Rare-earth solid-state qubits

Bertaina, Sylvain; Gambarelli, Serge; Ткачук, А. М.; Kurkin, I. N.; Малкин, Б. З.; Stepanov, Anatole; Barbara, B.

doi:10.1038/nnano.2006.174

Cited by 213 publications

(188 citation statements)

References 31 publications

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“…Measurement of the spin relaxation time t 2 in Cr 7 Ni was subsequently reported and found to be interestingly large 15,16 ; however, the important Rabi quantum oscillations were not observed, probably because electronic and nuclear degrees of freedom were too strongly linked to each other. As these oscillations have until now only been observed in non-molecular spin systems (see, for example, refs [17][18][19][20], it has remained an open question whether quantum oscillations could in principle be realized in molecular magnets 7,8 . This question is now answered by our observation of quantum oscillations of the Rabi type in V 15 .…”

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Quantum oscillations in a molecular magnet

Bertaina

Gambarelli

Mitra

et al. 2008

Nature

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The term 'molecular magnet' generally refers to a molecular entity containing several magnetic ions whose coupled spins generate a collective spin, S (ref. 1). Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field [2][3][4] . There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits-'qubits', the basic building blocks of a quantum computer-based on molecular magnets [5][6][7][8] . But strong decoherence 9 must be overcome if the envisaged applications are to become practical. Here we report the observation and analysis of Rabi oscillations (quantum oscillations resulting from the coherent absorption and emission of photons driven by an electromagnetic wave 10 ) of a molecular magnet in a hybrid system, in which discrete and wellseparated magnetic V IV 15 clusters are embedded in a self-organized non-magnetic environment. Each cluster contains 15 antiferromagnetically coupled S 5 1/2 spins, leading to an S 5 1/2 collective ground state [11][12][13] . When this system is placed into a resonant cavity, the microwave field induces oscillatory transitions between the ground and excited collective spin states, indicative of longlived quantum coherence. The present observation of quantum oscillations suggests that low-dimension self-organized qubit networks having coherence times of the order of 100 ms (at liquid helium temperatures) are a realistic prospect.In the context of quantum computing, it was recently discussed how the decoherence of molecular magnet spin quantum bits could be suppressed, with reference to the discrete low spin clusters V 15 and Cr 7 Ni (ref. 7; see also refs 8 and 14). In both systems, their low spin states cause weak environmental coupling 7 , making them candidates for the realization of a long-lived quantum memory. Measurement of the spin relaxation time t 2 in Cr 7 Ni was subsequently reported and found to be interestingly large 15,16 ; however, the important Rabi quantum oscillations were not observed, probably because electronic and nuclear degrees of freedom were too strongly linked to each other. As these oscillations have until now only been observed in non-molecular spin systems (see, for example, refs 17-20), it has remained an open question whether quantum oscillations could in principle be realized in molecular magnets 7,8 . This question is now answered by our observation of quantum oscillations of the Rabi type in V 15 . The main reason for this success lies in the fact that the important pairwise decoherence mechanism 7,8 associated with dipolar interactions could be strongly reduced.Before discussing the observed quantum oscillations, we first briefly describe the magnetic/electronic structure of the V IV 15 species as determined experimentally. Following the synthesis of the ...

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confidence: 99%

Quantum oscillations in a molecular magnet

Bertaina

Gambarelli

Mitra

et al. 2008

Nature

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320

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“…The standard spin-control technique is electron spin resonance (ESR) driven by ac magnetic fields B ac (t) [8,16,17,18]. For manipulation on the time scale of 1 ns (Rabi frequency Ω R ∼ 10 9 s −1 ) B ac should be of the order of 10 −2 T, which, however, is difficult to achieve.…”

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Spin-Electric Coupling in Molecular Magnets

