Electric field manipulation enhanced by strong spin-orbit coupling: promoting rare-earth ions as qubits

Coherent spin-control of S = 1 vanadium and molybdenum complexes

The burgeoning field of quantum sensing hinges on the creation and control of quantum bits. To date, the most well-studied quantum sensors are optically active, paramagnetic defects residing in crystalline hosts. We previously developed analogous optically addressable molecules featuring a ground-state spin-triplet centered on a Cr4+ ion with an optical-spin interface. In this work, we evaluate isovalent V3+ and Mo4+ congeners, which offer unique advantages, such as an intrinsic nuclear spin for V3+ or larger spin-orbit coupling for Mo4+, as optically addressable spin systems. We assess the ground-state spin structure and dynamics for each complex, illustrating that all of these spin-triplet species can be coherently controlled. However, unlike the Cr4+ derivatives, these pseudo-tetrahedral V3+ and Mo4+ complexes exhibit no measurable emission. Coupling absorption spectroscopy with computational predictions, we investigate why these complexes exhibit no detectable photoluminescence. These cumulative results suggest that design of future V3+ complexes should target pseudo-tetrahedral symmetries using bidentate or tridentate ligand scaffolds, ideally with deuterated or fluorinated ligand environments. We also suggest that spin-triplet Mo4+, and by extension W4+, complexes may not be suitable candidate optically addressable qubit systems due to their low energy spin-singlet states. By understanding the failures and successes of these systems, we outline additional design features for optically addressable V- or Mo-based molecules to expand the library of tailor-made quantum sensors.

Electrically Induced Crystal Field Distortion in a Ferroelectric Perovskite Revealed by Electron Paramagnetic Resonance

The magnetoelectric material has attracted multidisciplinary interest in the past decade for its potential to accommodate various functions. Especially, the external electric field can drive the quantum behaviors of such materials via the spin-electric coupling effect, with the advantages of high spatial resolution and low energy cost. In this work, the spin-electric coupling effect of Mn2+-doped ferroelectric organic-inorganic hybrid perovskite [(CH3)3NCH2Cl]CdCl3 with a large piezoelectric effect was investigated. The electric field manipulation efficiency for the allowed transitions was determined by the pulsed electron paramagnetic resonance. The orientation-included Hamiltonian of the spin-electric coupling effect was obtained via simulating the angle-dependent electric field modulated continuous-wave electron paramagnetic resonance. The results demonstrate that the applied electric field affects not only the principal values of the zero-field splitting tensor but also its principal axis directions. This work proposes and exemplifies a route to understand the spin-electric coupling effect originating from the crystal field imposed on a spin ion being modified by the applied electric field, which may guide the rational screening and designing of hybrid perovskite ferroelectrics that satisfy the efficiency requirement of electric field manipulation of spins in quantum information applications.

Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

A Trinuclear High-Spin Iron(III) Complex with a Geometrically Frustrated Spin Ground State Featuring Negligible Magnetic Anisotropy and Antisymmetric Exchange

The trinuclear high-spin iron(III) complex [Fe₃Cl₃(saltag^Br)(py)₆]ClO₄ {H₅saltag^Br = 1,2,3-tris[(5-bromo-salicylidene)amino]guanidine} was synthesized and characterized by several experimental and theoretical methods. The iron(III) complex exhibits molecular 3-fold symmetry imposed by the rigid ligand backbone and crystallizes in trigonal space group P3̅ with the complex cation lying on a crystallographic C₃ axis. The high-spin states (S = ⁵/₂) of the individual iron(III) ions were determined by Mößbauer spectroscopy and confirmed by CASSCF/CASPT2 ab initio calculations. Magnetic measurements show an antiferromagnetic exchange between the iron(III) ions leading to a geometrically spin-frustrated ground state. This was complemented by high-field magnetization experiments up to 60 T, which confirm the isotropic nature of the magnetic exchange and negligible single-ion anisotropy for the iron(III) ions. Muon-spin relaxation experiments were performed and further prove the isotropic nature of the coupled spin ground state and the presence of isolated paramagnetic molecular systems with negligible intermolecular interactions down to 20 mK. Broken-symmetry density functional theory calculations are consistent with the antiferromagnetic exchange between the iron(III) ions within the presented trinuclear high-spin iron(III) complex. Ab initio calculations further support the absence of appreciable magnetic anisotropy (D = 0.086, and E = 0.010 cm^-1) and the absence of significant contributions from antisymmetric exchange, as the two Kramers doublets are virtually degenerate (ΔE = 0.005 cm^-1). Therefore, this trinuclear high-spin iron(III) complex should be an ideal candidate for further investigations of spin-electric effects arising exclusively from the spin chirality of a geometrically frustrated S = ¹/₂ spin ground state of the molecular system.

