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Scientific Reports

Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

Jeson Chen, Oliver Y. Chen, Huan‐Cheng Chang

Published Aug 11, 2021• 6 citations
Publisher

Abstract

Abstract Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV−) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV− spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV− centers, which have shown promising applications in quantum computing and quantum metrology.

DOI
10.1038/s41598-021-95722-z

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Abstract Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV−) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV− spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV− centers, which have shown promising applications in quantum computing and quantum metrology.
Hybrid quantum systems, which combines the advantages of different quantum systems, play an essential role in the realisation of quantum computation, especially as quantum memory. This thesis discusses the very promising hybrid quantum system based on the ensemble of negatively charged nitrogen-vacancy centers (NV-centers) in diamond and superconducting microwave cavities. The decoherence of this system, due to the inhomogeneous spin broadening, seems to be the major obstacle of utilising the NV-centers as a quantum information storage. This works focuses on the study of the dynamics of our NV-center spin ensemble strongly coupled to a superconducting resonator driven by pulse sequences with a carrier frequency equaling the cavity frequency. A precise knowledge of the spin broadening, which has a non-Lorentzian distribution, led to the observation of the so called 'cavity protection effect'. Furthermore this work demonstrates the enhancement of the damped Rabi oscillations between the spin ensemble and the cavity mode through appropriate chosing of the microwave pulses, which could change in the order of two magnitudes. Last we also confirmed the theoretical analysis of the crossover from markovian to non-markovian dynamics for our system, which is achieved for increasing coupling strength.
We present results of our research on two-field (two-frequency) microwave spectroscopy in nitrogen-vacancy ($\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$) color centers in a diamond. Both fields are tuned to transitions between the spin sublevels of the $\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$ ensemble in the 3A2{}^{3}{A}_{2}3A2​ ground state (one field has a fixed frequency while the second one is scanned). Particular attention is focused on the case where two microwave fields drive the same transition between two $\mathrm{N}{\mathrm{V}}^{\ensuremath{-}}$ ground state sublevels (${m}_{\mathrm{s}}=0\ensuremath{\leftrightarrow}{m}_{\mathrm{s}}=+1$). In this case, the observed spectra exhibit a complex narrow structure composed of three Lorentzian resonances positioned at the pump-field frequency. The resonance widths and amplitudes depend on the lifetimes of the levels involved in the transition. We attribute the spectra to coherent population oscillations induced by the two nearly degenerate microwave fields, which we have also observed in real time. The observations agree well with a theoretical model and can be useful for investigation of the NV relaxation mechanisms.
Quantum computing holds the potential to outperform classical computing in certain complicated tasks by leveraging qubits and their manipulation through quantum gates. A compelling platform to physically realize qubits and their control is the Nitrogen-Vacancy (NV) center in diamond, where Rabi oscillation of spin qubit enables effective quantum operations. However, a significant challenge lies in mitigating qubit decoherence caused by external factors. Hence, this paper reports on the experimental demonstration of Rabi oscillation of spin qubit in NV center in diamond, focusing on investigating the impact of magnetic field and noises. Experiments conducted using CIQTEK Diamond Quantum Computer for Education (CIQTEK is a China quantum company) reveal that the magnetic field significantly impacts the resonant frequency which must align with the microwave pulse to observe clear Rabi oscillations. However, despite careful frequency tuning, noises from several sources lead to qubit decoherence, disrupting Rabi oscillations and causing them to decay over time. These results provide insights into key factors affecting qubit performance, paving the way in developing strategies to minimize decoherence.
Dense nitrogen-vacancy spin ensembles in diamond are exciting systems for exploring novel collective spin states and for advancing quantum-limited metrology and information technology. However, severe inhomogeneous broadening usually accompanies increasing densities, making ensemble characterization and control challenging when using conventional pulsed multiresonance protocols. Here, the authors demonstrate the utility of employing a continuous-wave double-resonance scheme and of generating spin-ensemble population oscillations. Through this approach, some unexpected aspects of the inhomogeneous broadening mechanism are revealed, while coupled nuclear spins are detected at energies that are challenging to measure via conventional pulsed schemes.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.
A concept combining optics and microwave pulses with the negative charge-state of the nitrogen-vacancy (NV—) center in diamond is demonstrated through experiments that are equivalent to single-qubit gates, and decoherence for this qubit is examined. The spin levels of the ground state provide the two-level system. Optical excitation provides polarization of these states. The polarized state is operated coherently by 35 GHz microwave pulses. The final state is read out through the photoluminescence intensity. Decoherence arises from different sources for different samples. For high-pressure, high-temperature synthetic diamonds, the high concentration of substitutional N limits the phase-memory to a few μs. In a single-crystal CVD diamond, the phase memory time is at least 32 μs at 100 K. 14N is tightly coupled to the electronic spin and produces modulation of the electron–spin echo decay under certain conditions. A two-qubit gate is proposed using this nuclear spin. This demonstration provides a great deal of insight into quantum devices in the solid state with some possibility for real application.