Spin-Controlled Quantum Interference of Levitated Nanorotors
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-08-25 |
| Journal | Physical Review Letters |
| Authors | Cosimo C. Rusconi, M. Perdriat, G. HĂ©tet, Oriol RomeroâIsart, Benjamin A. Stickler |
| Institutions | Université Paris Sciences et Lettres, Sorbonne Université |
| Citations | 21 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Spin-Controlled Quantum Interference of Levitated Nanorotors
Section titled âTechnical Documentation & Analysis: Spin-Controlled Quantum Interference of Levitated NanorotorsâReference: Rusconi et al., arXiv:2203.11717v2 [quant-ph] (2022)
Executive Summary
Section titled âExecutive SummaryâThis research paper proposes a theoretical protocol to achieve and observe quantum superposition states in the orientation (libration) of a massive, levitated nanodiamond. The core value proposition relies on leveraging the unique properties of diamond-based quantum systems:
- Ultra-Strong Coupling (USC): Demonstrates the feasibility of reaching the single-spin USC regime, where the coupling rate between a single embedded Nitrogen-Vacancy (NV) spin and the diamondâs rotational motion exceeds the characteristic frequencies of both systems.
- Non-Gaussian State Preparation: The large spin-libration coupling provides the necessary non-linearity to prepare non-Gaussian quantum superposition states of the particleâs orientation.
- Material Requirement: Successful implementation requires high-quality, isotopically purified nanodiamonds to ensure long spin coherence times ($T_2 \sim 0.5 \text{ ms}$) necessary for the interference protocol duration ($2\tau$).
- Experimental Feasibility: The protocol is argued to be realistically implementable with minor modifications to existing Paul trap and NV control setups.
- Application Potential: This work establishes levitated nanodiamonds as a highly attractive platform for massive superposition experiments and the detection of weak forces using mechanical squeezed states.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points and critical parameters were extracted from the theoretical model and experimental requirements outlined in the paper:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Particle Geometry | Prolate Spheroid | N/A | Modelled shape for levitation |
| Major Semiaxis Length ($a$) | 100 | nm | Model dimensions |
| Aspect Ratio ($a/b$) | 5 | N/A | $b = a/5$ |
| Mass Density ($\rho_M$) | 3.5 x 103 | Kg/m3 | Standard diamond density |
| NV Zero-Field Splitting ($D_{NV}/2\pi$) | 2.87 | GHz | Characteristic NV property |
| AC Voltage Frequency ($\omega_0/2\pi$) | 5 | MHz | Paul trap driving frequency |
| Critical Magnetic Field ($B_0$) | 102.4 | mT | Ground state level anti-crossing (USC regime) |
| Required Spin Coherence Time ($T_2$) | 0.5 | ms | Minimum required for high visibility interference |
| Required Initial Temperature | Few | mK | Necessary for low thermal occupation ($n_{\gamma}$) and clear rephasing detection |
| USC Condition (Example) | $g_{\gamma} \gg \omega_{\gamma}$ and $g_{\beta} \gg \omega_{\beta}$ | N/A | Coupling rates must exceed characteristic frequencies |
Key Methodologies
Section titled âKey MethodologiesâThe proposed protocol relies on precise material engineering, electromagnetic control, and a three-step quantum interference sequence:
- Material Selection and Geometry: Utilize a homogeneously charged nanodiamond (prolate spheroid, $a=100 \text{ nm}$) containing a single NV center. The NV spin quantization axis must be aligned orthogonal to the particleâs symmetry axis.
- Levitation and Confinement: Electrically levitate the particle in a ring Paul trap, which provides a confining potential for both center-of-mass and rotational (libration) dynamics.
- Magnetic Field Tuning: Apply a static external magnetic field ($B_0$) precisely tuned to achieve the desired coupling regime:
- USC Regime: Tune $B_0$ near the ground state level anti-crossing ($B_0 \approx 102.4 \text{ mT}$) to maximize spin-libration coupling ($g_{\nu} \gg \omega_{\nu}$).
- Dispersive Regime: Tune $B_0$ such that the qubit splitting $\Delta$ is large ($|\Delta| \gg g_{\gamma}, g_{\beta}$), enabling spin-dependent shifts of the oscillator frequencies.
- Interference Protocol (Preparation, Evolution, Measurement):
- Preparation: Use a $\pi/2$-microwave pulse to prepare the NV spin in a superposition state.
- Evolution: Allow the entangled spin-oscillator system to evolve for time $\tau$, generating a squeezed thermal state in the oscillator branch.
- Reversal & Rephasing: Apply a $\pi$-microwave pulse to reverse the spin state, followed by a second evolution time $\tau$. The total duration $2\tau$ is chosen to allow the two oscillator states to overlap perfectly (rephasing).
- Readout: Apply a final $\pi/2$-microwave pulse and perform a spin measurement to observe the probability of rephasing, confirming the coherent superposition of the particleâs orientation.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & Capabilitiesâ6CCVD is uniquely positioned to supply the high-specification MPCVD diamond materials required to replicate and advance this cutting-edge quantum levitation research. The feasibility of this protocol hinges on the quality and purity of the diamond substrate, particularly the NV center coherence time ($T_2$).
Applicable Materials
Section titled âApplicable Materialsâ| Research Requirement | 6CCVD Material Solution | Technical Justification |
|---|---|---|
| Long Spin Coherence ($T_2 \sim 0.5 \text{ ms}$) | Isotopically Purified SCD | Required for the protocol duration ($2\tau$). Achieved by growing Single Crystal Diamond (SCD) with ultra-low nitrogen and controlled isotopic purity (low $^{13}\text{C}$ concentration). |
| Single NV Center Host | Optical Grade SCD | SCD provides the necessary crystalline perfection and low defect density for reliable creation and control of isolated, high-quality NV centers. |
| Nanostructure Fabrication Source | Custom Thickness SCD/PCD Wafers | While the final particle is $100 \text{ nm}$, the starting material must be high-quality MPCVD diamond. We offer SCD and PCD substrates with precise thickness control (down to $0.1 \text{ ”m}$) for subsequent top-down fabrication (e.g., focused ion beam milling) into spheroids. |
| Future Integrated Systems | Boron-Doped Diamond (BDD) | For future experiments requiring integrated electrodes or conductive elements within the trap, our BDD material offers tunable conductivity while maintaining diamondâs structural integrity. |
Customization Potential
Section titled âCustomization PotentialâThe successful implementation of this protocol, and its extension into hybrid quantum systems, relies on precise material engineering and integration capabilities:
- Custom Dimensions and Thickness: 6CCVD supplies SCD and PCD plates/wafers up to $125 \text{ mm}$ in diameter, with thickness control ranging from $0.1 \text{ ”m}$ to $500 \text{ ”m}$. This allows researchers to optimize the source material volume and cost for nanostructure fabrication.
- Ultra-Smooth Polishing: We provide industry-leading polishing services (Ra < $1 \text{ nm}$ for SCD, Ra < $5 \text{ nm}$ for inch-size PCD), ensuring minimal surface defects that could interfere with subsequent nanostructure etching or levitation stability.
- Custom Metalization Services: For hybrid trap designs or on-chip integration, 6CCVD offers in-house deposition of critical metals, including Au, Pt, Pd, Ti, W, and Cu, directly onto the diamond substrate.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house team of PhD material scientists and quantum engineers specializes in optimizing MPCVD diamond growth recipes for specific quantum applications. We offer consultation services to assist researchers in selecting the optimal material specifications (e.g., isotopic purity, nitrogen concentration, and thickness) required for similar levitated quantum mechanics projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particleâs three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology.