Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-12-28 |
| Journal | Physical review. A/Physical review, A |
| Authors | Yuan Zhou, Sheng-li Ma, Bo Li, Xiaoxiao Li, Fuli Li |
| Institutions | Xiâan Jiaotong University |
| Citations | 29 |
| Analysis | Full AI Review Included |
Technical Analysis and Commercial Solutions for Hybrid Quantum Systems
Section titled âTechnical Analysis and Commercial Solutions for Hybrid Quantum SystemsâSource Paper: Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system (arXiv:1712.06234v1) Prepared for: 6CCVD Engineering and Sales Team
Executive Summary
Section titled âExecutive SummaryâThis research successfully demonstrates an experimentally feasible scheme for simulating the Lipkin-Meshkov-Glick (LMG) model using a hybrid quantum system composed of a dense Nitrogen-Vacancy (NV) center ensemble in diamond coupled magnetically to superconducting coplanar waveguide cavities.
- Core Material Requirement: The protocol relies critically on high-quality, high-density NV center ensembles in MPCVD diamond, requiring a total number of spins ($N$) approaching $10^{12}$ for achieving sufficient collective coupling strength.
- Demonstrated Phenomena: The system successfully simulates two key LMG applications: achieving a distinct non-equilibrium second-order quantum phase transition, and generating spin squeezed states.
- Squeezing Achievement: A spin squeezing degree of $\xi^{2} \sim -10$ dB was demonstrated by tailoring the LMG Hamiltonian into the two-axis counter-twisting form.
- Coherence Constraint: To maintain the nonclassical spin squeezed state for practical periods (up to $2$ ”s, and potentially longer), the material must possess long spin coherence times ($T_{2} > 600$ ”s), achievable only with high-purity, isotopically engineered SCD diamond (low $^{13}\text{C}$ abundance).
- Implementation Strategy: The model utilizes classical external microwave driving fields and leverages the large detuning/bad cavity limit to adiabatically eliminate the supermodes, resulting in an effective spin-spin interaction Hamiltonian.
- 6CCVD Value Proposition: Replicating or extending this research requires SCD wafers optimized for high NV incorporation, superior surface quality (Ra < 1 nm), and specific custom dimensions and metalization for integration into superconducting cavity circuits.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters are extracted from the experimental proposal, focusing on the material requirements and critical operational values.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Required NV Center Count (N) | $\sim 10^{12}$ | N/A | Critical threshold for sufficient collective coupling ($\sqrt{N}g_i$) |
| NV Center Density ($\rho$) | $\sim 10^{15}$ | cm-3 | Required concentration for target NV count in typical device geometry |
| Collective Coupling ($\sqrt{N}g_k/2\pi$) | 12 | MHz | Coupling strength required for LMG simulation feasibility |
| Spin Squeezing Degree ($\xi^{2}$) | $\sim -10$ | dB | Maximum squeezing achieved using two-axis counter-twisting LMG model |
| Minimum Coherence Time ($T_{2}$) | > 600 | $\mu$s | Demonstrated NV ensemble coherence time |
| Target Coherence Time ($T_{2}$) | $\sim 2$ | ms | Achievable with isotopically pure diamond |
| Cavity Coupling Coefficient ($\epsilon$) | $\sim 10$ | MHz | Coupling strength between the two coplanar waveguide cavities |
| Cavity Dissipation Rate ($\kappa$) | $> 2\pi \times 1$ | kHz | Minimum required rate (Bad Cavity Limit) |
| NV Zero-Field Splitting (D) | $2\pi \times 2.88$ | GHz | Ground state spin triplet degeneracy point |
Key Methodologies
Section titled âKey MethodologiesâThe LMG model simulation relies on precise engineering of the hybrid quantum system and manipulation of the effective Hamiltonian through external classical fields.
- System Integration: Two superconducting coplanar waveguide (CPW) cavities are strongly coupled ($\epsilon \sim 10$ MHz). An NV center ensemble is magnetically coupled to one of the cavities.
- Spin State Preparation: A homogeneous static magnetic field ($B_{1}$) is applied to split the degenerate $|\text{m}_{\text{s}} = \pm 1\rangle$ states, creating a three-level system: $|0\rangle$, $|+\rangle$, and $|-\rangle$.
- Supermode Transformation: The two cavity modes ($c_{1}, c_{2}$) are canonically transformed into two supermodes ($a, b$) to simplify the Hamiltonian.
