pd, Ti, W, Cu contacts
Substrate ThicknessRobust SubstratesSubstrates up to 10 mm thick for mechanical stability

Engineering Support

Section titled “Engineering Support”

The complexity of Floquet engineering and quantum simulation requires materials optimized for specific experimental parameters (e.g., high Jx, Jy coupling strengths).

  • Material Optimization: 6CCVD’s in-house PhD team specializes in optimizing diamond material properties—including orientation, surface termination, and defect density—specifically for NV Center Quantum Simulation projects.
  • Process Consultation: We provide consultation on the optimal diamond thickness and surface preparation necessary for high-fidelity NV center implantation and subsequent optical readout, ensuring minimal decoherence.
  • Global Logistics: We offer reliable global shipping (DDU default, DDP available) to ensure timely delivery of critical materials worldwide.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Abstract Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - Dynamical quantum phase transitions in the transverse-field Ising model [Crossref]
  2. 2010 - Dynamics after a sweep through a quantum critical point [Crossref]
  3. 2018 - Dynamical quantum phase transitions in non-Hermitian lattices [Crossref]
  4. 2014 - Dynamical quantum phase transitions in systems with broken-symmetry phases [Crossref]
  5. 2014 - First-order dynamical phase transitions [Crossref]
  6. 2014 - Disentangling dynamical phase transitions from equilibrium phase transitions [Crossref]
  7. 2015 - Scaling and universality at dynamical quantum phase transitions [Crossref]
  8. 2016 - Dynamical quantum phase transitions: role of topological nodes in wave function overlaps [Crossref]
  9. 2017 - Quenching a quantum critical state by the order parameter: dynamical quantum phase transitions and quantum speed limits [Crossref]
  10. 2019 - Quench dynamics and zero-energy modes: the case of the Creutz model [Crossref]

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