Generation of macroscopic Schrödinger cat state in diamond mechanical resonator
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2016-11-23 |
| Journal | Scientific Reports |
| Authors | Qizhe Hou, Wanli Yang, Changyong Chen, Zhang‐qi Yin |
| Institutions | Nanjing University, Tsinghua University |
| Citations | 16 |
| Analysis | Full AI Review Included |
Technical Analysis and Documentation for 6CCVD
Section titled “Technical Analysis and Documentation for 6CCVD”Reference Paper: Generation of macroscopic Schrödinger cat state in diamond mechanical resonator (Sci. Rep. 6, 37542, 2016)
Executive Summary
Section titled “Executive Summary”This research demonstrates a novel theoretical scheme for generating macroscopic Schrödinger Cat States (SCS) within a Diamond Mechanical Resonator (DMR) incorporating a single Nitrogen-Vacancy (NV) center. This platform represents a critical step toward high-coherence, solid-state quantum computing nodes.
- Core Mechanism: Achieves coherent spin-phonon interaction via a dynamical strain-mediated coupling, where the DMR lattice vibration creates a strain field directly coupling the NV center’s electron spin transitions ($|+1\rangle \leftrightarrow |-1\rangle$).
- State Generation: The SCS is created by combining the quantized mechanical strain field with a pair of external microwave fields, forming a cyclic A-type transition structure that allows for selective population transfer.
- Material Imperative: The scheme relies fundamentally on the long coherence times (T₂ up to 10 ms at low temperature) and highly stable spin properties inherent only to high-purity Single Crystal Diamond (SCD) containing isolated NV centers.
- Feasibility & Performance: The proposal utilizes currently achievable experimental parameters, including high-quality factor DMRs ($Q=10^5$ to $10^6$) and mechanical damping rates ($\kappa$ < 1 kHz).
- QIP Application: This SCS generation method is identified as a significant route for building distributed Quantum Information Processing (QIP) architectures using DMR units as scalable quantum nodes.
Technical Specifications
Section titled “Technical Specifications”The following hard parameters and physical properties, extracted from the analysis, define the operational requirements and material capabilities necessary for this quantum mechanical system.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Center Ground State Splitting ($D_{gs}/2\pi$) | 2.87 | GHz | Zero-field splitting between $ |
| Electron Spin Coherence Time ($T_2$) | 1 | ms | Standard room-temperature coherence for NV center. |
| Low-Temp Spin Dephasing Time ($T_2$) | 10 | ms | Achievable T₂ at low temperature. |
| Spin Relaxation Time ($T_1$) | 100 | seconds | Achievable T₁ at low temperature. |
| DMR Dimensions (Scale) | $\sim$µm | N/A | Assumed scale for the cantilever beam. |
| DMR Vibrational Frequency ($\omega_m$) | 0.1 to 10 | GHz | Required frequency range for mechanical modes. |
| Spin-Phonon Coupling Strength ($\lambda$) | Several | kHz | Estimated coupling strength between NV spin and DMR. |
| Required DMR Quality Factor ($Q$) | $10^5$ to $10^6$ | N/A | Required Q for minimizing mechanical damping. |
| Mechanical Damping Rate ($\kappa$) | < 1 | kHz | Required for high-fidelity SCS generation ($\kappa = \omega_m/Q$). |
| Simulation Dissipative Factor ($\kappa$) | 0.02, 0.05 | N/A | Used in simulations to model decoherence effects. |
Key Methodologies
Section titled “Key Methodologies”The scheme proposes a sophisticated method combining material engineering and microwave control to manipulate quantum states in the DMR.
- Monolithic Hybrid Device Construction: Fabrication of a Single Crystal Diamond (SCD) cantilever (DMR) with embedded NV centers, ensuring the NV center is positioned to maximize interaction with the local strain field.
- Strain Field Quantization: The DMR is modeled as a harmonic oscillator. Small beam displacements result in the perpendicular strain field ($E_x, E_y$) being quantized, leading to a spin-phonon coupling strength $\lambda$ connecting the $|+1\rangle \leftrightarrow |-1\rangle$ transition.
- Cyclic $\Lambda$-Type Transition Construction: Two external classical microwave fields ($\omega_1, \omega_2$) are applied to induce transitions between $|0\rangle \leftrightarrow |\pm 1\rangle$, completing a cyclic three-level transition structure, where $\omega_1 - \omega_2 = \omega_m$ (DMR frequency).
- Unitary Transformation and Effective Hamiltonian: The system Hamiltonian is transformed using a unitary transformation to create dressed states $|\pm\rangle$, resulting in an effective $\Lambda$-type structure coupled to two displaced quantized phonon fields ($p=a+k_1, q=a-k_2$).
