Full qubit control of the double quantum transition in NV centers for low-field or high-frequency sensing

At a Glance

Metadata	Details
Publication Date	2025-05-15
Journal	EPJ Quantum Technology
Authors	Alberto López-García, Javier Cerrillo
Analysis	Full AI Review Included

Executive Summary

This analysis summarizes a novel scheme for achieving full qubit control in the negatively charged Nitrogen-Vacancy (NV^-) center in diamond, specifically targeting the double quantum transition (DQT) for enhanced quantum sensing.

Core Achievement: Developed an analytical protocol for implementing fast, arbitrary single-qubit gates (rotations by arbitrary angles around two non-parallel axes) in the DQT subspace (|−1⟩ and |+1⟩).
Methodology: The scheme extends the NV Effective Raman Coupling (NV-ERC) technique, utilizing the |0⟩ state as an effective Raman coupler to drive the DQT without leakage to the third level.
Control Mechanism: Full control is achieved by concatenating microwave (MW) pulses of constant amplitude and frequency, where the arbitrary rotation angle and axis are determined by the judicious timing of phase changes between the pulses.
Sensing Regimes: The protocol is optimized for two critical sensing environments:
1. Low Magnetic Field: Zeeman splitting (µB) is smaller than the MW Rabi frequency (Ω).
2. High Frequency: Detection of signals comparable to the NV center’s Zeeman splitting.
Performance Gain: The DQT control provides a two-fold sensitivity improvement compared to conventional single-quantum transition sensing methods.
Robustness: The scheme is demonstrated to be robust against common experimental errors, including pulse timing inaccuracies, mischaracterization of system parameters (Ω or µB), and the presence of unknown static electric or strain fields (E_x, E_y, E_z).

Technical Specifications

Parameter	Value	Unit	Context
Qubit System	Spin-1 Triplet	N/A	Ground state of NV^- center in diamond.
Transition Frequency (D)	≈ 2.87	GHz	Zero-field splitting (MW pulse frequency is tuned to D).
Qubit Subspace		+1⟩,	−1⟩
Low Field Condition	Ω > µB	N/A	Rabi frequency must be greater than Zeeman splitting.
Fast Pulse Condition	Ω ≥ 2µB	N/A	Required for full depletion of the
Example Rabi Frequency	3µB	N/A	Used for NOT gate demonstration (Fig. 2).
High-Frequency Limit (Conventional)	ω_e ~ Ω/√2	N/A	Maximum frequency reliably sensed by conventional Hahn echo.
Sensitivity Improvement	Two-fold	N/A	Enhancement achieved by using the DQT.
Gate Control Method	Phase Timing (α, θ)	Radians	Controls the axis (φ) and angle (θ) of rotation R(±φ, θ).

Key Methodologies

The implementation of arbitrary qubit gates relies on a two-step parameter identification process followed by precise pulse concatenation:

Initial System Characterization:
- ODMR (Optically Detected Magnetic Resonance): Used to identify the energies of the three ground states, determine the required MW pulse frequency (D + E_z), and ensure correct magnetic field alignment.
- Rabi Experiment: Used to identify the total cycle time (T) and the characteristic pulse duration (T’) required to fully deplete the |0⟩ state, thereby capturing the effects of static strain/electric fields (E_x, E_y, E_z).
Hamiltonian Simplification and Control Derivation:
- Rotating Wave Approximation (RWA): The full spin-1 Hamiltonian is simplified in the interaction picture, revealing an effective Raman coupling (ERC) between the |0⟩ state and the symmetric superposition state |−⟩.
- Unitary Derivation: The complete unitary evolution U(T, α) is analytically derived for the characteristic pulse durations T’ and T”, providing the basis transformations and associated phase gains.
Arbitrary Gate Implementation:
- Pulse Concatenation: Arbitrary gates are constructed by concatenating six pulses, or minimally, two pulses of durations T’ and T” with a phase difference θ (e.g., R(−φ, θ) = U(T”, α + θ)U(T’, α)).
- Axis Control: The rotation axis (φ) is determined by the ratio Ω/µB (Rabi frequency to Zeeman splitting).
- Angle Control: The rotation angle (θ) is controlled by the phase difference between the concatenated pulses.
Adaptation to Static Fields:
- E_z Field: The effect of E_z is absorbed into the D term (D → D + E_z) and automatically corrected during the ODMR step.
- E_y Field: E_y acts as an effective enhancement of the magnetic field, shortening the Rabi period T. This effect is captured during the initial Rabi experiment.
- E_x Field: E_x requires the addition of an orthogonal MW pulse (Ω_y) to recover the Raman resonance. The required ratio Ω_y/Ω_x is determined experimentally by maximizing the depletion of the |0⟩ state.

Commercial Applications

The ability to perform fast, robust, arbitrary qubit control in the NV DQT opens doors for advanced quantum technologies, particularly in sensing and metrology:

Quantum Sensing and Metrology:
- Nanoscale Nuclear Magnetic Resonance (NMR): Enables high-sensitivity NMR spectroscopy at the nanoscale, crucial for elucidating molecular structure (J-coupling sensing).
- Ultra-Low Field Detection: Essential for applications where large bias fields mask signals (e.g., chemical bonds) or introduce unwanted magnetic susceptibilities.
- High-Frequency Signal Detection: Overcomes the frequency limitations of conventional dynamical decoupling (DD) sequences, allowing detection of signals comparable to the NV Zeeman splitting.
Condensed Matter Physics:
- Magnetic imaging and magnetometry of superconductors, multilayer systems hosting spin structures (skyrmions), and magnetic insulators.
Quantum Information Processing:
- Implementation of robust, fast single-qubit gates, supporting complex dynamical decoupling protocols (e.g., XY8) and quantum memory applications.
Environmental Quantum Control:
- Applications requiring precise control under ambient conditions, such as optical hyperpolarization of ¹³C.

View Original Abstract

Abstract We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV) defect in diamond. The protocol is especially useful for sensing in two regimes: on the one hand, in the low-field limit where the Zeeman splitting of the NV-center is smaller than the MW Rabi frequency; on the other hand, for the detection of high-frequency signals, comparable to the Zeeman splitting of the NV center. It constitutes an extension to the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis transformation for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast single qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields and numerically test its effectiveness in a Hahn echo sequence in the high-frequency or low-field regime.

Tech Support

Original Source

DOI: https://doi.org/10.1140/epjqt/s40507-025-00358-x