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The Journal of Physical Chemistry A

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates

Teffanie Goh, Riddhish Pandharkar, Laura Gagliardi

Published Aug 30, 2022• 16 citations
Publisher

Abstract

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound’s viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods (CASPT2, MC-PDFT, and HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

DOI
10.1021/acs.jpca.2c04730

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Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound’s viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods (CASPT2, MC-PDFT, and HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.
High Resolution Image Download MS PowerPoint Slide The development of molecular quantum bits (qubits) for quantum information processing is a lofty goal. While many contemporary works investigate their potential for error correction, fault-tolerance, memories, etc., there is still a lack of experimental examples of molecular multiqubit sequences. Herein, we perform a theoretical investigation of spin Hamiltonian parameter space to identify molecules that could be used to implement a 4-level superdense coding algorithm that has the least stringent requirements for experimental implementation. To do so, we analyze the zero-field splitting (ZFS) Hamiltonian of an S = 3/2 spin system to determine its effectiveness as a molecular qudit capable of performing the superdense coding circuit with X-band pulsed electron paramagnetic resonance (EPR), accounting for realistic constraints imposed by EPR spectrometers. For an S = 3/2 system, the optimal ZFS parameters are | D | ≈ 0.115 cm –1 and | E | ≈ −0.0383 cm –1 (| E / D | ≈ 0.33 approaching the rhombic limit of 1/3), with a field around 160 mT. Our findings highlight the need to maximize the rhombicity of the spin Hamiltonian for four-level molecular qudits.
Paramagnetic molecules offer unique advantages for quantum information science owing to their spatial compactness, synthetic tunability, room-temperature quantum coherence, and potential for optical state initialization and readout. However, current optically addressable molecular qubits are hampered by rapid spin-lattice relaxation (T1) even at sub-liquid nitrogen temperatures. Here we use temperature- and orientation-dependent pulsed electron paramagnetic resonance (EPR) to elucidate the negative sign of the ground-state zero-field splitting (ZFS) and assign T1 anisotropy to specific degrees of freedom in an optically addressable S = 1 Cr(IV) molecular qubit. The anisotropy displays a distinct sin2(2θ) functional form that is not observed in S = ½ Cu(II) or V(IV) microwave addressable molecular qubits. The Cr(IV) T1 anisotropy is ascribed to couplings between electron spins and rotational motion in low-energy acoustic or pseudo-acoustic phonons. Our findings suggest that rotational degrees of freedom should be suppressed to maximize the coherence temperature of optically addressable qubits.
Molecular spins represent a versatile platform for quantum information science, with the potential to offer chemically tunable, addressable qubits. However, achieving this requires understanding and mitigating quantum decoherence. This Chapter provides a theoretical overview of current state-of-the-art chemical theory connecting ab initio electronic structure with open quantum system dynamics to guide the rational design of long-lived molecular qubits. Beginning at the electronic level, multi-reference and relativistic electronic structure methods to parameterize effective spin Hamiltonians are discussed, with a primary focus on accurately capturing ggg-tensors, zero-field splitting, and hyperfine interactions. These parameters feed into models of spin-phonon and spin-spin coupling to quantify T1T_1T1​ and T2T_2T2​ relaxation across various environmental regimes. This Chapter evaluates a hierarchy of dynamical methods, ranging from factorization to matrix product state approaches, balancing computational cost against accuracy and generalizability. Ultimately, mapping these theoretical models to molecular architecture can establish design principles, such as isotopic substitution and spatial spin delocalization, to understand and extend coherence lifetimes.
Optically readable molecular spins are attractive as quantum sensors due to their nanoscale modularity, synthetic tunability, and scope for sensitive readout. In particular, photoexcited spin-triplet states in organic molecules are appealing in supporting high optical-spin contrast at room temperature. Their utility is underpinned by their coherence, which warrants a detailed understanding of it. Here, from first principles, we systematically explore the Hahn-echo decoherence of the benchmark molecular system for room-temperature optically detected spin coherence---pentacene guest molecules coupled to a para-terphenyl host. Using generalized cluster-correlation expansion methods, we investigate the mechanisms of nuclear-spin-induced decoherence from zero to high magnetic field, exploring the role of guest vs host molecules, specific nuclei, zero-field splitting interactions, and hyperfine parameters. We describe how zero-field decoherence is driven by ~6 nuclei on the guest, while high-field decoherence is driven by ~600 nuclei in the host; how the longitudinal zero-field splitting parameter, DDD, can prolong T2T_2T2​; and the magnetic-field-dependent processes which drive decoherence. These results advance our understanding of decoherence in optically readable molecular spins, providing insight for their synthetic enhancement and deployment as quantum probes.
We propose a protocol to prepare and probe dark states in a single-molecule electron spin resonance based on atomic force microscopy (ESR-AFM), thus extending existing techniques developed to address Rabi oscillations. To this end, we simulate in analogy to atomic physics the coherent manipulation of a three-level system in the V-configuration using a multifrequency magnetic field. More specifically, we consider a neutral molecule with a zero-field-split (ZFS) first excited triplet and analyze within a pump-probe scheme the dynamics of the total triplet population. In the triplet subspace, the dark state is a coherent superposition formed by two ZFS states which does not evolve in time despite a continuous resonant driving towards the third one. We characterize the properties of this state comparing it to its fully incoherent counterpart. Within a density-matrix formalism for open systems, we then compute the expected dark state signatures both for ideal scenarios and for the realistic parameterization of ESR-AFM on pentacene.