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arXiv:1110.2280 · Physical Review B

Rotating frame spin dynamics of a nitrogen-vacancy center in a diamond nanocrystal

Abdelghani Laraoui, Carlos A. Meriles

Published Oct 10, 2011• 22 citations
arXivHTMLPDF

Abstract

We investigate the spin dynamics of a nitrogen-vacancy (NV) center contained in an individual diamond nanocrystal in the presence of continuous microwave excitation. Upon periodic reversal of the microwave phase, we observe a train of ``Solomon echoes'' that effectively extends the system coherence lifetime to reach several tens of microseconds, depending on the microwave power and phase inversion rate. Starting from a model where the NV center interacts with a bath of paramagnetic defects on the nanocrystal surface, we use average Hamiltonian theory to compute the signal envelope from its amplitude at the echo maxima. A comparison between the effective Rabi and Solomon propagators shows that the observed response can be understood as a form of higher-order decoupling from the spin bath.

DOI
10.1103/physrevb.84.161403

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We investigate the spin dynamics of a nitrogen-vacancy (NV) center contained in an individual diamond nanocrystal in the presence of continuous microwave excitation. Upon periodic reversal of the microwave phase, we observe a train of ``Solomon echoes'' that effectively extends the system coherence lifetime to reach several tens of microseconds, depending on the microwave power and phase inversion rate. Starting from a model where the NV center interacts with a bath of paramagnetic defects on the nanocrystal surface, we use average Hamiltonian theory to compute the signal envelope from its amplitude at the echo maxima. A comparison between the effective Rabi and Solomon propagators shows that the observed response can be understood as a form of higher-order decoupling from the spin bath.
Decoherence is the biggest bottleneck in all quantum technologies. For nitrogen-vacancy (NV) centers in diamond, the loss of coherence is caused by the electron and nuclear spin bath of the diamond lattice. Here, we demonstrate that the spin bath - that typically causes decoherence - entangles the spin states of the NV electron and the host 14^{14}14N nucleus. The many-body interaction between the 14^{14}14N nucleus - electron - bath spins at an energy level anti-crossing occurring for an applied magnetic field orientation perpendicular to the NV axis is responsible for this effect. This is observed experimentally in NV ensembles via electron spin-echo measurements, where the echo envelope is modulated at the frequency of a 14^{14}14N nuclear spin transition. Using numerical simulations, we show that the spin bath coupling to the NV centers is essential for observing this modulation. Due to the zero first-order Zeeman effect at the anti-crossing, the observed oscillations have long spin-echo coherence times, 2--3 times those at the parallel magnetic field orientation. The oscillation frequency is highly stable and robust against environmental fluctuations. These findings provide new opportunities for fundamental studies of many-body physics and quantum sensing.
Nitrogen-vacancy (NV) centers in diamond as ideally individual spin quantum systems can be coherently manipulated by microwave fields. Compared to the traditional method using the IQ (In-phase/Quadrature) mixer with a local oscillator and intermediate-frequency (IF) signals, we report an effective and technically simple method to generate the required microwave field by frequency multiplication and realize coherent manipulation of the NV center’s electron spin. After frequency multiplication, the IF signal can be directly converted to the high-frequency microwave field with adjustable pulse width, frequency, phase, and amplitude. A series of spin dynamics applications such as Rabi oscillation, free induction decay, and spin-locking are executed, which verified its performance and feasibility. Frequency multiplication can overcome the problem of clock synchronization between the local oscillator and IF signal and greatly reduce the complexity of the experimental system. The method can be easily used to realize a more complex quantum control sequence such as dynamic decoupling and extended to a wide range of spin-based quantum information applications in the future.
We study dynamics of the electron spin of a nitrogen-vacancy (NV) center subjected to a strong driving field with periodically reversed direction (train of rotary echoes). We use analytical and numerical tools to analyze in detail the form and time scales of decay of the rotary echo train by modeling the decohering spin environment as a random magnetic field. We demonstrate that the problem can be exactly mapped onto a model of spin 1 coupled to a single bosonic mode with imaginary frequency. This mapping allows comprehensive analytical investigation beyond the standard Bloch-Redfield-type approaches. We explore the decay of the rotary echo train under assumption of strong driving and identify the most important regimes of the decay. The analytical results are compared with the direct numerical simulations to confirm quantitative accuracy of our study. We present the results for realistic environment of substitutional nitrogen atoms (P1 centers) and provide a simplified but accurate description for the decay of the rotary echo train of the NV center's spin. The approach presented here can also be used to study decoherence and longitudinal relaxation of other spin systems under conditions of strong driving.
Abstract Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units for a wide range of solid-state-based quantum technology applications. While such applications require the long spin coherence times of the NV centers, they are often limited due to decoherence. In this study, we theoretically investigate the decoherence of NV-spin ensembles induced by nitrogen impurities (P1 centers), which are one of the most dominant and inevitable magnetic field noise sources in diamond. We combined cluster correlation expansion and density functional theory to compute the Hahn-echo spin-coherence time of the NV centers for a broad range of P1 concentrations. Results indicate a clear linear dependence of T2 on P1 concentrations on a log scale with a slope of −1.06, which is in excellent agreement with previous experimental results. The interplay between the Jahn–Teller effect and the hyperfine interaction in the P1 center plays a critical role in determining the bath dynamics and the resulting NV decoherence. Our results provide a theoretical upper bound for the NV-spin T2 over a wide range of P1 densities, serving as a key reference for materials optimization and spin bath characterization to develop highly coherent NV-based devices for quantum information technology.
We theoretically investigate spin decoherence of a single nitrogen-vacancy (NV) center in diamond. Using the spin coherent-state PPP-representation method, we simulate coherence evolution of the NV center coupled to surrounding nitrogen electron (N) spins. In the system, the strength of N-N coupling is the same order as that of NV-N coupling (the strong intrabath coupling regime). We find that spin decoherence time as well as free-induction decay of the NV center depend on the spatial configuration of N spins. Both the spin decoherence rate (1/T21/{T}_{2}1/T2​) and dephasing rate (1/T2∗)1/{T}_{2}^{*})1/T2∗​) of the NV center increase linearly with the concentration of the N spins. Using the PPP-representation method, we also demonstrate extracting the noise spectrum of the N spin bath. The capability to calculate the noise spectrum will provide promising pathways to suppress decoherence of spin systems in the strong intrabath coupling regime.
We investigate coherent quantum control of a nitrogen vacancy (NV) center in diamond with microwave fields generated from a nanoscale magnet that is proximal to the NV center. Our results show remarkable coherent control with high contrast Rabi oscillations using nearfield microwaves from shape anisotropic nanomagnets of lateral dimensions down to 200 nm x 180 nm, driven remotely by surface acoustic wave (SAW) excitation that is at least 400 times and potentially 4 orders of magnitude more energy efficient than generating microwaves with an antenna. Furthermore, we show that varying the acoustic power driving such nanomagnets can achieve control over Rabi frequency. We also report spin-lattice relaxation time T1 is 103 +/-0.5 micro-seconds, the spin-spin relaxation time T2 is 1.23+/-0.29 micro-seconds, and the Ramsey coherence time T2* is 218+/-27 nanoseconds measured using microwave pulses generated by such nanomagnets. The use of the nanoscale magnets to implement highly localized and energy efficient coherent quantum control can replace thermally noisy microwave circuits and demonstrate a path to scalable quantum computing and sensing with NV-defects in diamond and other spin qubits.