Troiani²,

et al. 2008

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We study the triangular antiferromagnet Cu3 in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spin-electric coupling caused by an interplay between spin exchange, spin-orbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spin-electric effects. [5,6,7], or the decoherence and the transition from quantum to classical behavior [8]. SMMs with antiferromagnetic coupling between neighboring spins are especially promising for the encoding and manipulation of quantum information [9,10,11,12], for they act as effective two-level systems, while providing additional auxiliary states that can be exploited for performing quantum gates, even in the presence of untunable couplings between the qubits [13]. Intra-and inter-molecular couplings of SMMs can be engineered by molecular and supra-molecular chemistry [14], enabling a bottom-up design of molecule-based devices [15].While the properties of SMMs can be modfied during the synthesis, control on the time scales required for quantum information processing remains a challenge. The standard spin-control technique is electron spin resonance (ESR) driven by ac magnetic fields B ac (t) [8,16,17,18]. For manipulation on the time scale of 1 ns (Rabi frequency Ω R ∼ 10 9 s −1 ) B ac should be of the order of 10 −2 T, which, however, is difficult to achieve. The spatial resolution of 1 nm, required for addressing a single molecule, is also prohibitively small. At these spatial and temporal scales, the electric control is preferable, because strong electric fields can be applied to small regions by using, for example, STM tips [19,20,21]. Also, the quantized electric field inside a microwave cavity can be used [22,23,24,25] to control single qubits and to induce coupling between them even if they are far apart.Here we identify and study an efficient spin-electric coupling mechanism in SMMs which is based on an interplay of spin exchange, spin-orbit interaction (SOI), and lack of inversion symmetry. Spin-electric effects induced solely by SOI [26] have been proposed [27] and experimentally demonstrated [28] in quantum dots. However, these SOI effects scale with the system size L as L 3 [27], making them irrelevant for the much smaller SMMs. Thus, additional ingredients-such as broken symmetriesmust be present in SMMs for an efficient coupling between spin and applied electric field.In the following, we demonstrate the possibility of such spin-electric effects in SMMs by focusing on a specific example, namely an equilateral spin triangle, Cu 3 [29]. In this SMM, the low energy states exhibit a chiral spin texture and, due to the absence of inversion symmetry, electric fields couple states of opposite chirality. Moreover, SOI couples the chirality to the total spin, and thus an effective spin-electri...

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“…Dy 3 combines the slow dynamics of Single Molecule Magnets and the level crossing observed in antiferromagnetic rings [19,20]. Both types of systems are currently being investigated for their potential application in quantum computation [21,22,23,24] and systems with a non-magnetic nature of the ground doublet state could be used in order to reduce decoherence effects due to the fluctuation of local magnetic fields. In the ideal case when the spins lie exactly on the plane of the triangle the dynamics involving the ground doublet is however not directly accessible with magnetometry and requires to be further investigated with more sophisticated techniques, for instance using local probes like muons or neutrons.…”

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Spin Chirality in a Molecular Dysprosium Triangle: The Archetype of the Noncollinear Ising Model

et al. 2008

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Single crystal magnetic studies combined with a theoretical analysis show that cancellation of the magnetic moments in the trinuclear Dy 3+ cluster [Dy3(µ3-OH)2L3Cl(H2O)5]Cl3, resulting in a non-magnetic ground doublet, originates from the non-collinearity of the single ion easy axes of magnetization of the Dy 3+ ions that lie in the plane of the triangle at 120 • one from each other. This gives rise to a peculiar chiral nature of the ground non-magnetic doublet and to slow relaxation of the magnetization with abrupt accelerations at the crossings of the discrete energy levels.PACS numbers: 71.79. Ej, 75.10.Jm,75.50.Xx, 75.30.Cr Molecular nanomagnetism has provided benchmark systems to investigate new and fascinating phenomena in magnetism [1,2] like magnetic memory at the molecular level [3], quantum tunneling of the magnetization [4,5], or destructive interferences in the tunneling pathways [6]. In this field rare earth ions like dysprosium(III) are currently investigated because of their large magnetic anisotropy and high magnetic moment [7]. In the course of our synthetic efforts to obtain new molecular nanomagnets based on rare-earth ions we recently obtained the trinuclear(where L is the anion of ortho-vanillin) [8], hence abbreviated as Dy 3 , which possesses an almost trigonal (C 3h ) symmetry (see Figure 1 and EPAPS for more information) [9].Preliminary powder magnetic measurements measure- Figure 1. To the best of our knowledge an experimental realization of this simple but fascinating spin structure is unprecedented.To verify our hypothesis larger crystals (of size ca. 1 mm 3 ) of one of the two compounds were grown according to [8] through very slow evaporation of the solvent. This allowed an accurate face indexing of the crystal on the X-ray diffractometer and the investigation of the magnetic anisotropy by using an horizontal sample rotator in the SQUID magnetometer (see EPAPS for experimental details) [9]. Scans in different crystallographic planes allowed us to determine the three magnetic anisotropy axes, denoted as X, Y and Z. The two structurally equivalent Dy 3 molecules in the unit cell have the Dy 3 planes almost perpendicular to Z and one side of the triangle parallel to Y (see Fig. 1). Magnetization vs. field curves along these axes are given in Figure 2a. Along X and Y a sudden jump around 8 kOe is observed while an almost linear but weaker magnetization is observed along Z. In Figure 2b the temperature dependence of the magnetization along the three axes measured at 1 kOe, and thus before the jump to saturation, are shown. The inplane X and Y directions are very similar and M tends to zero at low temperatures, confirming a non-magnetic ground state, while a weaker signal is observed along Z.The observed behaviour has been modelled using the canonical formalism of the statistical thermodynamics

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Rare-earth solid-state qubits

Cited by 213 publications

References 31 publications

Quantum oscillations in a molecular magnet

Quantum oscillations in a molecular magnet

Spin-Electric Coupling in Molecular Magnets

Spin Chirality in a Molecular Dysprosium Triangle: The Archetype of the Noncollinear Ising Model

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