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arXiv:1704.01824 · Journal of Physics D Applied Physics

Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond

Wen-Qi Fang, Bang‐Gui Liu

Published Jul 11, 2017• 0 citations
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Abstract

Abstract Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct the exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields, and investigate the nonadiabatic geometric phases—both cyclic and non-cyclic—in these fast-manipulated NV spin systems. It is believed that the nonadiabatic geometric phases can be measured in future experiments, and that these fast quantum manipulations can be useful in designing spin-based quantum applications.

DOI
10.1088/1361-6463/aa7f1a

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•Jan 1, 2015•1 citation
Abstract Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct the exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields, and investigate the nonadiabatic geometric phases—both cyclic and non-cyclic—in these fast-manipulated NV spin systems. It is believed that the nonadiabatic geometric phases can be measured in future experiments, and that these fast quantum manipulations can be useful in designing spin-based quantum applications.
The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin zzz-components of +1, 0, and \ensuremath{-}1. Without external field, the +1 and \ensuremath{-}1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and antisymmetrical superpositions of the +1 and \ensuremath{-}1 states as our qubit basis, we obtain the exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-dependent quantum two-level systems with exact analytical solutions. With our exact evolution operator of the NV center spin including three levels, we show that arbitrary qubits can be prepared from the starting 0 state, and arbitrary rapid quantum logic gates of these qubits can be realized with magnetic fields. In addition, it is made clear that the typical quantum logic gates can be accomplished within a few nanoseconds and the fidelity can be very high because only magnetic field strength needs to be controlled in this approach. These results should be useful to realizing quantum computing with the NV center spin systems in diamond and exploring other effects and applications.
We propose a fast phase-gating of a single nuclear spin, which interacts with the single electronic spin of the nitrogen-vacancy center in diamond. Our gate operation is to be called the geometric quantum gate; a geometric phase shift of the electron spin induced by the rotating electric field, is utilized to control the nuclear-spin phase. The gate time is inversely proportional to the frequency of the electric-field rotation; we estimate that the phase-gate time is orders shorter than hitherto reported. We also show the robustness against decoherence and systematic errors.
A key challenge of magnetometry lies in the simultaneous optimization of magnetic field sensitivity and maximum field range. In interferometry-based magnetometry, a quantum two-level system acquires a dynamic phase in response to an applied magnetic field. However, due to the 2π periodicity of the phase, increasing the coherent interrogation time to improve sensitivity reduces field range. Here we introduce a route towards both large magnetic field range and high sensitivity via measurements of the geometric phase acquired by a quantum two-level system. We experimentally demonstrate geometric-phase magnetometry using the electronic spin associated with the nitrogen vacancy (NV) color center in diamond. Our approach enables unwrapping of the 2π phase ambiguity, enhancing field range by 400 times. We also find additional sensitivity improvement in the nonadiabatic regime, and study how geometric-phase decoherence depends on adiabaticity. Our results show that the geometric phase can be a versatile tool for quantum sensing applications.
The spin-1 carried by the nitrogen-vacancy (NV${}^{\ensuremath{-}}$) color center of a diamond is a promising candidate as a quantum bit (qubit) for the realization of a solid-state quantum computer. The interaction with the P1P1P1 center, which is a single substitutional nitrogen atom with spin-12\frac{1}{2}21​, converts the NV${}^{\ensuremath{-}}$ qubit to a multilevel system. The 18-level energy diagram of the NV${}^{\ensuremath{-}}$-P1P1P1 coupled defect pair exhibits several level anticrossings and the spin functions change sign at different values of the applied magnetic field. Beyond each resonance, the two electronic spins of the coupled triplet-doublet system flip individually or in concert, offering possibilities to implement quantum logic gates. Interlevel transitions are also possible. The transition probabilities can be predicted rigorously in the framework of the Landau-Zener theory. The spin flip occurs by quantum tunneling. It is also possible to introduce geometric phases, which can be useful for the realization of phase gates.
Abstract A nitrogen-vacancy (NV) center in a diamond enables the access to an electron spin, which is expected to present highly sensitive quantum sensors. Although exploiting a nitrogen nuclear spin improves the sensitivity, manipulating it using a resonant pulse requires a long gate time owing to its small gyromagnetic ratio. Another technique to control nuclear spins is a conditional rotation gate based on dynamical decoupling, which is faster but unavailable for nitrogen spins owing to the lack of transverse hyperfine coupling with the electron spin. In this study, we generated effective transverse coupling by applying a weak off-axis magnetic field. An effective coupling depends on the off-axis field; the conditional rotation gate on the nitrogen-14 spins of an NV center was demonstrated within 4.2 μs under an 1.8% off-axis field and a longitudinal field of approximately 280 mT. We estimated that a population transfer from the electron to nitrogen spins can be implemented with 8.7 μs. Our method is applicable to an ensemble of NV centers, in addition to a single NV center.
Color centers in diamond, and in particular the nitrogen-vacancy center (NV center), have proven promising for the emerging field of quantum technologies. In this thesis, new concepts for the manipulation of the NV center dynamics will be addressed, along with the proposal of novel fields of application. It comprises: (i) A study of the NV coupling to intrinsic acoustical phonons in nanocrystals, and concepts to exploit that mechanism for conditional quantum operations. (ii) The proposal for the bottom-up creation of NV arrangements on the nanoscale by the ordered arrangement of nanodiamonds directed by biological scaffold structures. A framework is developed for coherently addressing and manipulating NV centers in such structures along with studies of noise and imperfections. (iii) The interferometry with nanodiamonds in search of signatures of quantum gravity. (iv) The creation of an illustrative (filter-based) framework for the analysis and design of hybrid NV-nuclear spin couplings.