- Adiabatic Elimination (FNT): In the large detuning limit ($\Delta_{+} \gg \lambda_{1(2)}$), the upper state ($|+1\rangle$) is adiabatically eliminated using the Fröhlich-Nakajima transformation (FNT) method, yielding an effective Hamiltonian that describes a forced harmonic oscillator, crucial for generating the SCS.
- Quantum State Verification: The generated mechanical SCS is characterized by calculating the phase-space quasiprobability distributions, particularly the Wigner function, where the presence of interference fringes and negative values confirms nonclassicality.
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”6CCVD provides the specialized, high-coherence diamond materials and precision engineering services essential to replicate and advance this ground-breaking quantum research.
Applicable Materials
Section titled “Applicable Materials”The foundation of NV-center based quantum systems is the defect stability and long coherence time, which requires ultra-high purity diamond.
- Optimal Material: Optical Grade Single Crystal Diamond (SCD) Substrates. Replicating this research requires MPCVD-grown SCD wafers with extremely low nitrogen concentration (PPM levels) to ensure isolated NV centers and minimal decoherence.
- Thickness Control: 6CCVD offers custom SCD thickness from $0.1\text{ µm}$ to $500\text{ µm}$. This precision is critical for fabricating cantilever DMRs where thickness ($h$) directly influences the vibrational frequency ($\omega_m$) and coupling strength ($\lambda$) according to Euler-Bernoulli beam theory.
- PCD for Ancillary Systems: For bulk components or large-area heat dissipation layers associated with cryogenic systems, 6CCVD offers high-quality Polycrystalline Diamond (PCD) wafers up to $125\text{ mm}$ in diameter.
Customization Potential
Section titled “Customization Potential”The experimental feasibility hinges on fabricating DMRs with precise geometry and interfaces. 6CCVD’s engineering capabilities directly meet these complex requirements.
| Paper Requirement | 6CCVD Precision Service | Technical Relevance |
|---|---|---|
| Micro-Scale DMR Fabrication | Custom Dimensions & Laser Cutting. We provide precision processing to realize the required micro-scale cantilever geometries (L $\gg$ w, h, on the $\mu$m scale). | Ensures optimal mechanical mode frequency ($\omega_m$: 0.1-10 GHz). |
| Integration of Transducers | Custom Metalization Capabilities (Au, Pt, Ti, Cu). NV control requires external microwave fields. We deposit high-fidelity metal layers (e.g., Ti/Pt/Au stack) required for on-chip microwave antennas or coupling to superconducting circuits. | Facilitates required Rabi driving fields ($G_1, G_2$) and integration into hybrid quantum devices (e.g., coplanar waveguide cavities). |
| Low-Loss Surfaces | Ultra-Smooth Polishing (Ra < 1 nm for SCD). | Critical for maintaining the high-quality factors ($Q$) necessary to achieve low mechanical damping ($\kappa < 1 \text{ kHz}$) and minimize decoherence. |
| Initial State Preparation | Boron-Doped Diamond (BDD). Our BDD materials can be used for conductive electrodes or gate structures if future schemes require effective local electric field control via piezoelectric films. | Enables integration of piezo-electric layers ($^{11-17}$) or other external field controls for strain modulation. |
Engineering Support
Section titled “Engineering Support”Generating complex macroscopic quantum states, such as the SCS, demands collaboration between material science and quantum physics.
6CCVD’s in-house PhD engineering team possesses expertise in material selection, CVD growth optimization for NV creation, and surface preparation specifically tailored for quantum applications. We can assist researchers in optimizing material specifications (e.g., orientation, nitrogen concentration, thickness) required for high-fidelity NV center control and high-Q mechanical resonator design for similar quantum information processing (QIP) projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract We propose a scheme to generate macroscopic Schrödinger cat state (SCS) in diamond mechanical resonator (DMR) via the dynamical strain-mediated coupling mechanism. In our model, the direct coupling between the nitrogen-vacancy (NV) center and lattice strain field enables coherent spin-phonon interactions in the quantum regime. Based on a cyclic Δ-type transition structure of the NV center constructed by combining the quantized mechanical strain field and a pair of external microwave fields, the populations of the different energy levels can be selectively transferred by controlling microwave fields, and the SCS can be created by adjusting the controllable parameters of the system. Furthermore, we demonstrate the nonclassicality of the mechanical SCS both in non-dissipative case and dissipative case. The experimental feasibility and challenge are justified using currently available technology.