Molecular spin qubits are promising candidates for quantum technologies, but their performance is limited by decoherence arising from diverse mechanisms. The complexity of the environment makes it challenging to identify the main source of noise and target it for mitigation. Here we present a systematic experimental and theoretical framework for analyzing the mechanisms of transverse relaxation in copper(II) phthalocyanine (CuPc) diluted into diamagnetic phthalocyanine hosts. Using pulsed EPR spectroscopy together with first-principles cluster correlation expansion simulations, we quantitatively separate the contributions from hyperfine-coupled nuclear spins, spin--lattice relaxation, and electron--electron dipolar interactions. Our detailed modeling shows that both strongly and weakly coupled nuclei contribute negligibly to $T_2$, while longitudinal dipolar interactions with electronic spins, through instantaneous and spectral diffusion, constitute the main decoherence channel even at moderate spin densities. This conclusion is validated by direct comparison between simulated spin-echo dynamics and experimental data. By providing a robust modeling and experimental approach, our work identifies favorable values of the electron spin density for quantum applications, and provides a transferable methodology for predicting ensemble coherence times. These insights will guide the design and optimization of molecular spin qubits for scalable quantum devices.
Molecular spin qubits are promising candidates for quantum technologies, but their performance is limited by decoherence arising from diverse mechanisms. The complexity of the environment makes it challenging to identify the main source of noise and target it for mitigation. Here we present a systematic experimental and theoretical framework for analyzing the mechanisms of transverse relaxation in copper(II) phthalocyanine (CuPc) diluted into diamagnetic phthalocyanine hosts. Using pulsed EPR spectroscopy together with first-principles cluster correlation expansion simulations, we quantitatively separate the contributions from hyperfine-coupled nuclear spins, spin--lattice relaxation, and electron--electron dipolar interactions. Our detailed modeling shows that both strongly and weakly coupled nuclei contribute negligibly to T2, while longitudinal dipolar interactions with electronic spins, through instantaneous and spectral diffusion, constitute the main decoherence channel even at moderate spin densities. This conclusion is validated by direct comparison between simulated spin-echo dynamics and experimental data. By providing a robust modeling and experimental approach, our work identifies favorable values of the electron spin density for quantum applications, and provides a transferable methodology for predicting ensemble coherence times. These insights will guide the design and optimization of molecular spin qubits for scalable quantum devices.
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 50cm−1 dominate, whereas above 40 K, optical phonons above ~185cm−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.
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.
We herein probe the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagetic Resonance measurements at X-band (9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1 , 10^-2 and 10^-3 % doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, Tm, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields Tm is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a Tm in the range 1 – 11 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10^-3 %, and under dynamic decoupling conditions, the ratio of Tm versus the time it takes t0 implement a quantum gate, TG, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to a gate fidelity of 99.99 %, reaching thus the lower limit for implementations in Quantum Information Technologies.
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, D, can prolong T2; 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.
Optically addressable molecular triplet spins provide a chemically tunable platform for quantum application, but their coherence is often limited by interactions with surrounding spin baths. Here we demonstrate controlled suppression of nuclear-bath-induced decoherence in photoexcited triplet spins of pentacene co-crystallized in high-purity naphthalene single crystals. By hyperpolarizing the proton spin bath through triplet dynamic nuclear polarization (triplet-DNP), magnetic noise generated by the nuclear spins is suppressed, leading to an extension of the electron spin transverse coherence time. Experimentally, we observe a 25\% enhancement of the spin-echo decay time with 60% polarization of the proton spin bath. The measured scaling of the spin-echo decay time (T2) with nuclear polarization quantitatively follows the predicted dependence derived from the polarization-controlled nuclear second moment. Both the enhancement and the absolute value of the coherence time are quantitatively reproduced by cluster correlation expansion (CCE) simulations. These results establish nuclear spin hyperpolarization as a general and actively tunable approach to engineering coherence in molecular qubits. This work provides a broadly applicable design framework for high-coherence molecular and solid-state spin systems.
This dissertation is a study of the decoherence of a solid-state spin qubit, either that of a localized electron spin or a donor nucleus, caused by a nuclear spin bath relevant to semiconductor quantum computer architectures. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the qubit spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The qubit spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is motivated, developed, and tested for the spectral diffusion problem. The method is applicable to any ideal pulse sequence applied to the qubit. Dynamical decoupling sequences, which aim to prolong qubit coherence, are analyzed. In particular, concatenated dynamical decoupling sequences are shown to prolong not only the coherence time over the entire sequence but also the length of time between pulses necessary to maintain coherence. This is shown to result from successive low-order cancellations in applicable perturbative expansions with each level of concatenation. Each cancellation, however, will require the inclusion, in the cluster expansion, of increasingly large clusters to obtain the lowest-order results. These larger clusters in the lowest order often dominate decoherence and therefore invalidate, as being overly optimistic, the pair approximation as a means to study the effect of concatenated dynamical decoupling. We present numerical results from our cluster expansion technique for echoes of single (Hahn), concatenated, and periodic pulse sequences using realistic models of a localized electron in phosphorus doped Si and in a GaAs quantum dot and of a P donor nucleus in Si or GaAs. In the Si:P electron spin decoherence problem, we consider, along with spectral diffusion, the effects of anisotropic hyperfine (AHF) interactions and suggest a technique to suppress electron spin echo envelope modulations (ESEEM), an additional source of decoherence resulting from the AHF interactions. Our calculations for the Si:P Hahn echoes, including the effects of both anisotropic hyperfine interactions and spectral diffusion, are in excellent agreement with experimental results. Our calculations of concatenated pulse sequence echoes offer important predictions for the effectiveness of a promising strategy to preserve qubit coherence in semiconductor quantum computer architectures.