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Chemical Science

Probing decoherence in molecular 4f qubits

Steen Honoré Hansen, Christian D. Buch, Jonatan B. Petersen, Michelle Rix, Marc Ubach I. Cervera, Asger Strandfelt, Richard E. P. Winpenny, Eric J. L. McInnes, Stergios Piligkos

Published Jan 1, 2024• 18 citations
Publisher

Abstract

We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.

DOI
10.1039/d4sc05304d

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We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.
This dissertation is a study of the decoherence of a solid-state spin qubit, either that of a localized electron spin or a donor nucleus, caused by a nuclear spin bath relevant to semiconductor quantum computer architectures. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the qubit spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The qubit spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is motivated, developed, and tested for the spectral diffusion problem. The method is applicable to any ideal pulse sequence applied to the qubit. Dynamical decoupling sequences, which aim to prolong qubit coherence, are analyzed. In particular, concatenated dynamical decoupling sequences are shown to prolong not only the coherence time over the entire sequence but also the length of time between pulses necessary to maintain coherence. This is shown to result from successive low-order cancellations in applicable perturbative expansions with each level of concatenation. Each cancellation, however, will require the inclusion, in the cluster expansion, of increasingly large clusters to obtain the lowest-order results. These larger clusters in the lowest order often dominate decoherence and therefore invalidate, as being overly optimistic, the pair approximation as a means to study the effect of concatenated dynamical decoupling. We present numerical results from our cluster expansion technique for echoes of single (Hahn), concatenated, and periodic pulse sequences using realistic models of a localized electron in phosphorus doped Si and in a GaAs quantum dot and of a P donor nucleus in Si or GaAs. In the Si:P electron spin decoherence problem, we consider, along with spectral diffusion, the effects of anisotropic hyperfine (AHF) interactions and suggest a technique to suppress electron spin echo envelope modulations (ESEEM), an additional source of decoherence resulting from the AHF interactions. Our calculations for the Si:P Hahn echoes, including the effects of both anisotropic hyperfine interactions and spectral diffusion, are in excellent agreement with experimental results. Our calculations of concatenated pulse sequence echoes offer important predictions for the effectiveness of a promising strategy to preserve qubit coherence in semiconductor quantum computer architectures.
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
Molecular spin qubits are promising candidates for quantum technologies, but their performance is limited by decoherence arising from diverse mechanisms. The complexity of the environment makes it challenging to identify the main source of noise and target it for mitigation. Here we present a systematic experimental and theoretical framework for analyzing the mechanisms of transverse relaxation in copper(II) phthalocyanine (CuPc) diluted into diamagnetic phthalocyanine hosts. Using pulsed EPR spectroscopy together with first-principles cluster correlation expansion simulations, we quantitatively separate the contributions from hyperfine-coupled nuclear spins, spin--lattice relaxation, and electron--electron dipolar interactions. Our detailed modeling shows that both strongly and weakly coupled nuclei contribute negligibly to T2T_2T2​, while longitudinal dipolar interactions with electronic spins, through instantaneous and spectral diffusion, constitute the main decoherence channel even at moderate spin densities. This conclusion is validated by direct comparison between simulated spin-echo dynamics and experimental data. By providing a robust modeling and experimental approach, our work identifies favorable values of the electron spin density for quantum applications, and provides a transferable methodology for predicting ensemble coherence times. These insights will guide the design and optimization of molecular spin qubits for scalable quantum devices.
Solid-state molecular qubits with open-shell ground states have great potential for addressability, scalability, and tunability, but understanding the fundamental limits of quantum coherence in these systems is challenging due to the complexity of the qubit environment. To address this, we develop a random Hamiltonian approach where the molecular ggg-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic ggg-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation T1T_1T1​ and dephasing T2T_2T2​ times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, 1/T1/T1/T temperature scaling and 1/B31/B^31/B3 magnetic field scaling of T1T_1T1​ are established using atomistic bath correlation functions. Atomistic T1T_1T1​ predictions overestimate the available experimental data by orders of magnitude. Quantitative agreement with measurements at all magnetic fields is restored by introducing a magnetic field noise model to describe lattice nuclear spins, with field-dependent noise amplitude in the range δB∼10 μT−1 mTδB\sim 10\,μ{\rm T}- 1\,{\rm mT}δB∼10μT−1mT for the copper porphyrin system. We show that while T1T_1T1​ scales as 1/B1/B1/B experimentally due to a combination of spin-lattice and magnetic noise contributions, T2T_2T2​ scales strictly as $ 1/B^2$ due to low-frequency dephasing processes associated with magnetic field noise. Our work demonstrates the potential of dynamical methods for modeling the open quantum system dynamics of molecular spin qubits.
High Resolution Image Download MS PowerPoint Slide We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Yb III ions in Yb 0.01 Lu 0.99 (trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring Yb III centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.
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.