| 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 |
- Systematic NESS Calculation: A general, systematic high-frequency (HF) expansion theory (van Vleck approach) was developed for calculating Nonequilibrium Steady States (NESSs) in periodically driven dissipative quantum systems (Floquet-Lindblad equations).
- Computational Efficiency: The method transforms the complex task of numerically solving time evolution into an efficient linear algebraic problem: finding the zero-eigenvalue eigenvector of the effective Liouvillian (Leff).
- Deviation from Floquet-Gibbs State (FGS): The research reveals that NESSs can significantly deviate from the standard FGS when the driving frequency (ω) is comparable to or less than the bath spectral cutoff (Λ), due to active k-photon exchange processes.
- Dissipation-Assisted Engineering: The framework was used to propose the dissipation-assisted terahertz (THz) inverse Faraday effect in isotropic Heisenberg spin chains, where magnetization is induced by the dissipation breaking spin rotation symmetry.
- Model Validation: The HF expansion approach was quantitatively validated against exact numerical integration for models including the nitrogen-vacancy (NV) center in diamond and an open XY spin chain.
- Accuracy Guarantee: The N-th order HF approximation systematically describes the NESS with an accuracy scaling as O(ω-(N+1)) for high frequencies.
The paper is highly theoretical, utilizing dimensionless parameters for numerical examples.
| Parameter | Value | Unit | Context |
|---|
| Driving Frequency (ω) | 10 | (Dimensionless) | Standard frequency used in NV center examples (Sec 5.3, 6.2). |
| Inverse Temperature (β) | 3 or 10 | (Dimensionless) | Thermal bath coupling strength (β = 1/kBT). |
| Bath Spectral Cutoff (Λ) | 10, 102, 104, 106 | (Dimensionless) | Gaussian cutoff for the Ohmic boson bath spectral function. |
| System-Bath Coupling (γ0) | 0.2 or 0.1 | (Dimensionless) | Strength of dissipation used in numerical examples. |
| Static Zeeman Field (Bz) | 0.3 | (Dimensionless) | NV center Hamiltonian parameter. |
| AC Field Amplitude (Bd) | 0.1 | (Dimensionless) | Circularly polarized drive amplitude (NV center). |
| Nematic Anisotropy (Nz) | 1 | (Dimensionless) | NV center S=1 spin system parameter. |
| Nematic Anisotropy (Nxy) | 0.05 | (Dimensionless) | NV center S=1 spin system parameter. |
| Expansion Accuracy (δρN) | Proportional to ω-(N+1) | (Dimensionless) | Accuracy measure for the N-th order HF approximation. |
| Heisenberg Exchange (J) | 1 | (Dimensionless) | Antiferromagnetic coupling constant (Heisenberg chain). |
| Chain Length (L) | 6 or 8 | Sites | System size for Heisenberg chain simulations. |
- Floquet-Lindblad Equation (FLE) Framework: The dynamics of the periodically driven dissipative quantum system are modeled using the Lindblad master equation, ensuring the density operator remains completely positive and trace-preserving.
- Van Vleck High-Frequency (HF) Expansion: The time-periodic Liouvillian (Lt) is expanded in powers of 1/ω, yielding a time-independent effective Liouvillian (Leff) and a periodic micromotion superoperator (Gt). This approach involves fewer terms than the Floquet-Magnus expansion.
- NESS Calculation via Zero Mode: The NESS is obtained by finding the eigenvector (η0,α) corresponding to the zero eigenvalue of the effective Liouvillian Leff, a process solved efficiently using linear algebra (e.g., Lanczos algorithm).
- RWA-Derived Dissipators: For microscopically derived dissipators (weak thermal contact), the FLE is transformed into the interaction picture, resulting in a time-independent Lindbladian where the NESS population (Pss) is determined by solving a classical master equation based on transition rates (Wnm).
- k-Photon Process Analysis: The transition rates (Wnm) are analyzed to include contributions from k-photon processes (k ≠ 0), which involve the exchange of energy kħω between the system and the bath, crucial for accurately modeling NESS when ω is less than the bath cutoff Λ.
- Model Specific Implementations:
- XY Chain: Mapped to quadratic Majorana fermions to analyze bulk properties and the robustness of topological phases against boundary dissipation.
- NV Center: Modeled as an effective three-level system (S=1 spin) under a circularly polarized AC magnetic field.
| Industry/Field | Relevance to Research | Specific Functionality/Product |
|---|
| Quantum Computing & Sensing | Analysis of the NV center in diamond, a leading solid-state qubit platform, under realistic dissipative conditions. | Engineering robust, long-lived Floquet states for quantum memory, magnetometry, and quantum information processing. |
| Ultrafast Spintronics | Theoretical framework for the dissipation-assisted THz inverse Faraday effect in quantum magnets. | Developing novel, non-thermal optical control mechanisms for magnetization in magnetic insulators using high-frequency (THz) lasers. |
| Quantum Materials Engineering | Study of topological XY spin chains and the stability of Floquet topological states against boundary dissipation. | Designing and stabilizing functional topological quantum materials and devices for low-power electronics. |
| High-Frequency Device Design | General methodology for efficiently calculating NESS in systems driven at high frequencies (ω). | Optimizing the performance and stability of quantum devices operating in the high-frequency regime, where heating and dissipation are critical factors. |
| Quantum Thermodynamics | Detailed investigation into the conditions under which NESS deviates from the FGS (i.e., when ω is less than Λ). | Improving the design and efficiency of periodically driven quantum heat engines and thermal management systems by controlling photon-exchange processes. |
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.