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Science

Gigahertz Dynamics of a Strongly Driven Single Quantum Spin

Gregory D. Fuchs, V. V. Dobrovitski, D.M. Toyli, F. Joseph Heremans, D. D. Awschalom

Published Nov 19, 2009• 392 citations
Publisher

Abstract

Two-level systems are at the core of numerous real-world technologies such as magnetic resonance imaging and atomic clocks. Coherent control of the state is achieved with an oscillating field that drives dynamics at a rate determined by its amplitude. As the strength of the field is increased, a different regime emerges where linear scaling of the manipulation rate breaks down and complex dynamics are expected. By calibrating the spin rotation with an adiabatic passage, we have measured the room-temperature "strong-driving" dynamics of a single nitrogen vacancy center in diamond. With an adiabatic passage to calibrate the spin rotation, we observed dynamics on sub-nanosecond time scales. Contrary to conventional thinking, this breakdown of the rotating wave approximation provides opportunities for time-optimal quantum control of a single spin.

DOI
10.1126/science.1181193

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Two-level systems are at the core of numerous real-world technologies such as magnetic resonance imaging and atomic clocks. Coherent control of the state is achieved with an oscillating field that drives dynamics at a rate determined by its amplitude. As the strength of the field is increased, a different regime emerges where linear scaling of the manipulation rate breaks down and complex dynamics are expected. By calibrating the spin rotation with an adiabatic passage, we have measured the room-temperature "strong-driving" dynamics of a single nitrogen vacancy center in diamond. With an adiabatic passage to calibrate the spin rotation, we observed dynamics on sub-nanosecond time scales. Contrary to conventional thinking, this breakdown of the rotating wave approximation provides opportunities for time-optimal quantum control of a single spin.
The strong-driving regime occurs when a quantum two-level system is driven with an external field whose amplitude is greater than or equal to the energy splitting between the system's states and is typically identified with the breaking of the rotating wave approximation (RWA). We report an experimental study in which the spin of a single nitrogen-vacancy (NV) center in diamond is strongly driven with microwave fields of arbitrary polarization. We measure the NV center spin dynamics beyond the RWA and characterize the limitations of this technique for generating high-fidelity quantum gates. Using circularly polarized microwave fields, the NV spin can be harmonically driven in its rotating frame regardless of the field amplitude, thus allowing rotations around arbitrary axes. Our approach can effectively remove the RWA limit in quantum-sensing schemes and assist in increasing the number of operations in QIP protocols.
Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single nitrogen-vacancy (NV) center in diamond coupled to a first-shell 13C^{13}\mathrm{C}13C nuclear spin at a level anticrossing point. This near degeneracy occurs in the ${m}_{s}=\ifmmode\pm\else\textpm\fi{}1$ manifold of the electron spin when the energy level splitting between the ${m}_{s}=\ensuremath{-}1$ and +1+1+1 states due to the static magnetic field is $\ensuremath{\approx}127$ MHz and thus equal to the splitting due to the 13C^{13}\mathrm{C}13C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the component of the radio-frequency (RF) field along the NV symmetry axis. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is small compared to the transition frequency evolve into complex patterns when the driving field amplitude is comparable to or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.
We report on a theoretical and experimental study of time-optimal construction of arbitrary single-qubit rotations under a single strong driving field of finite amplitude. Using radiation-dressed states of nitrogen vacancy centers in diamond we realize a strongly driven two-level system, with driving frequencies four times larger than its precession frequency. We implement time-optimal universal rotations on this system, characterize their performance using quantum process tomography, and demonstrate a dual-axis multiple-pulse control sequence where the qubit is rotated on time scales faster than its precession period. Our results pave the way for applying fast qubit control and high-density pulse schemes in the fields of quantum information processing and quantum metrology.
We study the applicability of the time-optimal bang-bang control designed for spin 12\frac{1}{2}21​ [Boscain and Mason, J. Math. Phys. 47, 062101 (2006)] to the rotation of the electron spin of a nitrogen-vacancy (NV) center in diamond. The spin of the NV center is a three-level system, with two levels forming a relevant qubit subspace where the time-varying magnetic control field performs rotation, and the third level being idle. We find that the bang-bang control protocol decreases the rotation time by 20%--25% in comparison with the traditional oscillating sinusoidal driving. We also find that for most values of the bias field, the leakage to the idle level is very small, so that the NV center is a suitable testbed for experimental study of the time-optimal protocols. For some special values of the bias field, however, the unwanted leakage is greatly increased. We demonstrate that this is caused by the resonance with higher-order Fourier harmonics of the bang-bang driving field.
Magnetic resonance techniques provide a powerful tool for controlling spin systems, with applications ranging from quantum information processing to medical imaging. Nevertheless, the behavior of a spin system under strong excitation remains a rich dynamical problem. In this paper, we examine spin resonance of the nitrogen-vacancy center in diamond under conditions outside the regime where the usual rotating-wave approximation applies, focusing on effects of multifrequency excitation and excitation with orientation parallel to the spin quantization axis. Strong-field phenomena such as multiphoton transitions and coherent destruction of tunneling are observed in the spectra and analyzed via numerical and analytic theory. In addition to illustrating the response of a spin system to strong multifrequency excitation, these observations may inform techniques for manipulating electron-nuclear spin quantum registers.
Rabi oscillations and adiabatic passage of single electron spins in a diamond nitrogen vacancy center are demonstrated with two Raman-resonant optical pulses that are detuned from the respective dipole optical transitions. We show that the optical spin control is nuclear-spin selective and can be robust against rapid decoherence, including radiative decay and spectral diffusion, of the underlying optical transitions. A direct comparison between the Rabi oscillation and the adiabatic passage, along with a detailed theoretical analysis, provides significant physical insights into the connections and differences between these coherent spin processes and also elucidates the role of spectral diffusion in these processes. The optically driven coherent spin processes enable the use of nitrogen vacancy excited states to mediate coherent spin-phonon coupling, opening the door to combining optical control of both spin and mechanical degrees of freedom.