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arXiv:1006.4960

Driven spin-bath decoherence in the molecular magnet V15

Jeong Hyun Shim, Serge Gambarelli, Sylvain Bertaina, Tamoghna Mitra, Boris Tsukerblat, Achim Müller, B. Barbara

Published Mar 1, 2010• 2 citations
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Abstract

The measured Rabi oscillations of an ensemble of spins (here the spins 3/2 of the V15 single molecular magnet) are strongly damped by the excitation ac-field. The corresponding decoherence mechanism is attributed to an electromagnetic noise created by the dipolar spin-bath, inhomogeneously driven by the microwave field. Decoherence by electronic and nuclear spin-baths express themselves very differently vs microwave power. This decoherence mechanism should apply to all types of weakly interacting ensembles of qubits, beyond magnetism.

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The measured Rabi oscillations of an ensemble of spins (here the spins 3/2 of the V15 single molecular magnet) are strongly damped by the excitation ac-field. The corresponding decoherence mechanism is attributed to an electromagnetic noise created by the dipolar spin-bath, inhomogeneously driven by the microwave field. Decoherence by electronic and nuclear spin-baths express themselves very differently vs microwave power. This decoherence mechanism should apply to all types of weakly interacting ensembles of qubits, beyond magnetism.
Rabi oscillations in the V15{\mathrm{V}}_{15}V15​ single molecule magnet embedded in the surfactant (CH3)2[CH3(CH2)16CH2]2N+(\mathrm{C}{\mathrm{H}}_{3}{)}_{2}[\mathrm{C}{\mathrm{H}}_{3}(\mathrm{C}{\mathrm{H}}_{2}{)}_{16}\mathrm{C}{\mathrm{H}}_{2}{]}_{2}{\mathrm{N}}^{+}(CH3​)2​[CH3​(CH2​)16​CH2​]2​N+ 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{\mathrm{V}}_{15}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{\mathrm{V}}_{15}V15​, should also take place, e.g., in Fe8{\mathrm{Fe}}_{8}Fe8​ and Mn12{\mathrm{Mn}}_{12}Mn12​.
We study decoherence of central spins by a spin bath, focusing on the difference between measurement of a single central spin and measurement of a large number of central spins (as found in typical spin-resonance experiments). For a dilute spin bath, the single spin demonstrates Gaussian free-induction decay, in contrast to exponential decay characteristic of spin ensembles. A strong difference between a single spin and a spin ensemble also exists for the Rabi oscillation decay: for a repeated Rabi oscillation experiment, suppression of decoherence happens for a single spin while acceleration takes place for a spin ensemble. The mathematical origin of such behavior is similar to quantum Zeno/anti-Zeno effects.
Decoherence mechanisms in crystals of weakly anisotropic magnetic molecules, such as V15, are studied. We show that an important decohering factor is the rapid thermal fluctuation of dipolar interactions between magnetic molecules. A model is proposed to describe the influence of this source of decoherence. Based on the exact solution of this model, we show that at relatively high temperatures, about 0.5 K, the quantum coherence in a V15 molecule is not suppressed and, in principle, can be detected experimentally. Therefore, these molecules may be suitable prototype systems for study of physical processes taking place in quantum computers.
We develop a mathematical description of the decoherence caused by "spin baths", such as nuclear spins or magnetic impurities. In contrast to the usual oscillator bath models of quantum environments, decoherence in the spin bath can occur without any dissipation. Given the almost ubiquitous presence of nuclear spins in nature, our results have important consequences for quantum measurement theory, particularly as the decoherence mechanisms in spin baths work very differently from those in oscillator baths.
An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings, and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for long times. The loss of entanglement for the maximally entangled two-qubit states can be controlled by tuning the frequency of the rotating field. The decay rates of entanglement and purity for all the Bell states are the same when the qubits are noninteracting, and different when they are interacting.
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.