Optimal frequency measurements with quantum probes
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-04-01 |
| Journal | npj Quantum Information |
| Authors | Simon Schmitt, Tuvia Gefen, Daniel Louzon, Christian Osterkamp, Nicolas Staudenmaier |
| Institutions | Hebrew University of Jerusalem, Element Six (United Kingdom) |
| Citations | 18 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research outlines and experimentally validates optimal quantum strategies for frequency metrology using Nitrogen-Vacancy (NV) centers in diamond, achieving performance significantly beyond classical limits.
- Optimal Discrimination: Demonstrated frequency discrimination of two signals separated by 2 kHz in a single 44 ”s measurement, achieving a speed factor of ten below the classical Fourier limit (1/T).
- Near-Quantum Limit Estimation: Achieved a frequency estimation sensitivity of 1.6 ”Hz/Hz2 for a 1.7 ”T amplitude signal, which is within a factor of two of the theoretical Quantum Fisher Information (QFI) limit.
- Optimal Control Protocol: The key innovation is the use of optimal coherent control (pi-pulses) synchronized to the signal, driving the sensor phase accumulation quadratically (t2) to maximize the angle between the states being discriminated.
- Readout Comparison: Explicitly compared Ensemble Averaging (EA) and Single-Shot Readout (SSR) using a 13C ancilla qubit. SSR is shown to be advantageous (faster total measurement time) for long interaction periods (greater than 17 ”s) due to reduced overhead.
- Foundational Impact: These results establish the fundamental limits and optimal protocols for discrimination and estimation problems critical to nanoscale Nuclear Magnetic Resonance (nano-NMR) spectroscopy.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Frequency Discrimination Time (Topt) | 44 | ”s | Time required to discriminate 2 kHz separation |
| Discrimination Speedup | 10x | Factor | Improvement over the classical Fourier limit |
| Signal Amplitude (B) | 1.7 | ”T | Used during frequency estimation experiments |
| Frequency Estimation Sensitivity (Experimental) | 1.6 | ”Hz/Hz2 | Achieved using Single-Shot Readout (SSR) |
| Quantum Fisher Information (QFI) Limit | 0.9 | ”Hz/Hz2 | Theoretical limit for the 1.7 ”T signal (Eq. 8) |
| Bias Magnetic Field | 400 | G | Used to lift NV ground state degeneracy |
| Microwave Control Timing Resolution | 20 | ps | Arbitrary Waveform Generator (AWG) specification |
| NV Phase Memory Time (T2*) | ~50 | ”s | Typical for 0.1% 13C diamond sample |
| 13C Content (QND Sample) | 0.1 | % | Diamond sample used for SSR experiments |
| Ancilla Readout Fidelity (NRR = 104) | >99 | % | Fidelity of the 13C nuclear spin readout |
| Ensemble Averaging Readout Overhead | ~1.5 | ”s | Initialization plus readout time per cycle |
| SSR Ancilla Readout Overhead (treadanc) | ~17 | ”s | Time required for repetitive mapping onto NV electron spin |
Key Methodologies
Section titled âKey MethodologiesâThe experiments utilize a single NV center in diamond as a quantum probe, employing precise microwave control and comparing two distinct readout strategies.
- Quantum Probe Setup: A single NV center is used, optically initialized and read out via spin-dependent fluorescence detection using a confocal microscope. A 400 G magnetic field is applied along the NV axis to define the qubit states (0 and -1).
- Optimal Coherent Control: The sensor is driven using sequences of pi-pulses (e.g., XY8-N) generated by a high-resolution AWG (20 ps timing). For optimal discrimination, pi-pulses are applied whenever the sign of the Hamiltonian difference (H1 - H2) changes, ensuring a continuous, quadratic (t2) accumulation of the phase difference (α).
- Frequency Estimation Control: For optimal estimation, pi-pulses are applied at the signal antinodes (where the signal amplitude is maximal, corresponding to an initial phase Ξ = 0), maximizing the rate of phase accumulation.
- Ensemble Averaging (EA): The standard method where the full sequence (initialization, sensing, optical readout) is repeated Nens times. Discrimination relies on reducing photon shot noise by increasing the total number of detected photons.
- Single-Shot Readout (SSR) / Hybrid Strategy: The NV electron spin state is mapped onto a weakly coupled 13C nuclear spin (ancilla qubit). The ancilla state is then probed NRR times using a Quantum Non-Demolition (QND) measurement, allowing for high-fidelity readout (greater than 99% for NRR = 104).
- Diamond Material: Experiments utilized ultrapure diamond, including samples with 0.1% 13C content for SSR, and isotopically enriched (99.999% 12C) layers for other tests. Samples were cleaned using a tri-acid mixture (H2SO4:HNO3:HClO4) at 130 °C.
Commercial Applications
Section titled âCommercial ApplicationsâThe demonstrated optimal quantum metrology protocols are critical for applications requiring ultra-precise and fast frequency measurements, particularly in resource-limited environments.
- Nanoscale NMR Spectroscopy: Enables high-resolution chemical analysis of extremely small sample volumes (e.g., single cells, single proteins) by maximizing the signal-to-noise ratio and minimizing measurement time.
- Quantum Sensing and Metrology: Provides the fundamental protocols for constructing next-generation quantum sensors that operate at the theoretical limits of precision and speed.
- Quantum System Characterization: Used for precise characterization of quantum systems, including measuring energy levels, estimating Hamiltonians, and determining coherence properties.
- Improved Frequency Standards: The techniques for achieving near-quantum-limit frequency estimation can be applied to build more stable and accurate frequency standards.
- Diagnostic and Screening Tools: The ability to perform rapid, high-fidelity frequency discrimination (e.g., âyes/noâ questions about chemical presence) is valuable for fast diagnostic tests in medical or environmental monitoring.
- Search for Dark Matter: The high sensitivity to small magnetic field oscillations makes these probes relevant for searches for exotic physics, such as axion-like dark matter.