Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Decoherence Window and Electron-Nuclear Cross Relaxation in the Molecular Magnet V15

Jeong Hyun Shim, Sylvain Bertaina, Serge Gambarelli, Tamoghna Mitra, Achim Müller, E. I. Baibekov, Malkin Boris Zalmanovich, Boris Tsukerblat, B. Barbara

Published Jul 31, 2012• 26 citations
Publisher

Abstract

Rabi oscillations in the ${\mathrm{V}}_{15}$ single molecule magnet embedded in the surfactant $(\mathrm{C}{\mathrm{H}}_{3}{)}_{2}[\mathrm{C}{\mathrm{H}}_{3}(\mathrm{C}{\mathrm{H}}_{2}{)}_{16}\mathrm{C}{\mathrm{H}}_{2}{]}_{2}{\mathrm{N}}^{+}$ 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 ${\mathrm{V}}_{15}$. 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 ${\mathrm{V}}_{15}$, should also take place, e.g., in ${\mathrm{Fe}}_{8}$ and ${\mathrm{Mn}}_{12}$.

DOI
10.1103/physrevlett.109.050401

Related papers

Driven spin-bath decoherence in the molecular magnet V15

Jeong Hyun Shim, Serge Gambarelli, Sylvain Bertaina +4 more

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.

arXiv:1006.4960•Mar 1, 2010•2 citations

Direct Observation of Quantum Coherence in Single-Molecule Magnets

Christoph Schlegel, Joris van Slageren, M. Manoli +2 more

Direct evidence of quantum coherence in a single-molecule magnet in a frozen solution is reported with coherence times as long as T{2}=630+/-30 ns. We can strongly increase the coherence time by modifying the matrix in which the single-molecule magnets are embedded. The electron spins are coupled to the proton nuclear spins of both the molecule itself and, interestingly, also to those of the solvent. The clear observation of Rabi oscillations indicates that we can manipulate the spin coherently, an essential prerequisite for performing quantum computations.

arXiv:0807.0303•Physical Review Letters•Oct 2, 2008•196 citations

Probing decoherence in molecular 4f qubits

Steen Honoré Hansen, Christian D. Buch, Jonatan B. Petersen +6 more

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.

Chemical Science•Jan 1, 2024•18 citations

Sustaining Rabi oscillations by using a phase-tunable image drive

Hans A. De Raedt, Seiji Miyashita, Kristel F. L. Michielsen +3 more

Abstract Recent electron spin resonance experiments on CaWO $$_4$$ 4 :Gd $$^{3+}$$ 3 + and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally. Graphic abstract

arXiv:2205.14863•The European Physical Journal B•Sep 1, 2022•4 citations

Observing Quantum Oscillation of Ground States in Single Molecular Magnet

Jiahui Yang, Ya Wang, Zixiang Wang +4 more

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.

Physical Review Letters•Jun 4, 2012•56 citations

Spin quantum dynamics in molecular magnets

John J. Henderson

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.

Journal of International Crisis and Risk Communication Research•Jan 1, 2009•0 citations
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 \ensuremathΩR{\ensuremath{\Omega}}_{R}\ensuremathΩR​ falls in the vicinity of the Larmor frequency of protons \ensuremathωN{\ensuremath{\omega}}_{N}\ensuremathωN​. The experiments are interpreted by a model showing that the damping (or Rabi) time \ensuremathτR{\ensuremath{\tau}}_{R}\ensuremathτR​ is directly associated with decoherence caused by electron-nuclear cross relaxation in the rotating reference frame. This decoherence induces energy dissipation in the range \ensuremathωN\ensuremath−\ensuremathσe<\ensuremathΩR<\ensuremathωN{\ensuremath{\omega}}_{N}\ensuremath{-}{\ensuremath{\sigma}}_{e}<{\ensuremath{\Omega}}_{R}<{\ensuremath{\omega}}_{N}\ensuremathωN​\ensuremath−\ensuremathσe​<\ensuremathΩR​<\ensuremathωN​, where \ensuremathσe{\ensuremath{\sigma}}_{e}\ensuremathσe​ 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​.
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.
Direct evidence of quantum coherence in a single-molecule magnet in a frozen solution is reported with coherence times as long as T{2}=630+/-30 ns. We can strongly increase the coherence time by modifying the matrix in which the single-molecule magnets are embedded. The electron spins are coupled to the proton nuclear spins of both the molecule itself and, interestingly, also to those of the solvent. The clear observation of Rabi oscillations indicates that we can manipulate the spin coherently, an essential prerequisite for performing quantum computations.
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.
Abstract Recent electron spin resonance experiments on CaWO 4_44​ 4 :Gd 3+^{3+}3+ 3 + and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally. Graphic abstract
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{\mathrm{V}}_{15}V15​ ($[{\mathrm{V}}_{15}^{\mathrm{IV}}{\mathrm{As}}_{6}^{\mathrm{III}}{\mathrm{O}}_{42}({\mathrm{H}}_{2}\mathrm{O}){]}^{6\ensuremath{-}}$) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time T2{T}_{2}T2​ for the ground states of the V15{\mathrm{V}}_{15}V15​ ion of collective spin S=1/2S=1/2S=1/2, in addition to confirming the previously reported results for the S=3/2S=3/2S=3/2 excited states. The oscillations of S=3/2S=3/2S=3/2 and S=1/2S=1/2S=1/2 states are of different frequencies, and so can be separately selected for purposive manipulations. T2{T}_{2}T2​ of $188\ifmmode\pm\else\textpm\fi{}4\text{ }\text{ }\mathrm{ns}$ (S=3/2S=3/2S=3/2) and $149\ifmmode\pm\else\textpm\fi{}10\text{ }\text{ }\mathrm{ns}$ (S=1/2S=1/2S=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.
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.