Organometallic Lanthanide Complexes as Molecular Qubits with Robust Quantum Coherence Properties

There is significant current interest in the development of molecular quantum bits (MQBs) whose properties are suitable for the implementation of logic operations and algorithms. Metal complexes are promising MQB candidates due to their tunable properties and ability to form qubit arrays [1]. One impediment in using metal complexes as MQBs is the occurrence of quantum decoherence [2], a phenomenon that accelerates electron spin relaxation, reducing the longevity of the qubit and diminishing its ability to safely store and process the information carried in spins.<br/><br/>This talk will focus on how to engineer MQBs with improved coherence times. We will show that sufficiently long phase memory times allowing quantum spin manipulations even at ambient temperature are achievable in organometallic molecular systems with either <i>C</i>₃ or <i>C</i>₄ symmetry, even when the coordinated ligands are rich in nuclear spins. Examples include low-valent lanthanide and transition metal complexes bearing cyclopentadienyl derivatives, aryloxides and imides as ligands. The exceptionally long coherence times of these systems enabled mapping the spin densities that elucidate the decoherence path, with the aid of state of the art pulsed EPR methods, including HYSCORE, ESEEM, ENDOR. As an example, for [LnCp’₃][K(2.2.2-cryptand)] (Ln = Y, La or Lu; Cp’ = C₅H₄SiMe), coherent Rabi oscillations were measured, including at 300 K in a single crystal [3]. We found that the <i>pseudo</i>-<i>C₃ </i>symmetry of these systems enables direct mixing of the metal valence <i>s</i>- and <i>dz</i>² atomic orbitals, resulting in a large and near isotropic metal hyperfine interaction, with a knock-on effect of retarding electron spin <i>T</i>₁relaxation driven by spin−orbit coupling since the orbital angular momentum is largely quenched. The longer <i>T</i>₁ then does not limit <i>T</i>m, the phase memory time, and thus allows coherent manipulation of the spin to higher temperatures (up to room temperature for the Y(II) example).<br/><br/>To further deepen our understanding of quantum decoherence, we have examined using HYSCORE the effect of different substituents (R) anchored to the cyclopentadienyl rings of La(II)Cp^R systems (R = SiMe₃ or CMe₃) [4], and found that the spin−lattice relaxation time <i>T</i>₁and the electronic coherence <i>T</i>_CPMG times varies in line with the 6s-orbital character of SOMO. We measured significant spin density at the ¹H protons of Cp rings, as well as ²⁹Si of SiMe₃ groups, indicating that these nuclei participate to decoherence. Coherent spin<br/>manipulations were probed for up to eight hyperfine transitions, and the coherence times could be extended by CPMG methods up to 161 µs.<br/><br/>Reference:<br/><b>[1 ] E. </b>Moreno-Pineda, E.; D. Martins, F. Tuna, Molecules as qubits, qudits and quantum gates, in <i>SPR</i>-<i>Electron Paramagnetic Resonance: </i>2021, <i>27</i>, 146−185.<br/>[2] McAdams, A. M. Ariciu, A. Kostopulos, J. Walsh, F. Tuna, Molecular single-ion magnets based on lanthanides and actinides: Design considerations and new advances in the context of quantum technologies, <i>Coord. Chem. Rev.</i> <b>2017</b>, <i>346</i>, 216.<br/>[3] A. M. Ariciu, D. H. Woen, D. N. Huh, A. K. Kostopoulos, C. A. P. Goodwin, N. F. Chilton, E. J. L. McInnes, R. E. P. Winpenny, W. J. Evans, F. Tuna. Engineering electronic structure to prolong relaxation times in molecular qubits by minimising orbital angular momentum. <i>Nature Commun</i>. <b>2019</b>, <i>10</i>, 3330.<br/>[4] L. E Nodaraki, A.-M. Ariciu, D. N. Huh, J. Liu, D. O. T. A. Martins, F. Ortu, R. E. P. Winpenny, N. F. Chilton, E. J. L. McInnes, D. P. Mills, W. J. Evans, F. Tuna, Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qu<i>d</i>its. <i>J. Am. Chem. Soc</i>. <b>2024</b>, <i>146</i>, 15000.