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arXiv:2312.01205 · Physical Review Letters

Understanding Central Spin Decoherence Due to Interacting Dissipative Spin Baths

Mykyta Onizhuk, Yuxin Wang, Jonah Nagura, Aashish A. Clerk, Giulia Galli

Published Jun 18, 2024• 17 citations
arXivHTMLPDF

Abstract

We propose a new approach to simulate the decoherence of a central spin coupled to an interacting dissipative spin bath with cluster-correlation expansion techniques. We benchmark the approach on generic 1D and 2D spin baths and find excellent agreement with numerically exact simulations. Our calculations show a complex interplay between dissipation and coherent spin exchange, leading to increased central spin coherence in the presence of fast dissipation. Finally, we model near-surface nitrogen-vacancy centers in diamond and show that accounting for bath dissipation is crucial to understanding their decoherence. Our method can be applied to a variety of systems and provides a powerful tool to investigate spin dynamics in dissipative environments.

DOI
10.1103/physrevlett.132.250401

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We propose a new approach to simulate the decoherence of a central spin coupled to an interacting dissipative spin bath with cluster-correlation expansion techniques. We benchmark the approach on generic 1D and 2D spin baths and find excellent agreement with numerically exact simulations. Our calculations show a complex interplay between dissipation and coherent spin exchange, leading to increased central spin coherence in the presence of fast dissipation. Finally, we model near-surface nitrogen-vacancy centers in diamond and show that accounting for bath dissipation is crucial to understanding their decoherence. Our method can be applied to a variety of systems and provides a powerful tool to investigate spin dynamics in dissipative environments.
We investigate nitrogen-vacancy center (NV) ensembles in diamond under the influence of strongly correlated electron-spin baths. We thoroughly calculate the decoherence properties of the NV central spin for bath concentrations of 0.1–1000.1\text{--}1000.1–100 ppm using the cluster-correlation expansion (CCE) method. We systematically analyze possible origins of the significant deviations in the values of the T2{T}_{2}T2​ coherence time reported in the literature. We demonstrate that significant variations can originate from the choice of averaging and fitting procedures used for the ensemble average and we point out the respective aspects that need to be considered when comparing the various theoretical studies. Our study may inspire readers to perform reliable simulations on the central spin problem. It provides an understanding and interpretation of the outcome parameters describing the dynamics of the local bath spins.
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.
Due to interest in both solid state based quantum computing architectures and the application of quantum mechanical systems to nanomagnetometry, there has been considerable recent attention focused on understanding the microscopic dynamics of solid state spin baths and their effects on the coherence of a controllable, coupled central electronic spin. Many analytic approaches are based on simplified phenomenological models in which it is difficult to capture much of the complex physics associated with this system. Conversely, numerical approaches reproduce this complex behaviour, but are limited in the amount of theoretical insight they can provide. Using a systematic approach based on the spatial statistics of spin bath constituents, we develop a purely analytic theory for the central spin decoherence problem of Nitrogen Vacancy centres in diamond that reproduces the experimental and numerical results found in the literature, whilst correcting a number of limitations and inaccuracies associated with existing analytical approaches.
The study of spin decoherence is often performed by assuming that spin-phonon interactions lead to relaxation at high temperatures, and spin-spin dipolar interactions instead contribute to pure dephasing at low temperatures. This has resulted in the neglect of spin relaxation due to spin-spin dipolar interactions and its influence on decoherence at low temperatures. For a complete understanding of low temperature spin dynamics, it is then imperative to focus also on the latter mechanism. One such method which has shown great promise in the efficient calculation of central spin dynamics due to spin-spin dipolar interactions with a surrounding spin bath is the Cluster-Correlation Expansion (CCE). An extension of this method through the explicit inclusion of the central spin degrees of freedom, known as the generalized Cluster-Correlation Expansion (gCCE) is capable of simulating the transfer of energy from the central spin into the bath, and thus could have the potential to investigate spin relaxation in this setting. In this work, we show that gCCE, in its standard form, is insufficient for providing even a qualitatively accurate description of spin-spin relaxation. A full mathematical deconstruction of the underlying theory of gCCE clearly points to the origin of such a breakdown and provides a starting point for its potential future resolution.
The clock transitions (CTs) or optimal working points (OWPs) of central qubits have long coherence times because their frequency fluctuations vanish in the linear order of external field noise (such as Overhauser fields from nuclear spin baths). Therefore, CTs (or OWPs) are useful for quantum technologies. Also, the quadratic dependence of frequencies on noises makes the CT decoherence an interesting physics problem. Thus we are motivated to study the decoherence of CTs. We consider noise from spin baths, which is one of the most relevant mechanisms of qubit decoherence. Various quantum many-body methods have been developed to study the decoherence of a central spin in spin baths. In particular, the cluster-correlation expansion (CCE) systematically accounts for the many-body correlations that cause the central spin decoherence. However, the CCE cannot be straightforwardly applied to CTs in spin baths, for the expansion may fail to converge due to the effective long-range interactions resulting from the quadratic term of the noise (e.g., the second-order interaction mediated by hyperfine interactions for a nuclear spin bath). In this work, we develop a modified CCE method to tackle this class of decoherence problems. By diagonalizing the central spin Hamiltonian for each bath eigenstate of the hyperfine interaction, we find that the effects of long-range interactions are absorbed as fluctuations of central spin eigenenergies in the form of single-spin correlations. We apply the method to two important systems, namely, nitrogen vacancy center electron spins in near zero magnetic field and the singlet-triplet transition of two electrons in a double quantum dot. The numerical simulation shows that the modified CCE converges rapidly for the CTs. This modified cluster correlation expansion provides a nonperturbative approach to treating the central spin mediated long-range interactions in central spin decoherence problems.
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.