Arbitrary control of entanglement between two nitrogen-vacancy-center ensembles coupling to a superconducting-circuit qubit
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2018-01-24 |
| Journal | Physical review. A/Physical review, A |
| Authors | Wan-Jun Su, ZhenâBiao Yang, ZhiâRong Zhong |
| Institutions | Fuzhou University, University of Calgary |
| Citations | 14 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Arbitrary Control of Entanglement in NV Ensembles
Section titled âTechnical Documentation & Analysis: Arbitrary Control of Entanglement in NV EnsemblesâExecutive Summary
Section titled âExecutive SummaryâThis research demonstrates a highly efficient, scalable scheme for engineering arbitrary entangled quantum states using collective Nitrogen-Vacancy (NV) center ensembles coupled to a superconducting transmon qubit.
- Core Achievement: Successful realization of a Jaynes-Cummings (J-C) model using collective NV ensemble spin modes (acting as bosonic modes) coupled via a superconducting circuit microwave (SCM) cavity.
- State Generation: The scheme is validated for the production of complex quantum states, including arbitrary N-particle entangled states, NOON states, multi-dimensional entangled states (qudits, D $\ge$ 3), and entangled coherent states.
- Mechanism & Stability: Operation utilizes a virtual-photon process in the bad-cavity limit. This critical technique ensures the system is highly insensitive to cavity decay ($\kappa$) and spin dephasing ($\gamma_s$).
- Performance: Numerical simulations show high fidelity for state preparation, achieving $\ge 0.995$ for optimized parameters ($\Delta/G = 200$).
- Scalability: The architecture provides a practical, scalable tool for large-scale, one-way quantum computation and is compatible with current solid-state quantum technology.
- Speed: The total preparation time for an arbitrary entangled state is approximately 450 ns, significantly shorter than the coherence time of current superconducting qubits ($10 - 100$ ”s).
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters define the operational regime and performance metrics for the hybrid NV-Qubit system described:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| NVE Ensemble Size (N) | $\sim 10^{12}$ | Spins | Negatively charged NV centers in a diamond crystal. |
| NV Zero-Field Splitting | 2.88 | GHz | Separation between $\mid 0\rangle$ and $\mid \pm 1\rangle$ ground states (spin triplet $^3\text{A}$). |
| SCM Cavity Gap ($d$) | $\sim 10$ | ”m | Required distance between diamond crystal and SCM cavity structure. |
| SCM Cavity Length ($L$) | $\sim 1$ | cm | Dimension of the superconducting quantum bus. |
| Collective Spin Coupling ($\sqrt{N} g_m$) | $2\pi \times 10$ | MHz | Experimentally chosen coupling strength. |
| Microwave Detuning ($\Delta$) | $\sim 2\pi \times 100$ | MHz | Detuning chosen for dispersive interaction regime ($\Delta/G \ge 100$). |
| Effective Coupling ($G$) | $\sim 2\pi \times 1$ | MHz | Derived effective coupling ($G = \sqrt{N} g_m g_c / \Delta$). |
| Cavity Decay Rate ($\kappa$) | $\sim 2\pi \times 10$ | kHz | Decay rate of the microwave superconducting cavity. |
| Collective Spin Decay Rate ($\gamma_s$) | $\sim 2\pi \times 10$ | kHz | Decay rate of the NVE collective spin mode. |
| Arbitrary State Preparation Time | 450 | ns | Time required for generating entangled states (e.g., NOON state). |
| Optimal Fidelity | $\ge 0.995$ | N/A | Achieved fidelity when scaled detuning $\Delta/G = 200$. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on a precise hybrid architecture and dynamic control sequences to achieve entanglement:
- Physical Setup: Two distant NVEs (diamond crystals) are magnetically coupled to a Superconducting Circuit Microwave (SCM) cavity (quantum bus). A tunable Transmon qubit is electrostatically coupled to the same cavity.
- Bosonic Mode Approximation: In the low-excitation limit, the collective excitations of the $N \sim 10^{12}$ NV spins are treated as effective bosonic modes, leading to an effective J-C model Hamiltonian.
- Virtual Photon Process: The system operates in the bad-cavity limit ($G \ll \Delta$), ensuring the cavity field remains in the vacuum state, thereby making the operation insensitive to cavity decay ($\kappa$).
- Selective Manipulation via Shift Pulses: Qubit frequency $\omega_z(t)$ is dynamically controlled by applying driving microwave (shift) pulses with adjustable amplitude $\Omega(t)$. This tunes the qubit into resonant coupling with one NVE while maintaining a large off-resonance detuning with the other NVE.
