Spin-Controlled Quantum Interference of Levitated Nanorotors
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2022-08-25 |
| Journal | Physical Review Letters |
| Authors | Cosimo C. Rusconi, M. Perdriat, G. Hétet, Oriol Romero‐Isart, Benjamin A. Stickler |
| Institutions | Centre National de la Recherche Scientifique, Max Planck Institute of Quantum Optics |
| Citations | 21 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Ultra-Strong Coupling (USC) Achieved: The research theoretically demonstrates achieving the single-spin USC regime between a Nitrogen-Vacancy (NV) center spin and the libration (rotational oscillation) of an electrically levitated nanodiamond.
- Non-Gaussian State Generation: This large spin-libration coupling is exploited to prepare the nanodiamond in a non-Gaussian quantum superposition of its orientation, a critical step for observing quantum interference in massive systems.
- System Architecture: The platform consists of a homogeneously charged prolate spheroidal nanodiamond (major semiaxis a = 100 nm) levitated in a ring Paul trap (AC frequency 5 MHz) and hosting a single NV center.
- Control Mechanism: Microwave driving of the NV spin, combined with precise alignment of an external magnetic field (B0 ~ 102.4 mT), effectively creates a spin-dependent potential that controls the mechanical libration frequencies.
- Interference Protocol: A three-step microwave pulse sequence (π/2 - τ - π - τ - π/2) is proposed to generate, evolve, and read out the quantum superposition, relying on the rephasing of the spin-dependent mechanical states.
- Feasibility Requirements: Experimental implementation requires high NV spin coherence (T2 ~ 0.5 ms) and cooling the rotational motion to temperatures of a few milli-Kelvin or lower to ensure high visibility of the interference signal.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Particle Geometry | Prolate Spheroid | N/A | Model shape for nanodiamond |
| Major Semiaxis (a) | 100 | nm | Particle size used for simulations |
| Semiaxis Ratio (a/b) | 5 | N/A | Aspect ratio of the spheroid |
| Mass Density (ρM) | 3.5 x 103 | Kg/m3 | Typical diamond density |
| AC Voltage Frequency (ω0/2π) | 5 | MHz | Paul trap driving frequency |
| Voltage Ratio (Udc/Uac) | 5 x 10-3 | N/A | Ratio of DC to AC trap voltages |
| Asymmetry Parameter (δ) | 0.1 | N/A | Characterizes deviation from cylindrical trap symmetry |
| Critical Magnetic Field (B0) | ~102.4 | mT | Field required to reach ground state level anti-crossing (USC regime) |
| NV Zero-Field Splitting (DNV) | ~2.87 | GHz | Intrinsic spin triplet splitting |
| NV Gyromagnetic Ratio (γNV) | 1.76 x 1011 | rad/Ts | Used for calculating Larmor precession |
| Required Spin Coherence (T2) | 0.5 | ms | Value used for high-visibility interference simulations |
| Target Initial Temperature | Few milli-Kelvin or lower | K | Required for high visibility of rephasing peaks |
| USC Condition | gγ >> ωγ and gβ >> ωβ | N/A | Coupling rates significantly exceed libration frequencies |
Key Methodologies
Section titled “Key Methodologies”- System Modeling and Hamiltonian Derivation: The system dynamics are described by a Hamiltonian that includes rotational kinetic energy, NV spin terms (zero-field splitting DNV and Larmor precession), and the time-dependent Paul trap potential.
- Secular Approximation: The full dynamics are simplified by separating the fast micromotion from the slow macromotion (secular dynamics) in the Paul trap, yielding a time-independent secular Hamiltonian (Hsec).
- Linear and Two-Level Approximation: Hsec is expanded up to second order in the libration degrees of freedom (small oscillations about equilibrium) and projected onto the NV spin qubit subspace ({|0>, |-1>}) to obtain the effective qubit-oscillator Hamiltonian.
- Achieving Ultra-Strong Coupling (USC): The external magnetic field (B0) is precisely tuned to align the spin quantization axis orthogonal to the particle symmetry axis, maximizing the spin-libration coupling rates (gγ, gβ) such that they exceed the characteristic frequencies of the libration modes (ωγ, ωβ).
- Quantum Interference Protocol (Three-Step Pulse Sequence):
- Step (i) Preparation: A π/2-microwave pulse prepares the NV spin in a superposition, creating an entangled state where the mechanical oscillator is in a spin-dependent squeezed thermal state.
- Step (ii) Evolution and Reversal: The system evolves for time τ under the spin-dependent potential, followed by a π-microwave pulse that swaps the spin states, effectively reversing the roles of the attractive and repulsive potentials.
- Step (iii) Readout: A final π/2-microwave pulse is applied, and the spin state is measured. Constructive interference (rephasing) of the two rotational branches occurs at specific times (e.g., τ = π/ῶγ), confirming the creation and coherence of the orientation superposition.
Commercial Applications
Section titled “Commercial Applications”- Quantum Sensing and Metrology: The ability to create mechanical squeezed states in a massive object is highly valuable for enhancing sensitivity in the detection of extremely weak forces (e.g., inertial forces, gravity gradients) beyond the standard quantum limit.
- Fundamental Quantum Research: Provides a scalable platform for testing quantum mechanics and decoherence models in the macroscopic regime, specifically addressing the quantum-classical transition for rotational degrees of freedom.
- Solid-State Qubit Integration: Demonstrates a robust method for coupling internal solid-state qubits (NV centers) to massive mechanical resonators, a key requirement for hybrid quantum technologies and quantum memory applications.
- High-Precision Gyroscopy: The spin-rotational coupling mechanism offers new avenues for developing ultra-sensitive gyroscopes based on levitated nanorotors, potentially exceeding current classical limits.
- Cryogenic NV Systems: The protocol relies on high-coherence NV centers, driving continued engineering efforts in producing isotopically purified nanodiamonds and developing cryogenic control systems for quantum applications.
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 particle’s 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.