Proposal for a quantum delayed-choice experiment with a spin-mechanical setup

At a Glance

Metadata	Details
Publication Date	2016-10-27
Journal	Physical review. A/Physical review, A
Authors	Fuli Li, Fuli Li
Institutions	Kavli Institute for Theoretical Sciences, Xi’an Jiaotong University
Citations	4
Analysis	Full AI Review Included

Technical Documentation & Analysis: Quantum Delayed-Choice Experiment using NV-Diamond

This document analyzes the requirements for implementing a quantum delayed-choice experiment using a spin-mechanical setup based on Nitrogen-Vacancy (NV) centers in diamond, as proposed in the attached research. It outlines how 6CCVD’s advanced MPCVD diamond materials and customization services are essential for the successful realization and extension of this macroscopic quantum mechanics protocol.

Executive Summary

The proposed research leverages the unique properties of the Nitrogen-Vacancy (NV) center in diamond, coupled to a mechanical resonator, to perform fundamental tests of quantum mechanics on a macroscopic scale. Successful implementation hinges entirely on the quality and precise engineering of the diamond material.

Core Application: Implementation of a quantum delayed-choice experiment using a Ramsey interferometer in a hybrid spin-mechanical system.
Material Requirement: Ultra-high purity, low-strain Single Crystal Diamond (SCD) is mandatory to ensure long spin coherence times (T₂) necessary for the 10 µs process window.
Key Mechanism: Dispersive coupling between the NV spin and the mechanical resonator enables selective spin rotations conditional on the resonator’s number state.
Performance Constraint: The total experimental time (approx. 10 µs) must be significantly shorter than the spin dephasing time ($\gamma_s$) and mechanical dissipation time ($\gamma_m$).
6CCVD Value Proposition: We provide the necessary foundation material—high-quality, isotopically engineered SCD plates—and offer custom fabrication (laser cutting, polishing) required for creating high-Q nanomechanical resonators.
Scalability: 6CCVD capabilities support the development of integrated quantum devices, offering custom metalization (Au, Pt, Ti) for microwave control structures.

Technical Specifications

The following parameters and constraints are critical for the feasibility of the proposed spin-mechanical quantum experiment, extracted directly from the numerical simulations and experimental considerations (Section III).

Parameter	Value	Unit	Context
NV Center Zero-Field Splitting (D)	2π * 2.87	GHz	Ground state transition frequency
Dispersive Coupling Strength ($\chi$)	100	kHz	$\chi/2\pi$ (Required for selective drive)
Second Rabi Frequency ($\Omega_2$)	10	kHz	$\Omega_2/2\pi$ (Conditional $\pi/2$ pulse)
First Rabi Frequency ($\Omega_1$)	500	kHz	$\Omega_1/2\pi$ (Initial $\pi/2$ pulse)
Detuning ($\Delta$)	1	MHz	$\Delta/2\pi$ (Used for phase tuning)
Total Process Time	10	µs	Required time to complete Ramsey sequence
Required Visibility (V)	0.84 (Simulated)	N/A	Achieved with initial state $\vert g, 1 \rangle$
Mechanical Resonator Q-Factor	> 1 Million	N/A	Required for low mechanical dissipation
Spin Dephasing Rate ($\gamma_s$)	0.1 $\Omega_2$	N/A	Constraint for successful operation

Key Methodologies

The experiment relies on a temporally based double-pulse Ramsey interferometer sequence, where the mechanical resonator coherently controls the second spin rotation.

Initial Spin Preparation: The NV spin is prepared in the ground state ($\vert g \rangle$).
First $\pi/2$ Pulse (R$_{1\pi/2}$): A microwave pulse with Rabi frequency $\Omega_1(t)$ is applied, rotating the spin into a superposition state: $\vert \psi_p \rangle = \frac{1}{\sqrt{2}} (\vert g \rangle + i e^{-i\phi} \vert e \rangle)$.
Quantum Phase Tuning: The spin is subjected to a magnetic field pulse for time $T$, shifting the spin transition frequency by a variable detuning $\Delta$, thereby tuning the phase $\phi = \Delta T$.
Dispersive Coupling Activation: The dispersive coupling ($\chi$) between the NV spin and the mechanical resonator is turned ON.
Conditional Second $\pi/2$ Pulse (R$_{2\pi/2}$): A second microwave pulse with Rabi frequency $\Omega_2(t)$ is applied, tuned to the specific resonance frequency ($\omega_0 + n_0 \chi$) corresponding to the selected number state ($\vert n_0 \rangle$).
- Condition: This rotation only occurs if the resonator is in state $\vert n_0 \rangle$. If the resonator is in state $\vert 0 \rangle$, the rotation is suppressed, acting as a quantum beam splitter control.
- Constraint: $\Omega_2$ must be much smaller than the dispersive coupling strength $\chi$ ($\Omega_2 \ll \chi$) to ensure selectivity.
Final Measurement: The probability of detecting the NV spin in the excited state ($\vert e \rangle$) is measured, revealing the interference pattern (or lack thereof), which is controlled by the mechanical resonator’s superposition state.

6CCVD Solutions & Capabilities

The successful realization of this advanced spin-mechanical protocol requires diamond material of the highest quality, coupled with precise micro-fabrication capabilities. 6CCVD is uniquely positioned to supply the foundational materials and engineering services necessary for this research.

Applicable Materials

The core of this experiment is the NV center’s long coherence time, which necessitates ultra-low impurity levels and isotopic control.

Material Requirement	6CCVD Solution	Technical Specification
High Spin Coherence	Optical Grade Single Crystal Diamond (SCD)	Ultra-low [N] & [B] impurities (PPM level). Essential for maximizing $T_2$.
Isotopic Purity	Isotopically Engineered SCD	Available with controlled ¹²C enrichment (e.g., > 99.99%) to suppress nuclear spin bath decoherence [49].
Mechanical Resonator	Custom Thin SCD Wafers	SCD plates available from 0.1 µm to 500 µm thickness, ideal for fabricating low-mass, high-Q nanomechanical cantilevers.
Robust Substrate	SCD Substrates	Available up to 10 mm thickness for robust mounting and thermal management of the quantum device.

Customization Potential

6CCVD’s in-house engineering and fabrication capabilities directly address the structural and electrical requirements of hybrid spin-mechanical systems.

Custom Dimensions and Shaping: The creation of nanomechanical resonators (cantilevers/oscillators) requires precise structuring of the diamond plate. 6CCVD offers custom laser cutting and shaping services for SCD plates up to 125 mm (PCD) and large SCD areas, ensuring the starting material geometry is optimized for subsequent etching processes.
Surface Quality: Achieving high-Q mechanical resonance and minimizing surface-related spin decoherence requires pristine surfaces. 6CCVD guarantees ultra-low roughness polishing for SCD, achieving Ra < 1 nm.
Integrated Microwave Control: The Ramsey sequence relies on external microwave fields. If the design requires on-chip waveguides or contacts for magnetic gradient control [24], 6CCVD offers internal metalization services including:
- Metals: Au, Pt, Pd, Ti, W, Cu.
- Process: Custom layer deposition and patterning to integrate control electronics directly onto the diamond substrate.

Engineering Support

The complexity of hybrid quantum systems demands specialized material expertise.

Material Selection for Quantum Projects: 6CCVD’s in-house PhD team specializes in the material science of diamond for quantum applications. We assist researchers in selecting the optimal SCD grade (e.g., specific isotopic purity, nitrogen concentration, and crystal orientation) required to replicate or extend this Spin-Mechanical Delayed-Choice Experiment.
Strain Management: The dispersive coupling mechanism is sensitive to strain [30-35]. We provide SCD materials with certified low internal strain, crucial for maintaining the precise energy level structure of the NV center.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We describe an experimentally feasible protocol for performing a variant of the quantum delayed-choice experiment with massive objects. In this scheme, a single nitrogen-vacancy (NV) center in diamond driven by microwave fields is dispersively coupled to a massive mechanical resonator. A double-pulse Ramsey interferometer can be implemented with the spin-mechanical setup, where the second Ramsey microwave pulse drives the spin conditioned on the number states of the resonator. The probability for finding the NV center in definite spin states exhibits interference fringes when the mechanical resonator is prepared in a specific number state. On the other hand, the interference is destroyed if the mechanical resonator stays in some other number states. The wavelike and particlelike behavior of the NV spin can be superposed by preparing the mechanical resonator in a superposition of two distinct number states. Thus a quantum version of Wheeler’s delayed-choice experiment could be implemented, allowing of fundamental tests of quantum mechanics on a macroscopic scale.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.94.042130

References

1984 - Quantum Theory and Measurement
1997 - Quantum Optics [Crossref]
1978 - Mathematical Foundations of Quantum Mechanics
1984 - Quantum Theory and Measurement
2009 - Compendium of Quantum Physics