Observation of a Quantum Phase from Classical Rotation of a Single Spin
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-01-17 |
| Journal | Physical Review Letters |
| Authors | A. A. Wood, Lloyd C. L. Hollenberg, R. E. Scholten, A. Martin |
| Institutions | The University of Melbourne, Centre for Quantum Computation and Communication Technology |
| Citations | 26 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research reports the first direct measurement of a quantum phase shift in a single electron spin (Nitrogen-Vacancy center) caused purely by classical physical rotation, without relying on magnetic field transduction.
- Core Achievement: Observation of a rotationally-induced phase shift (δφ) in a single NV electron spin located within a diamond rotating at 200,000 rpm (3.33 kHz).
- Measurement Technique: Spin-echo interferometry was used to measure the phase difference between a microwave (MW) driving field and the rotating NV qubit system.
- Key Innovation (Nonlinearity): The phase shift accumulates nonlinearly in time due to the effective rotation of the MW field in the qubit’s rotating frame. This nonlinearity is crucial as it allows the use of spin-echo sequences to decouple the signal from linear phase noise (e.g., static magnetic fields or temperature drifts).
- System Robustness: The experiment was conducted at room temperature, leveraging the long coherence times (T2 ≈ 1 ms) and robust nature of the NV center in a 99.99% 12C diamond substrate.
- Fundamental Validation: The results demonstrate the fundamental connection between spin, physical rotation, and quantum phase, validating theoretical proposals for rotation sensing.
- Engineering Relevance: The methodology is directly applicable to developing high-precision, diamond-based quantum rotation sensors (gyroscopes) and studying the dynamics of nanoparticles.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Isotope Purity | 99.99% | 12C | Host substrate material. |
| Rotation Frequency (ωrot) | 3.33 | kHz | Physical rotation rate of the diamond motor. |
| Rotation Speed | 200,000 | rpm | Equivalent rotation speed. |
| NV Center Location | ~3 | µm | Distance from the rotation axis. |
| NV Axis Tilt (θNV) | 54.7 | ° | Angle relative to the rotation axis (z). |
| Zero-Field Splitting (Dzfs) | 2.870 | GHz | Energy splitting of the NV ground state. |
| Microwave Driving Frequency | 2.846 | GHz | Used for ms = 0 ↔ ms = -1 transition. |
| MW Tilt Angle Range (θmw) | 28 to 67 | ° | Angle varied by translating the MW wire position. |
| Rabi Frequency (Ω) Variation | 1 to 6 | MHz | Maximum variation across a single spin-echo sequence. |
| Spin-Echo Interrogation Time (τ) | 100 | µs | Free evolution period duration (equivalent to 120° rotation). |
| Typical Coherence Time (T2) | ~1 | ms | Coherence time of the single NV center. |
| Readout Cycles | > 105 | cycles | Number of repetitions over 2-3 minutes duration. |
Key Methodologies
Section titled “Key Methodologies”The experiment utilized a highly synchronized, pulsed quantum control sequence applied to a solid-state qubit under rapid classical rotation.
- Sample Preparation and Setup: A 99.99% 12C diamond was mounted on an electric motor, rotating about the z-axis. A single NV center, located ~3 µm from the rotation center, served as the qubit.
- Optical Pumping and Readout: The NV spin was initialized and read out using 532 nm laser light and fluorescence detection (600-800 nm). The scanning confocal microscope illumination was pulsed synchronously with the motor rotation.
- Microwave (MW) Field Control: Quantum rotations (π/2 and π pulses) were driven by a 2.846 GHz MW field generated by a 20 µm copper wire. The wire position was translated to vary the MW tilt angle (θmw) relative to the rotation axis, thereby controlling the effective phase accumulation (φeff).
- Spin-Echo Interferometry: A standard spin-echo sequence (π/2 - τ - π - τ - π/2) was applied. The sequence was designed to measure the nonlinear component of the effective phase (δφ), defined as: $$ \text{δφ} = \frac{\text{φ}{\text{eff}}(\text{T})}{2} - \text{φ}{\text{eff}}(\frac{\text{T}}{2}) $$ Note: The refocusing π-pulse cancels linear phase accumulation, making the measurement insensitive to static magnetic fields or linear drifts.
- Synchronization and Phase Extraction: The entire quantum sequence was synchronized to the motor trigger. The rotationally-induced phase shift (δφ) was extracted by measuring spin-echo interference fringes as a function of an applied DC transverse magnetic field (Bx) and fitting the resulting signal to a cos2(2πf0 - δφ) function.
- Phase Regime Selection: Measurements were performed in two regimes: a “linear regime” (where δφ ≈ 0) for calibration, and a “nonlinear regime” (high sensitivity) where the MW tilt angle maximized the nonlinear phase accumulation.
Commercial Applications
Section titled “Commercial Applications”This technology provides a foundation for advanced quantum sensing and metrology, particularly in environments involving high-speed motion.
- Quantum Rotation Sensors (Gyroscopes):
- Development of NV-based gyroscopes that measure rotation directly via quantum phase shifts, offering potential sensitivity improvements over classical and fiber-optic gyroscopes.
- Applicable in high-G environments or where extreme precision is required (e.g., aerospace, defense, and deep-space navigation).
- Inertial Measurement Units (IMUs):
- Integration of NV quantum sensors into compact IMUs for autonomous systems, providing robust, drift-free rotational data independent of external magnetic fields.
- Nanoscale Dynamics and Rheology:
- Probing the rotational diffusion and Brownian motion of optically or electrically trapped nanodiamonds in fluidic environments on quantum-relevant timescales.
- Studying complex fluid dynamics and material properties at the nanoscale.
- Fundamental Quantum Mechanics Probes:
- Realizing sensitive torque detectors for probing fundamental quantum mechanical effects related to rotation and motion (e.g., testing collapse models).
- Advanced Quantum Control:
- Utilizing physical rotation as a novel, non-magnetic control parameter for manipulating quantum states in solid-state systems, expanding the toolkit for quantum computing and sensing.
View Original Abstract
The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. We report on a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and it can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200 000 rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation, and quantum phase, and they will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.