Multiprocessing Quantum Computing through Hyperfine Couplings in Endohedral Fullerene Derivatives

Magnetic molecules have shown great potential in quantum information processing due to the chemical tunablity of their quantum behaviors. Chemical derivatives of endohedral nitrogen fullerenes with long coherence time and rich energy levels were synthesized and studied to demonstrate the ability of multiprocessing in quantum information using electron magnetic resonance. After initialization of the 12-levelled spin system, subgroups of spin energy levels coursed by the hyperfine couplings can be selectively manipulated. The cooperatively combining of the parallel calculations enabled quantum error correction, increasing the correct rate by up to 17.82 %. Also, different subgroups of transitions divided by hyperfine coupling can be treated as independent qubits, and multi-task quantum computing were realized by performing Z-gate and X-gate simultaneously, which accelerates the overall gating speed.

First-principles study of the electronic and optical properties of Ho[Formula: see text] impurities in single-layer tungsten disulfide

The electronic and optical properties of single-layer (SL) tungsten disulfide (WS[Formula: see text]) in the presence of substitutional Holmium impurities (Ho[Formula: see text]) are studied. Although Ho is much larger than W, density functional theory (DFT) including spin-orbit coupling is used to show that Ho:SL WS[Formula: see text] is stable. The magnetic moment of the Ho impurity is found to be 4.75[Formula: see text] using spin-dependent DFT. The optical selection rules identified in the optical spectrum match exactly the optical selection rules derived by means of group theory. The presence of neutral Ho[Formula: see text] impurities gives rise to localized impurity states (LIS) with f-orbital character in the band structure. Using the Kubo-Greenwood formula and Kohn-Sham orbitals we obtain atom-like sharp transitions in the in-plane and out-of-plane components of the susceptibility tensor, Im[Formula: see text] and Im[Formula: see text]. The optical resonances are in good agreement with experimental data.

Spin-Electric Coupling with Anisotropy-Induced Vanishment and Enhancement in Molecular Ferroelectrics

Manipulating quantum properties by electric fields using spin-electric coupling (SEC) effects promises spatial addressability. While several studies about inorganic materials showing the SEC functionality have been reported, the vastly tunable crystal structures of molecular ferroelectrics provide a range of rationally designable materials yet to be exploited. In this work, Mn²⁺-doped molecular ferroelectrics are chosen to experimentally demonstrate the feasibility of achieving the quantum coherent SEC effect in molecular ferroelectrics for the first time. The electric field pulse applied between Hahn-echo pulses in electron paramagnetic resonance (EPR) experiments causes controllable phase shifts via manipulating of the zero-field splitting (ZFS) of the Mn(II) ions. Detailed investigations of the aMn crystal showed unexpected SEC vanishment and enhancement at different crystal orientations, which were elucidated by studying the spin Hamiltonian and magnetic anisotropy. With the enhanced SEC efficiency being achieved (0.68 Hz m/V), this work discovers an emerging material library of molecular ferroelectrics to implement coherent quantum control with selective and tunable SEC effects toward highly scalable quantum gates.

Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy

A cobalt(II)-based spin triangle shows a significant spin-electric coupling. [Co3 (pytag)(py)6 Cl3 ]ClO4 ⋅3 py crystallizes in the acentric monoclinic space group P21 . The intra-triangle antiferromagnetic interaction, of the order of ca. -15 cm-1 (H=-JSa Sb ), leads to spin frustration. The two expected energy-degenerate ground doublets are, however, separated by a few wavenumbers, as a consequence of magnetic anisotropy and deviations from threefold symmetry. The Co3  planes of symmetry-related molecules are almost parallel, allowing for the determination of the spin-electric properties of single crystals by EFM-ESR spectroscopy. The spin-electric effect detected when the electric field is applied in the Co3  plane was revealed by a shift in the resonance field. It was quantified as ΔgE /E=0.11×10-9  m V-1 , which in terms of frequency corresponds to approximately 0.3 Hz m V-1 . This value is comparable to what was determined for a Cu3  triangle despite the antiferromagnetic interaction being 20 times larger for the latter.

Halogen regulation triggers NLO and dielectric dual switches in hybrid compounds with green fluorescence

An effective strategy of using halogens to modify organic–inorganic hybrid materials to obtain NLO switching characteristics, which is expected to be used for the directional adjustment of NLO switch activity.

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case

The coherence time of the 17-electron, mixed sandwich complex [CpTi(cot)], (η⁸ -cyclooctatetraene)(η⁵ -cyclopentadienyl)titanium, reaches 34 μs at 4.5 K in a frozen deuterated toluene solution. This is a remarkable coherence time for a highly protonated molecule. The intramolecular distances between the Ti and H atoms provide a good compromise between instantaneous and spin diffusion sources of decoherence. Ab initio calculations at the molecular and crystal packing levels reveal that the characteristic low-energy ring rotations of the sandwich framework do not yield a too detrimental spin-lattice relaxation because of their small spin-phonon coupling. The volatility of [CpTi(cot)] and the accessibility of the semi-occupied, non-bonding d z 2 orbital make this neutral compound an ideal candidate for single-qubit addressing on surface and quantum sensing in combination with scanning probe microscopy.

Orientation mapping of Rabi frequencies in a rare-earth molecular qudit

Utilizing the S = 7/2 4f spin and the D₄ symmetry of a Gd(iii) complex, we propose and demonstrate an eight-leveled rare-earth molecular qudit, which can be coherently manipulated between adjacent energy levels with precompiled pulse durations.