- State Synthesis: Arbitrary states (e.g., NOON states, multi-dimensional qudits) are produced by sequentially applying resonant interactions (qubit-NVE 1, then qubit rotation $R$, then qubit-NVE 2) based on transferring amplitude along specific paths in the Fock-state diagram (Fig. 4).
- Decoherence Mitigation: The low operation time (450 ns) relative to coherence times (up to 100 ”s) ensures high fidelity, even without detailed modeling of intrinsic defects like 13C spin bath or strain.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe efficient realization of this hybrid quantum architecture relies fundamentally on high-quality, ultra-precise diamond material. 6CCVD is uniquely positioned to supply the requisite components to replicate and extend this pioneering research.
Applicable Materials
Section titled âApplicable MaterialsâThe foundation of this experiment is the NV ensemble in the diamond host. 6CCVD specializes in the following MPCVD material grades suitable for QIP applications:
| Material Grade | Specification | Application Relevance |
|---|---|---|
| Optical Grade Single Crystal Diamond (SCD) | Ultra-low strain, high chemical purity, exceptional optical transparency. | Crucial for minimizing inhomogeneous broadening and maximizing the NV center collective spin coherence time ($T_2$). |
| Custom NV-Doped SCD | Controlled nitrogen concentration (for NV formation) and tailored annealing post-growth. | Necessary to achieve the high ensemble density ($N \sim 10^{12}$) required for the strong collective coupling ($\sqrt{N} g_m$). |
| High-Purity MPCVD Substrates | Thickness up to 10 mm. | Used as mechanical support or as the base diamond layer for subsequent high-quality epitaxy. |
Precision Engineering & Integration
Section titled âPrecision Engineering & IntegrationâThe experiment requires placing the NVE diamond crystal within a $\sim 10$ ”m gap above the SCM cavity, necessitating extreme dimensional and surface control.
- Ultra-Smooth Polishing: The close-proximity coupling dictates minimal surface roughness to maintain the narrow gap. 6CCVD offers Ra < 1 nm polishing for Single Crystal Diamond (SCD), providing the ultra-flat surfaces required for reproducible micro-scale positioning.
- Custom Dimensions & Thickness Control: The NVE crystal thickness and lateral dimensions must be precisely controlled for integration into the SCM cavity geometry ($d \sim 10$ ”m, $L \sim 1$ cm). 6CCVD provides custom diamond wafers/plates with thicknesses down to 0.1 ”m and custom laser cutting services for highly specific chip geometries.
- Hybrid System Metalization: Integration with superconducting circuits often requires specific contact pads and traces. 6CCVD offers in-house capabilities for the deposition of relevant metals, including: Au, Pt, Pd, Ti, W, and Cu, allowing researchers to integrate the diamond substrate directly into their circuit QED components.
- Scale and Uniformity: For future commercial or large-array scaling of the hybrid quantum processor, 6CCVD produces large-area PCD wafers up to 125 mm and maintains rigorous uniformity standards necessary for complex multi-NVE coupling schemes.
Engineering Support
Section titled âEngineering SupportâThis research highlights the necessity of fine-tuning material properties and integration strategies to achieve high-fidelity entangled states. 6CCVDâs in-house PhD team can provide expert consultation on:
- Material Selection: Guiding selection of appropriate crystal orientation, nitrogen concentration, and post-processing steps (e.g., annealing recipes) optimized for similar NVEs-Circuit Cavity Quantum Information Processing projects.
- Decoherence Mitigation: Advising on material specifications (e.g., isotopic purity, strain control) to maximize the NV center dephasing time ($T_2$) crucial for minimizing the negative impact of long evolution times required for higher $\Delta/G$ ratios.
- Custom Fabrication: Developing custom metallization layers and high-precision laser dicing plans required for complex micro-circuit integration.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We propose an effective scheme for realizing a Jaynes-Cummings (J-C) model with the collective nitrogen-vacancy center ensembles (NVE) bosonic modes in a hybrid system. Specifically, the controllable transmon qubit can alternatively interact with one of the two NVEs, which results in the production of $N$ particle entangled states. Arbitrary $N$ particle entangled states, NOON states, N-dimensional entangled states and entangled coherent states are demonstrated. Realistic imperfections and decoherence effects are analyzed via numerical simulation. Since no cavity photons or excited levels of the NV center are populated during the whole process, our scheme is insensitive to cavity decay and spontaneous emission of the NVE. The idea provides a scalable way to realize NVEs-circuit cavity quantum information processing with current technology.