Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM ${\mathrm{V}}_{15}$ ($[{\mathrm{V}}_{15}^{\mathrm{IV}}{\mathrm{As}}_{6}^{\mathrm{III}}{\mathrm{O}}_{42}({\mathrm{H}}_{2}\mathrm{O}){]}^{6\ensuremath{-}}$) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time ${T}_{2}$ for the ground states of the ${\mathrm{V}}_{15}$ ion of collective spin $S=1/2$, in addition to confirming the previously reported results for the $S=3/2$ excited states. The oscillations of $S=3/2$ and $S=1/2$ states are of different frequencies, and so can be separately selected for purposive manipulations. ${T}_{2}$ of $188\ifmmode\pm\else\textpm\fi{}4\text{ }\text{ }\mathrm{ns}$ ($S=3/2$) and $149\ifmmode\pm\else\textpm\fi{}10\text{ }\text{ }\mathrm{ns}$ ($S=1/2$) are much less than ${T}_{1}\ensuremath{\sim}12\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ and are further extendible via various approaches for qubit implementations.
Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM V15 ([V15IVAs6IIIO42(H2O)]6\ensuremath−) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time T2 for the ground states of the V15 ion of collective spin S=1/2, in addition to confirming the previously reported results for the S=3/2 excited states. The oscillations of S=3/2 and S=1/2 states are of different frequencies, and so can be separately selected for purposive manipulations. T2 of 188\ifmmode±\else\textpm\fi4ns (S=3/2) and 149\ifmmode±\else\textpm\fi10ns (S=1/2) are much less than T1\ensuremath∼12\ensuremathμs and are further extendible via various approaches for qubit implementations.
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.
Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like relaxation of S(z) with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.
In this work we study theoretically the coupling of single-molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main result of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (~ µs), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.
Rabi oscillations in the V15 single molecule magnet embedded in the surfactant (CH3)2[CH3(CH2)16CH2]2N+ have been studied at different microwave powers. An intense damping peak is observed when the Rabi frequency ${\ensuremath{\Omega}}_{R}$ falls in the vicinity of the Larmor frequency of protons ${\ensuremath{\omega}}_{N}$. The experiments are interpreted by a model showing that the damping (or Rabi) time ${\ensuremath{\tau}}_{R}$ is directly associated with decoherence caused by electron-nuclear cross relaxation in the rotating reference frame. This decoherence induces energy dissipation in the range ${\ensuremath{\omega}}_{N}\ensuremath{-}{\ensuremath{\sigma}}_{e}<{\ensuremath{\Omega}}_{R}<{\ensuremath{\omega}}_{N}$, where ${\ensuremath{\sigma}}_{e}$ is the mean superhyperfine field induced by protons at V15. Weaker decoherence without dissipation takes place outside this window. Specific estimations suggest that this rapid cross relaxation in a resonant microwave field, observed for the first time in V15, should also take place, e.g., in Fe8 and Mn12.
In this work we study theoretically the coupling of single-molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main result of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (∼ μ s), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.
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 g-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic g-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation T1 and dephasing T2 times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, 1/T temperature scaling and 1/B3 magnetic field scaling of T1 are established using atomistic bath correlation functions. Atomistic T1 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∼10μT−1mT for the copper porphyrin system. We show that while T1 scales as 1/B experimentally due to a combination of spin-lattice and magnetic noise contributions, T2 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.