Nonequilibrium steady states in the Floquet-Lindblad systems - van Vleck's high-frequency expansion approach
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-12-24 |
| Journal | SciPost Physics Core |
| Authors | Tatsuhiko N. Ikeda, Koki Chinzei, Masahiro Sato |
| Institutions | The University of Tokyo, Ibaraki University |
| Citations | 29 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Floquet-Lindblad Systems and MPCVD Diamond
Section titled âTechnical Documentation & Analysis: Floquet-Lindblad Systems and MPCVD DiamondâExecutive Summary
Section titled âExecutive SummaryâThis research paper presents a robust theoretical framework for analyzing Nonequilibrium Steady States (NESSs) in periodically driven dissipative quantum systems, directly impacting the design and optimization of next-generation quantum devices, particularly those utilizing diamond-based spin systems.
- Systematic NESS Analysis: Developed a generalized van Vleck high-frequency (HF) expansion for the Liouvillian, enabling systematic calculation of NESSs in Floquet-Lindblad systems without resorting to computationally expensive time-evolution simulations.
- Direct Diamond Application: The theory is quantitatively validated using an effective three-level model for the Nitrogen-Vacancy (NV) center in diamond, a critical platform for quantum sensing and computing.
- Efficiency and Scalability: The HF expansion approach leverages linear algebra (e.g., Lanczos algorithm) to efficiently obtain NESS solutions, making it highly suitable for analyzing complex, many-body quantum systems like spin chains.
- Dissipation-Assisted Engineering: Proposes the concept of dissipation-assisted Floquet engineering, exemplified by the terahertz (THz) inverse Faraday effect in isotropic Heisenberg spin chains, where dissipation breaks symmetry to induce magnetization.
- Accuracy Quantification: Demonstrates that the N-th order HF approximation accurately describes the NESS up to a precision scaling of O(Ï-(N+1)) for high driving frequencies (Ï).
- Material Relevance: The core examplesâNV centers and high-frequency magnetic systemsârequire high-purity, low-defect diamond materials, aligning perfectly with 6CCVDâs Single Crystal Diamond (SCD) and Boron-Doped Diamond (BDD) offerings.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters were extracted from the numerical simulations and theoretical scaling laws presented in the paper, particularly concerning the NV center and spin chain models.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| SCD Thickness Range (6CCVD Capability) | 0.1 ”m to 500 ”m | ”m | Required for thin-film NV device integration. |
| PCD Wafer Diameter (6CCVD Capability) | Up to 125 | mm | Maximum size for large-scale quantum array substrates. |
| Driving Frequency (Ï) | 10 | Arbitrary (rad/T) | Simulation parameter for NV Center NESS calculation. |
| Static Zeeman Field (Bs) | 0.3 | Arbitrary | Simulation parameter for NV Center Hamiltonian. |
| AC Magnetic Field Coupling (Bd) | 0.1 | Arbitrary | Simulation parameter for NV Center external drive. |
| Inverse Temperature (ÎČ) | 3, 10 | Arbitrary | Bath thermal equilibrium parameter. |
| System-Bath Coupling (Îł0) | 0.1, 0.2 | Arbitrary | Dissipation strength in phenomenological models. |
| Bath Spectral Cutoff (Î) | 5, 10, 106 | Arbitrary | Critical energy scale determining NESS deviation from Floquet-Gibbs state. |
| HF Expansion Accuracy Scaling (ÎŽÏN) | â Ï-(N+1) | N/A | Theoretical scaling of N-th order approximation error. |
| SCD Surface Roughness (6CCVD Capability) | Ra < 1 | nm | Ultra-smooth polishing for high-fidelity optical interfaces (NV readout). |
Key Methodologies
Section titled âKey MethodologiesâThe research relies on advanced theoretical physics techniques applied to open quantum systems.
