Electronic spin superposition states enable nanoscale sensing through their sensitivity to the local environment, yet their sensitivity to vibrational motion also limits their coherence times. In molecular spin systems, chemical tunability and atomic-scale resolution are accompanied by a dense, thermally accessible phonon spectrum that introduces efficient spin relaxation pathways. Despite extensive theoretical work, there is little experimental consensus on which vibrational energies dominate spin relaxation or how molecular structure controls spin-phonon coupling (SPC). We present a fully experimental method to quantify SPC coefficients by combining temperature-dependent vibrational spectra from inelastic neutron scattering with spin relaxation rates measured by electron paramagnetic resonance. We apply this framework to two model S = 1/2 systems, copper(II) phthalocyanine (CuPc) and copper(II) octaethylporphyrin (CuOEP). Two distinct relaxation regimes emerge: below 40 K, weakly coupled lattice modes below
50 cm−1 dominate, whereas above 40 K, optical phonons above ~
185 cm−1 become thermally populated and drive relaxation with SPC coefficients nearly three orders of magnitude larger. Structural distortions in CuOEP that break planar symmetry soften the crystal lattice and enhance anharmonic scattering, but also raise the energy of stretching modes at the molecular core where the spins reside. This redistributes vibrational energy toward the molecular periphery and out of plane, ultimately reducing SPC relative to CuPc and enabling room-temperature spin coherence in CuOEP. Although our method does not provide mode-specific SPC coefficients, it quantifies contributions from distinct spectral regions and establishes a broadly applicable, fully experimental link between crystal structure, lattice dynamics, and spin relaxation.
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.
The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time (
T1). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of
T1 without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.
Optical interfaces that connect long-lived spin qubits to photons are a central requirement for quantum networking and distributed quantum information processing. Currently, solid-state atomic defects are leading candidates due to their inherent spin and optical coherence. Building on these advancements, synthetically tailored molecular systems represent a fundamental change in the field, utilizing precise atomic control and consistent bottom-up assembly. However, the lack of a robust spin-photon interface combining bright fluorescence, high spectral stability, and the persistent spin lifetimes inherent to ground-state systems has prohibited the detection of individual molecular qubits. Here we show that a triplet ground state carbene molecule, embedded within a structurally matched host crystal, functions as a robust spin-photon interface with single-molecule addressability. The system exhibits narrow zero-phonon lines, spectral stability over more than an hour, spin-selective optical transitions and single-molecule optically detected magnetic resonance. Coherent control yields millisecond-scale dynamical-decoupling coherence and tens-of-milliseconds spin relaxation at a temperature of 4.5 K. These results establish molecular qubits as a viable platform for single-emitter quantum optics while preserving the advantages of bottom-up chemical design and processable materials.
Solid-state molecular qubits with open-shell ground states have great potential for addressability, scalability, and tunability, but understanding the fundamental limits of quantum coherence in these systems is challenging due to the complexity of the qubit environment. To address this, we develop a random Hamiltonian approach where the molecular
g-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic
g-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation
T1 and dephasing
T2 times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes,
1/T temperature scaling and
1/B3 magnetic field scaling of
T1 are established using atomistic bath correlation functions. Atomistic
T1 predictions overestimate the available experimental data by orders of magnitude. Quantitative agreement with measurements at all magnetic fields is restored by introducing a magnetic field noise model to describe lattice nuclear spins, with field-dependent noise amplitude in the range
δB∼10μT−1mT for the copper porphyrin system. We show that while
T1 scales as
1/B experimentally due to a combination of spin-lattice and magnetic noise contributions,
T2 scales strictly as $ 1/B^2$ due to low-frequency dephasing processes associated with magnetic field noise. Our work demonstrates the potential of dynamical methods for modeling the open quantum system dynamics of molecular spin qubits.
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.