| Metadata | Details |
|---|
| Publication Date | 2020-03-01 |
| Journal | New Journal of Physics |
| Authors | Eleanor Scerri, Erik M. Gauger, Cristian Bonato, Eleanor Scerri, Erik M. Gauger |
| Institutions | Heriot-Watt University |
| Citations | 14 |
| Analysis | Full AI Review Included |
- Core Achievement: Demonstrated an adaptive quantum measurement protocol that deterministically extends the coherence time (T2) of a central electron spin (qubit) by learning and narrowing the distribution of its surrounding nuclear spin environment.
- System Focus: The protocol is simulated for a Nitrogen-Vacancy (NV) center electron spin in diamond coupled to a dilute bath of 13C nuclear spins.
- Mechanism: Utilizes Bayesian estimation to track the classical probability distribution P(Az) of the hyperfine field. Measurement back-action is harnessed to project and steer this distribution.
- Performance Gain: The adaptive strategy achieved a significant increase in T2, raising the coherence time from an initial few µs (non-adaptive result) to approximately 100 µs in simulations of a 7-spin bath.
- Narrowing Factor (N.F.): The protocol achieved an average enhancement of the Narrowing Factor (N.F. = σz,0 / σz) by at least a factor of 10 across 100 simulated spin baths.
- Deterministic Control: Unlike non-adaptive Ramsey sequences which result in random, multi-modal distributions, the adaptive method ensures deterministic convergence to a narrow, uni-modal distribution.
- Repeatability: The extended coherence can be maintained indefinitely through intermittent narrowing sequences (spin bath refocussing), even when the free precession periods are significantly longer (e.g., 10 times) than the narrowing steps.
| Parameter | Value | Unit | Context |
|---|
| Qubit System | NV Center Electron Spin (S=1) | N/A | Central spin in diamond. |
| Spin Bath | 13C Nuclear Spins (I=1/2) | N/A | Dilute environment in diamond lattice. |
| 13C Abundance (Natural) | ~1.1 | % | Standard material composition. |
| Simulation Bath Size | 7 (up to 10) | Nuclear Spins | Restricted due to 2N exponential scaling of density matrix. |
| Initial Coherence Time (T2) | 10 | µs | Example T2 before narrowing sequence. |
| Achieved Coherence Time (T2) | ~100 | µs | Result after adaptive narrowing (7-spin bath). |
| Narrowing Factor (N.F.) Improvement | Factor of 10 | N/A | Average enhancement over initial state (σz,0 / σz). |
| Shortest Sensing Time (τ0) | 1 | µs | Minimum Ramsey measurement time. |
| Applied Magnetic Field (Bz) | 250 | mT | Field used in primary simulations. |
| Measurement Repetitions (Mk) | Mk = G + kF | N/A | G=3, F=2 used in examples (k is sensing time index). |
| Initialization Fidelity (Cryogenic) | > 99 | % | State-of-the-art experimental context assumed. |
| Readout Fidelity (Cryogenic) | > 96 | % | State-of-the-art experimental context assumed. |
- System Definition and Hamiltonian: The system is modeled using the full quantum dynamics of the central electron spin coupled to a limited number of 13C nuclear spins (up to 10). The Hamiltonian includes central spin, bath, and hyperfine interaction terms, simplified using the secular approximation for high magnetic fields.
- Bayesian State Estimation: The knowledge of the nuclear spin bath state is represented by a classical probability distribution P(Az) of the hyperfine field projection (Az). This distribution is updated iteratively after each Ramsey measurement using Bayes’ theorem, efficiently calculated in Fourier space.
- Adaptive Parameter Optimization:
- Sensing Time (τ): The optimal sensing time (τopt) is chosen to be as close as possible to the current estimated coherence time (T2). T2 is derived from the Holevo variance (VH) of P(Az), ensuring operation in the regime of maximum sensitivity (τ ~ T2*).
- Detection Phase (φ): The optimal rotation angle (φopt) for the detection basis is determined by minimizing the Holevo variance in Fourier space.
- Deterministic Distribution Steering: A conditional phase shift (π/2) is applied to the detection phase (φopt) whenever the measurement outcome (μk) differs from the previous outcome (μk-1). This mechanism ensures the distribution P(Az) is steered toward a narrow, uni-modal shape, overcoming the probabilistic nature of individual measurement outcomes.
- Intermittent Refocussing: To counteract the natural broadening of P(Az) due to inter-nuclear coupling (diffusion) over long periods, the adaptive narrowing sequence is applied intermittently. This allows the extended coherence to be maintained and exploited during long free precession intervals (e.g., 8 ms).
- Quantum Computing (Qubit Stability): Essential for developing robust solid-state quantum processors, particularly those based on spin qubits (NV centers, silicon carbide defects, quantum dots), where environmental noise is the primary limitation on gate fidelity and scalability.
- High-Precision Quantum Sensing: Enables the realization of Heisenberg-limited quantum metrology by reducing the intrinsic magnetic field fluctuations felt by the central sensor spin, leading to improved sensitivity in nanoscale magnetometry.
- Solid-State Qubit Manufacturing and Control: Provides a real-time, resource-efficient method for Hamiltonian learning, which can be integrated into control electronics to compensate for environmental detuning and maintain coherence in manufactured quantum devices.
- Quantum Network Infrastructure: Enhances the performance and stability of solid-state spins used as quantum memory or communication nodes, critical for long-distance quantum entanglement distribution.
- Novel Quantum State Engineering: The ability to precisely control and project the nuclear spin bath distribution opens pathways for engineering exotic many-body states with tailored entanglement properties for fundamental research or specialized applications.
View Original Abstract
Abstract Decoherence, resulting from unwanted interaction between a qubit and its environment, poses a serious challenge towards the development of quantum technologies. Recently, researchers have started analysing how real-time Hamiltonian learning approaches, based on estimating the qubit state faster than the environmental fluctuations, can be used to counteract decoherence. In this work, we investigate how the back-action of the quantum measurements used in the learning process can be harnessed to extend qubit coherence. We propose an adaptive protocol that, by learning the qubit environment, narrows down the distribution of possible environment states. While the outcomes of quantum measurements are random, we show that real-time adaptation of measurement settings (based on previous outcomes) allows a deterministic decrease of the width of the bath distribution, and hence an increase of the qubit coherence. We numerically simulate the performance of the protocol for the electronic spin of a nitrogen-vacancy centre in diamond subject to a dilute bath of 13 C nuclear spin, finding a considerable improvement over the performance of non-adaptive strategies.
- 2008 - Nanoscale imaging magnetometry with diamond spins under ambient conditions [Crossref]
- 2011 - Laser cooling and real-time measurement of the nuclear spin environment of a solid-state qubit [Crossref]
- 2013 - Nanoscale magnetic imaging of a single electron spin under ambient conditions [Crossref]
- 2017 - Quantum metrology with a single spin- 3 2 defect in silicon carbide [Crossref]
- 2011 - Electric-field sensing using single diamond spins [Crossref]
- 2015 - Hybrid optical-electrical detection of donor electron spins with bound excitons in silicon [Crossref]
- 2019 - Probing magnetism in 2d materials at the nanoscale with single-spin microscopy [Crossref]
- 2018 - Wide-field imaging of superconductor vortices with electron spins in diamond [Crossref]
- 2017 - Real-space imaging of non-collinear antiferromagnetic order with a single-spin magnetometer [Crossref]
- 2019 - Atomic-scale imaging of a 27-nuclear-spin cluster using a single-spin quantum sensor [Crossref]