Exploring 2D Synthetic Quantum Hall Physics with a Quasiperiodically Driven Qubit
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-10-16 |
| Journal | Physical Review Letters |
| Authors | Eric Boyers, Philip J. D. Crowley, Anushya Chandran, Alexander O. Sushkov |
| Institutions | Boston University |
| Citations | 50 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Synthetic Topological Qubit: A single Nitrogen-Vacancy (NV) center spin qubit in diamond was used to experimentally realize a synthetic two-dimensional (2D) quantum Hall system, implementing the half-BHZ Hamiltonian.
- Chern Number Quantification: Topological properties were quantified by measuring the frequency of quantum state overlap (fidelity) oscillations, which is directly proportional to the integrated Berry curvature and the Chern number ($C$).
- Key Results: Integer ($C = 1$) and half-integer ($C = 1/2$) quantized Chern numbers were successfully measured, confirming the topological and critical Dirac point regimes, respectively.
- Coherence Extension: A counter-diabatic potential (VCD) was applied alongside a spin-echo sequence, extending the topological evolution time to approximately 61 µs, significantly suppressing non-adiabatic excitations.
- Measurement Technique: The method utilizes projective qubit measurements to extract the geometric phase accumulated along a closed path in the synthetic Brillouin zone, offering a robust alternative to traditional transport measurements.
- Platform Versatility: The approach demonstrates that driven qubit platforms are highly effective tools for studying complex higher-dimensional topological physics using only two mutually incommensurate RF drive tones.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit System | NV Center in C12 enriched diamond | N/A | Electronic spin (ms = 0 ↔ ms = +1) |
| Static Magnetic Field (B0) | ~500 | G | Tuned to Excited State Level Anti-Crossing (LAC) |
| Rabi Frequency (γB0) | 2π * 0.25 | MHz | Characteristic energy scale of the Hamiltonian |
| Drive Frequencies (Ω) | 2π * (0.5, 0.5φ) | MHz | Incommensurate driving (φ is the golden ratio) |
| Topological Chern Number (Cexp) | 0.97 ± 0.03 | N/A | Measured in the topological regime (m=1) |
| Critical Chern Number (Cexp) | 0.50 ± 0.02 | N/A | Measured at the critical Dirac point (m=2) |
| Trivial Chern Number (Cexp) | less than 0.042 | N/A | Upper bound measured in the trivial regime (m=3) |
| Topological Decay Time (τ) (with echo) | 61 ± 4 | µs | Lifetime of overlap oscillations, extended by spin echo |
| Topological Decay Time (τ) (without echo) | 29 ± 3 | µs | Lifetime without counter-diabatic pulse |
| NV T2* Coherence Time | 125 ± 7 | µs | Measured via detuned Ramsey experiment |
| AWG Bandwidth Requirement | 20 | MHz | Required for VCD implementation (less than 100 MHz AWG capability) |
| Laser Wavelength | 532 | nm | Optical pumping and fluorescence detection |
Key Methodologies
Section titled “Key Methodologies”- NV Center Fabrication: The NV centers were created in C12 enriched diamond via N15 ion bombardment followed by annealing.
- Qubit Tuning and Initialization: A static magnetic field (B0) was aligned along the NV symmetry axis and tuned to the excited state Level Anti-Crossing (LAC) (~500 G) to create an effective two-level qubit system (|0> and |+1>). Optical pumping initialized the spin in the |↑z> state.
- Synthetic Dimension Generation: Two RF drive tones (Ω1, Ω2) were generated by an Arbitrary Waveform Generator (AWG) and modulated onto a carrier signal (ω0 ~ 1.46 GHz) to implement the half-BHZ Hamiltonian in the rotating frame.
- Counter-Diabatic Driving Implementation: A calculated counter-diabatic potential (VCD) was added to the driving fields (Bx, By, Bz) via the AWG to suppress diabatic Landau-Zener transitions between instantaneous eigenstates.
- Closed-Path Trajectory Setup: Two quantum states were prepared in the same superposition spin state but with slightly different initial drive phases (θ0 and θ0 + δθ). The phase difference δθ defined the area of the closed path in the synthetic Brillouin zone.
- Decoherence Mitigation: A spin-echo sequence (π pulse) was applied mid-evolution to mitigate low-frequency noise and extend the coherence time of the topological dynamics.
- Fidelity Measurement: The quantum state overlap, or fidelity $F(t) = |\langle\psi(t)|\psi’(t)\rangle|^{2}$, was measured using projective qubit measurements (Pauli matrix expectation values) and normalized using bright and dark counts.
- Chern Number Extraction: The frequency of the resulting fidelity oscillation was fitted to a model $F(t) \approx 1/2 + (1/2 - A \sin^{2}(\omega_{\tau} t)) e^{-t/\tau} + \delta$, where the topological frequency $\omega_{\tau}$ is proportional to the Chern number $C$.
Commercial Applications
Section titled “Commercial Applications”- Quantum Simulation: The NV center platform offers a scalable and highly controllable testbed for simulating complex condensed matter phenomena, such as fractional quantum Hall physics, relevant for designing new quantum materials.
- Quantum Information Processing: The demonstrated techniques for suppressing diabatic errors (VCD) and extending coherence (spin echo) are critical for building robust, high-fidelity quantum gates and memories.
- Quantum Metrology and Sensing: The ability to precisely measure Berry curvature is foundational for topological quantum metrology, potentially leading to ultra-sensitive sensors for magnetic fields or inertial forces.
- RF and Microwave Engineering: The synthetic Hall effect mediates an energy current between the two drive tones, suggesting applications in novel quantum frequency converters and high-efficiency signal processing devices.
- Topological Device Design: The experimental validation of the half-BHZ model provides crucial data for engineering topological insulators and superconductors in solid-state systems.
View Original Abstract
Quasiperiodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our Letter opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semimetals in synthetic dimensions.