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A Chemical Approach to Molecular Spin Qubits: Decoherence and Organisation of Rare Earth Single Ion Magnets

Periodic Reporting for period 4 - DECRESIM (A Chemical Approach to Molecular Spin Qubits: Decoherence and Organisation of Rare Earth Single Ion Magnets)

Reporting period: 2020-02-01 to 2021-01-31

All electronics “runs on quantum mechanics”, from semiconductors and lasers to giant-magnetoresistance-based hard drives and memories. A number of technologies even depend very explicitly of quantum effects, from medical MRIs to quantum dots. Nevertheless, there is ample room for research, development and innovation in the next-generation quantum technologies such as quantum computation, quantum key distribution and quantum metrology, which all revolve around the coherent manipulation of the wave function and the concept of quantum two-state system or qubit. Very different physical, chemical or even biological systems can embody a qubit, but not all are equally well suited. For decades, a large number of physicists –including giants such as Haroche and Cirac– have performed experiments on trapped ions and resonant cavities, performing quantum manipulations that often were beyond the capabilities of quantum dots or SQUIDs. However, in recent times the spectacular results using Nitrogen-Vacancy (NV) defects in a diamond matrix have shown the potential of systems in the domain of Chemistry and Materials Science. In the last few years, the study of quantum effects in a chemical context is also becoming a hot topic for biophysicists. Whatever the hardware, the key to quantum technologies are basic quantum effects: quantum superposition and quantum correlations. In real systems, and specially in the solid state, these quantum states are very fragile: uncontrolled interaction with the environment destroy, they lose any existing quantum superposition and/or quantum correlations. This phenomenon, called decoherence, is a major obstacle for quantum aplications. As a result, it will not be possible to exploit the advantages of solid state systems, such as stable circuits or scalability, that would make them disruptive technologies, until we have a realistic model for decoherence. Of course, to give practical answers we will need to choose and focus on a particular qubit architecture. In our case we will focus on molecular spin qubits, as this molecular approach appears to be very promising to chemically design and manipulate spins in solid matter. A major advantage of molecular spin qubits over other candidates stems from the power of chemistry for a tailored and inexpensive synthesis of systems for their experimental study. Molecular Magnetism has produced an array of tools to study, design and fine-tune magnetic molecules, and, in particular, Single-Molecule Magnets (SMMs). Experimentally, magnetic molecules have already been used to perform experiments on coherent oscillations, and there have been recent theoretical studies about coherently manipulating a single qubit with electric fields. Note that Quantum Tunneling of the Magnetization, which can be seen as a particular case of decoherence, is the main phenomenon in SMMs. Moreover, SMMs typically have a doubly (near-)degenerate ground state with a large separation to the first excited state, that is, a qubit, and a crucial parameter to describe this qubit is the tunneling splitting breaking its near degeneracy. Thus, SMMs have a potential to be crucial in understanding and solving the decoherence problem for the Solid State, much like in the first days of Quantum Computing, NMR was key to implement the first quantum circuits. The general goal of this project will be to model decoherence in molecular spin systems of various nuclearities based on lanthanoid complexes.
We have combined theoretical and experimental work, and in-house work with international collaborations. We have studied how the coordination environment determines the crystal field Hamiltonian in lanthanoid SIMs and spin qubits. We have expanded this Hamiltonian to include the hyperfine, the coupling with the spin bath and, most challenging of all, with the molecular vibrations. We have developed methodologies to predict the time evolution of the wave function. We have theoretically guided the synthesis of lanthanoid complexes with the goal of predicting, delaying and controling magnetic relaxation, and to manipulate quantum states via pulsed EPR. We extended these coherent manipulations to multi-qubit systems and explored different chemical approaches to advance towards a more complex organisation of a high number of spins: Metal Organic Frameworks and biomolecules.
Overall, our work has been rather productive, with Web of Knowledge reporting 36 papers during the duration of the action, including several high-impact journals (first decile) such as Nature (1), Nature Chemistry (1) Chemical Science (4), Jounal of the American Chemical Society (1), Nanoscale (1) and Journal of Chemical Physics Letters (3), overall attracting over 800 citations so far.
Note that some important results of DECRESIM have not been published yet, and will significantly alter the count of high-tier papers, since the impact of our research has been increasing during these 5 years. In particular, at the end of the project we have 4 articles under peer review: one on “Quantum coherent spin-electric control in molecular nanomagnets”, another on “Spectroscopic analysis of vibronic relaxation pathways in molecular spin qubit [Ho(W5O18)2]9-”, one on “Binding Sites, Vibrations and Spin-Lattice Relaxation Times in Europium(II)-based Metallofullerene Spin Qubits” and one on “Near isotropic D4d spin qubits as nodes of a Gd(III)-based Metal-Organic Framework”. We are also about to submit a work on “Data mining, dashboard and statistical analysis: a powerful framework for the chemical design of molecular nanomagnets”.
In a few words, during this project we have found systems, conditions and recipes to achieve improved quantum coherence and molecular spin qubit organisation. Likewise, our theoretical framework is now more sophisticated and our computational capabilities are more powerful. Neighbouring fields, in particular Single Ion Magnets and Spintronics, have benefitted from our work.
Our studies of the interplay between the electron spin and molecular vibrations was challenging, but constituted a surprisingly bountiful research line, which also awoke interest in the field of Single Ion Magnets. Together with our international colleagues and competitors, we have sowed new seeds in this field and the whole community is now benefitting as a result.
Our studies of magnetic biomolecules, which was planned in the project as an exploration effort, gave unexpected fruits, and we and our collaborators are now considering paramagnetic metallopeptides not just as interesting hardware for qubit organisation, but also for spintronics. The Chirality Induced Spin Selectivity effect might even be eventually used as a mechanism to initialize qubits at room temperature.
In the last stages of the project, we employed the modern tool of Data Science including modern dashboard-style visualization to gain insights into chemical design of molecules with the desired spin dynamics:
While this is part of an existing trend, we expect our contribution to help propagate it among some of our colleagues that had perhaps not yet thought about how it could be applied to their own fields.