Quantum Computing in Molecular Magnets

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 10^5, with access times as short as 10^{-10} seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.Comment: 13 pages, 2 figures, PDF, version published in Nature, typos correcte

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet

The spin-lattice relaxation rate $T_{1}^{-1}$ and NMR spectra of $^1$H in single crystal molecular magnets of Fe8 have been measured down to 15 mK. The relaxation rate $T_1^{-1}$ shows a strong temperature dependence down to 400 mK. The relaxation is well explained in terms of the thermal transition of the iron state between the discreet energy levels of the total spin S=10. The relaxation time $T_1$ becomes temperature independent below 300 mK and is longer than 100 s. In this temperature region stepwise recovery of the $^1$H-NMR signal after saturation was observed depending on the return field of the sweep field. This phenomenon is attributed to resonant quantum tunneling at the fields where levels cross and is discussed in terms of the Landau-Zener transition.Comment: 13 pages, 5 figure

Characterization of the S = 9 excited state in Fe8Br8 by Electron Paramagnetic Resonance

High Frequency electron paramagnetic resonance has been used to observe the magnetic dipole, $\Delta$ M$_s$ = $\pm$ 1, transitions in the $S = 9$ excited state of the single molecule magnet Fe$_8$Br$_8$. A Boltzmann analysis of the measured intensities locates it at 24 $\pm$ 2 K above the $S = 10$ ground state, while the line positions yield its magnetic parameters D = -0.27 K, E = $\pm$0.05 K, and B$_4^0$ = -1.3$\times$ 10$^{-6}$ K. D is thus smaller by 8% and E larger by 7% than for $S = 10$. The anisotropy barrier for $S = 9$ is estimated as 22 K,which is 25% smaller than that for $S = 10$ (29 K). These data also help assign the spin exchange constants(J's) and thus provide a basis for improved electronic structure calculations of Fe$_8$Br$_8$.Comment: 7 pages, Figs included in text, submitted to PR

Feedback Effect on Landau-Zener-Stueckelberg Transitions in Magnetic Systems

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intra-molecular couplings.Comment: 4 pages, 3 Postscript figures; paper reorganized, conclusions modifie

Phase transition between quantum and classical regimes for the escape rate of a biaxial spin system

Employing the method of mapping the spin problem onto a particle one, we have derived the particle Hamiltonian for a biaxial spin system with a transverse or longitudinal magnetic field. Using the Hamiltonian and introducing the parameter $p (\equiv (U_{max}-E)/(U_{max}-U_{min}))$ where $U_{max}$ (U_{min}) corresponds to the top (bottom) of the potential and $E$ is the energy of the particle, we have studied the first- or second-order transition around the crossover temperature between thermal and quantum regimes for the escape rate, depending on the anisotropy constant and the external magnetic field. It is shown that the phase boundary separating the first- and second-order transition and its crossover temperature are greatly influenced by the transverse anisotropy constant as well as the transverse or longitudinal magnetic field.Comment: 5 pages + 3 figures, to be published in Phys. Rev.

The interplay between single particle anisotropy and interparticle interactions in ensembles of magnetic nanoparticles

This paper aims to analyze the competition of single particle anisotropy and interparticle interactions in nanoparticle ensembles using a random anisotropy model. The model is first applied to ideal systems of non-interacting and strongly dipolar interacting ensembles of maghemite nanoparticles. The investigation is then extended to more complex systems of pure cobalt ferrite CoFe2O4 (CFO) and mixed cobalt-nickel ferrite (Co,Ni)Fe2O4 (CNFO) nanoparticles. Both samples were synthetized by the polyol process and exhibit the same particle size (DTEM 48 5 nm), but with different interparticle interaction strengths and single particle anisotropy. The implementation of the random anisotropy model allows investigation of the influence of single particle anisotropy and interparticle interactions, and sheds light on their complex interplay as well as on their individual contribution. This analysis is of fundamental importance in order to understand the physics of these systems and to develop technological applications based on concentrated magnetic nanoparticles, where single and collective behaviors coexist

Coherence Window in the dynamics of Quantum Nanomagnets

Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow field region in which both phonon and nuclear spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the $Fe$-8 nanomolecule, for $Ni$ particles, and for $Ho$ ions in $LiHo_xY_{1-z}F_4$. The reduction in the decoherence, compared to low field rates, can exceed 6 orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.Comment: 5 LaTeX pages, 3 figure

Observation of a Distribution of Internal Transverse Magnetic Fields in a Mn12-Based Single Molecule Magnet

A distribution of internal transverse magnetic fields has been observed in single molecule magnet (SMM) Mn12-BrAc in the pure magnetic quantum tunneling (MQT) regime. Magnetic relaxation experiments at 0.4 K are used to produce a hole in the distribution of transverse fields whose angle and depth depend on the orientation and amplitude of an applied transverse ``digging field.'' The presence of such transverse magnetic fields can explain the main features of resonant MQT in this material, including the tunneling rates, the form of the relaxation and the absence of tunneling selection rules. We propose a model in which the transverse fields originate from a distribution of tilts of the molecular magnetic easy axes.Comment: 4 page

Strong coupling theory for driven tunneling and vibrational relaxation

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled non-Markovian master equations. We present analytical treatments that describe the dynamics in the regime of strong system-bath coupling. Our findings are corroborated by ``ab-initio'' real-time path integral calculations.Comment: 4 LaTeX pages including 3 figure

Driving-Induced Symmetry Breaking in the Spin-Boson System

A symmetric dissipative two-state system is asymptotically completely delocalized independent of the initial state. We show that driving-induced localization at long times can take place when both the bias and tunneling coupling energy are harmonically modulated. Dynamical symmetry breaking on average occurs when the driving frequencies are odd multiples of some reference frequency. This effect is universal, as it is independent of the dissipative mechanism. Possible candidates for an experimental observation are flux tunneling in the variable barrier rf SQUID and magnetization tunneling in magnetic molecular clusters.Comment: 4 pages, 4 figures, to be published in PR