- Floquet-Lindblad Equation (FLE) Definition: The dynamics of the periodically driven dissipative quantum system are governed by the quantum master equation $\frac{d}{dt}\rho(t) = \mathcal{L}_t[\rho(t)]$, where the Liouvillian $\mathcal{L}_t$ is periodic and in the Lindblad (GKSL) form, consisting of Hamiltonian ($\mathcal{H}_t$) and dissipator ($\mathcal{D}_t$) superoperators.
- Van Vleck High-Frequency Expansion: The Liouvillian $\mathcal{L}t$ is expanded in powers of the inverse driving frequency ($1/\omega$) to yield a time-independent effective Liouvillian ($\mathcal{L}{\text{eff}}$) and a micromotion superoperator ($\mathcal{G}_t$).
- NESS Calculation: The Nonequilibrium Steady State (NESS) density matrix ($\rho_{\text{NESS}}$) is obtained by finding the zero-eigenvalue eigenvector ($\eta_{0,\alpha}$) of the effective Liouvillian ($\mathcal{L}_{\text{eff}}$), utilizing linear algebra techniques (e.g., Lanczos algorithm) for computational efficiency.
- Dissipator Modeling: The study employed two classes of dissipators:
- Phenomenological Time-Independent Dissipators: Used for initial modeling of systems like the open XY chain and the NV center.
- Microscopically-Derived Time-Dependent Dissipators (RWA): Derived using the Rotating Wave Approximation (RWA) for systems weakly coupled to a thermal bath, revealing conditions for NESS deviation from the Floquet-Gibbs state (FGS) based on the relationship between $\omega$ and the bath spectral cutoff $\Lambda$.
- Quantum System Examples: Applied the methodology to specific models:
- Three-level system (NV center in diamond) under circularly polarized AC magnetic field.
- Open XY spin chain with boundary dissipation (topological phase analysis).
- Isotropic Heisenberg spin chain under circularly polarized AC magnetic field (Inverse Faraday Effect).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe theoretical models analyzed in this paper, particularly the diamond NV center and THz-driven magnetic systems, require materials with exceptional purity, precise geometry, and specialized surface engineeringâall core competencies of 6CCVD.
| Applicable Materials | Customization Potential | Engineering Support & Call to Action |
|---|---|---|
| Optical Grade Single Crystal Diamond (SCD) | Custom Dimensions & Thickness: We provide SCD wafers with thicknesses ranging from 0.1 ”m to 500 ”m, crucial for integrating NV centers near the surface for sensing, or for bulk quantum memory applications. | NV Center Optimization: Our in-house PhD team specializes in material selection for quantum applications. We can assist researchers in selecting the optimal SCD grade (e.g., low nitrogen content) to maximize NV center coherence times and yield. |
| Heavy Boron-Doped Diamond (BDD) | Advanced Metalization Services: Replication or extension of these experiments often requires precise microwave delivery. We offer internal metalization capabilities including Au, Pt, Pd, Ti, W, and Cu deposition, enabling high-frequency contacts and waveguides directly on the diamond substrate. | THz and High-Frequency Projects: The dissipation-assisted Inverse Faraday Effect operates in the THz regime. BDD offers tunable conductivity, making it an ideal platform for integrated THz components and low-loss contacts necessary for high-frequency Floquet engineering. |
| Polycrystalline Diamond (PCD) | Ultra-Low Roughness Polishing: For optical readout and integration of NV centers, surface quality is paramount. We guarantee SCD polishing to Ra < 1 nm and inch-size PCD to Ra < 5 nm, minimizing scattering and maximizing device fidelity. | Global Supply Chain: We offer global shipping (DDU default, DDP available) ensuring reliable and timely delivery of custom diamond substrates worldwide. |
| Custom Substrates (up to 10 mm thick) | Laser Cutting and Shaping: Custom geometries are available for integration into specific experimental setups (e.g., microwave cavities or cryostats). | For custom specifications or material consultation regarding Floquet engineering, NV centers, or THz quantum systems, visit 6ccvd.com or contact our engineering team directly. |
View Original Abstract
Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.