- Raman Transitions via Microwave Fields: Four microwave classical fields ($\omega_{k}$) are introduced to induce four distinct two-photon Raman transitions between the spin states $|+\rangle$ and $|-\rangle$.
- Adiabatic Elimination: By operating under the condition of large detuning and the bad cavity limit ($\sqrt{\kappa_{a,b}^{2} + \zeta^{2}} \gg \sigma_{i}, \mu_{0}$), the weakly excited cavity supermodes are adiabatically eliminated from the dynamics.
- Effective Hamiltonian Tailoring: This process results in the generalized LMG Hamiltonian ($H_{\text{LMG}}$), which is tuned to desired forms (Isotropic, One-Axis Twisting, or Two-Axis Counter-Twisting) by adjusting detunings ($\Delta_{i}$), Rabi frequencies ($\Omega_{i}$), and coupling coefficients ($g_{k}$).
- Squeezing Protocol: Spin squeezed states are generated using the LMG Hamiltonian in the two-axis counter-twisting form, requiring maximized collective coupling strength ($N \sim 10^{12}$).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis quantum simulation protocol requires specialized diamond materials that 6CCVD is uniquely positioned to supply, ensuring reliable integration and high performance necessary for next-generation quantum technologies.
Applicable Materials
Section titled âApplicable Materialsâ| Research Requirement | 6CCVD Solution | Technical Justification & Value |
|---|---|---|
| High Spin Count ($N \sim 10^{12}$) | High Concentration SCD (Single Crystal Diamond) or PCD | We offer controlled growth for high NV concentration ($\sim 10^{15} \text{cm}^{-3}$) necessary to meet the critical collective coupling threshold. SCD provides superior structural uniformity. |
| Long Coherence Time ($T_{2}$ > 2 ms) | Isotopically Pure Optical Grade SCD (Low $^{13}\text{C}$ < 0.1%) | Isotopically pure diamond is essential for minimizing decoherence caused by nuclear spins, enabling the long $T_{2}$ needed to maintain spin squeezing fidelity. |
| System Integration | Custom Thin-Film SCD/PCD | Our ability to grow layers in the $0.1 \mu\text{m} - 500 \mu\text{m}$ range allows seamless integration with delicate CPW cavity architectures. |
| Surface Quality | Precision Polishing (Ra < 1 nm) | Ultra-smooth surfaces are required to minimize scatter losses and facilitate high-fidelity interfacing with superconducting circuits and applied microwave fields. |
Customization Potential for Hybrid Integration
Section titled âCustomization Potential for Hybrid IntegrationâThe implementation of hybrid quantum systems often involves unique geometry and interfacing constraints. 6CCVD offers the following customization services:
- Custom Dimensions: We provide diamond wafers and plates up to 125 mm (PCD) and offer precise laser cutting to match specific CPW cavity dimensions or required substrate sizes for chip integration.
- Advanced Metalization: Successful interfacing with superconducting circuits requires high-quality contacts. 6CCVD offers in-house metalization capabilities, including common stack materials like Ti/Pt/Au, Pt, Pd, W, and Cu, allowing engineers to design optimal ohmic contacts and resonant structure interfaces directly on the diamond substrate.
- Optimized Substrates: The paper suggests using diamond wafers as substrates. We can provide robust substrates up to 10 mm thick for mechanical stability in cryogenic environments, while ensuring the active NV layer maintains optimal quality.
Engineering Support
Section titled âEngineering SupportâDeveloping complex hybrid quantum simulators, especially those involving adiabatic elimination and fine Hamiltonian control, presents significant material challenges related to NV density control and coherence preservation.
6CCVDâs in-house PhD-level engineering team specializes in the material science of MPCVD diamond and NV engineering. We are prepared to assist researchers and technical engineers in material selection and growth recipe optimization specifically for projects targeting large-scale quantum simulation and spin squeezing protocols.
Call to Action
Section titled âCall to ActionâFor custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available) to support your cutting-edge quantum research.
View Original Abstract
We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG)\nmodel with nitrogen-vacancy (NV) center ensembles in diamond magnetically\ncoupled to superconducting coplanar waveguide cavities. With the assistance of\nexternal microwave driving fields, we show that the interaction of the NV spins\ncan be easily controlled, and several types of the LMG model can be realized by\ntuning the different parameters. Under the thermal dynamical limit, the\ndistinct non-equilibrium second order quantum phase transition of the spin\nensemble can be achieved at the critical point. Furthermore, we show that the\nspin squeezed state can be generated by tailoring the LMG Hamiltonian to\npossess the two-axis counter-twisting form in this hybrid quantum system.\n