Non-Hermitian topological phases and dynamical quantum phase transitions - a generic connection
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-05-26 |
| Journal | New Journal of Physics |
| Authors | Longwen Zhou, Qianqian Du |
| Institutions | Ocean University of China |
| Citations | 39 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Non-Hermitian Topological Phases in Diamond Quantum Systems
Section titled âTechnical Documentation & Analysis: Non-Hermitian Topological Phases in Diamond Quantum SystemsâThis document analyzes the research concerning Dynamical Quantum Phase Transitions (DQPTs) in non-Hermitian systems, focusing on the proposed experimental verification using Nitrogen-Vacancy (NV) centers in diamond. This application directly aligns with 6CCVDâs expertise in high-purity, custom MPCVD Single Crystal Diamond (SCD) for quantum technologies.
Executive Summary
Section titled âExecutive Summaryâ- Fundamental Discovery: An intrinsic connection is established between Non-Hermitian Topological Phases (NHTPs) and Dynamical Quantum Phase Transitions (DQPTs) in one-dimensional systems with chiral symmetry.
- Dynamic Probing: DQPTs, characterized by nonanalytic behavior in the return probability rate function $g(t)$, serve as a dynamic probe to distinguish and characterize different NHTPs.
- Topological Invariants: The critical momenta ($k_c$) and critical time periods ($T(k_c)$) of the DQPTs are directly related to the bulk topological invariant (winding number, $w$) of the post-quench non-Hermitian phase.
- Model Validation: The connection is explicitly demonstrated across three prototypical models: the Lossy Kitaev Chain (LKC), the NNN LKC, and the Nonreciprocal Su-Schrieffer-Heeger (NRSSH) model.
- Experimental Feasibility: The authors propose experimental verification by manipulating the spin states of a Nitrogen-Vacancy (NV) center in diamond, confirming the materialâs critical role as a platform for non-Hermitian quantum dynamics.
- Methodology: The experimental scheme relies on dilating the non-Hermitian Hamiltonian into a Hermitian counterpart using the NV centerâs ancilla qubit, a technique recently validated in similar NV center setups.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters and results are extracted from the theoretical models and experimental proposals discussed in the paper.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Topological Invariant (Winding Number) | $w = 0, 1, 2$ | Dimensionless | Characterizes NHTPs in LKC and NNN LKC models. |
| Half-Quantized Winding Number | $w = 1/2$ | Dimensionless | Unique NHTP observed in the Nonreciprocal SSH model. |
| Critical Time Period $T(k_c)$ (LKC) | $\pi / \sqrt{\Delta^2(1 - u^2/J^2) - v^2}$ | Time (Arbitrary Units) | Period of DQPTs when the system is quenched to $w=1$. |
| Critical Momentum Condition (LKC) | $u + J \cos k = 0$ | Quasimomentum ($k$) | Determines the gapless quasimomenta $k_0$. |
| Geometric Phase Jump | $2\pi$ | Radians | Quantized jump observed in $\Phi_G(k, t)$ at critical momenta during a DQPT. |
| Experimental Platform | NV Center in Diamond | Material System | Proposed setup for realizing PT-symmetric non-Hermitian two-level Hamiltonian dynamics. |
| Hamiltonian Dilation Scheme | Hermitian $Hâ(k, t)$ | N/A | Strategy to simulate non-Hermitian dynamics using an ancilla qubit (NV spin). |
Key Methodologies
Section titled âKey MethodologiesâThe research establishes the NHTP-DQPT connection through a combination of theoretical modeling and a specific quantum quench protocol, culminating in a diamond-based experimental proposal.
- Non-Hermitian Hamiltonian Formulation: The study utilizes 1D lattice models (LKC, NNN LKC, NRSSH) whose Bloch Hamiltonians $H(k)$ are non-Hermitian ($H \neq H^{\dagger}$) but possess chiral (sublattice) symmetry $S$.
- Topological Invariant Calculation: The bulk topological phase is characterized by the winding number $w$, derived from the winding angle $\phi(k)$ across the first Brillouin Zone (BZ).
- Quantum Quench Protocol: The system is initialized in an infinite-temperature state ($\rho_0 = \sigma_0/2$) and then quenched, allowing the dynamics to be governed by the post-quench non-Hermitian Hamiltonian $H(k)$.
- DQPT Detection via Return Amplitude: Dynamical Quantum Phase Transitions are identified when the return amplitude $G(k, t) = \cos[E(k)t]$ equals zero, yielding real critical times $t_n(k_c)$ only at specific critical momenta $k_c$ where the dispersion $E(k)$ is real.
- Dynamical Topological Order Parameter (DTOP): The connection is further confirmed by analyzing the noncyclic geometric phase $\Phi_G(k, t)$ and the DTOP $\nu(t)$, which exhibits quantized jumps ($|\Delta\nu(t)| = 1$) at critical times.
- NV Center Experimental Proposal: The non-Hermitian dynamics are realized experimentally by dilating the two-level non-Hermitian Hamiltonian $H(k)$ into a four-level Hermitian Hamiltonian $Hâ(k, t)$ using the electron and nuclear spins of a solid-state Nitrogen-Vacancy (NV) center in diamond.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe proposed experimental verification using NV centers in diamond requires materials of the highest quality, purity, and customization. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond substrates and engineering services to enable this cutting-edge quantum research.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage for Quantum Research |
|---|---|---|
| High-Purity Quantum Host Material | Optical Grade Single Crystal Diamond (SCD) | MPCVD growth ensures ultra-low strain and high chemical purity, critical for maximizing the coherence time ($T_2$) of NV center qubits used in dynamic quantum simulation. |
| Custom Substrate Dimensions | Plates/Wafers up to 125 mm | SCD and PCD available in custom dimensions, accommodating large-scale integration or specialized chip designs required for complex quantum lattice simulations. |
| Precise Material Thickness | SCD Thickness: 0.1 ”m to 500 ”m | Allows researchers to select optimal thickness for NV center creation (e.g., shallow implantation for surface-based control or deep centers for bulk coherence). Substrates up to 10 mm available. |
| Surface Preparation for Optical Access | Ultra-Low Roughness Polishing | SCD polishing achieves $R_a < 1$ nm, minimizing optical scattering and ensuring efficient collection of NV center photoluminescence, vital for high-fidelity readout. |
| Qubit Control and Readout Circuitry | Custom Metalization Services | In-house deposition of Au, Pt, Pd, Ti, W, and Cu for creating microwave strip lines, electrodes, and gate structures necessary for manipulating the NV center spin states and implementing the quench protocols. |
| Material Optimization for NV Density | Engineering Support for Doping Control | Our experts assist in controlling the nitrogen concentration during growth, optimizing the density and spatial distribution of NV centers for specific lattice model simulations. |
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View Original Abstract
Abstract The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomenaâtopological phases and dynamical quantum phase transitions (DQPTs)âin non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su-Schrieffer-Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
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