The Jiang Group works in the field of molecular magnetism and focuses on the quantum coherence manipulation of magnetic molecules and EPR spectroscopy. We use the time resolved microwave, electric field and laser to generate and manipulate the superposition state of the magnetic molecules, which are further applied to the quantum information processing, i.e., the quantum computing, the quantum sensing etc. To manipulate the spin state of the magnetic molecules, we need to detailly study the electronic structures and magnetic anisotropy of the magnetic molecules, our major tools for this purpose are high field and high frequency EPR, magnetometer and polarized neutron diffraction. The majority of our research takes an intensive interdisciplinary approaches to hit the application of magnetic molecules in quantum technology.

（1）Electronic Structures and Magnetic Anisotropy of Magnetic Molecules

Whether applying magnetic molecules to classical bits for information storage or qubits for quantum information processing, it is necessary to understand the molecules’ electronic structures and accurately characterize their magnetic anisotropy. We have designed and synthesized a series of rare earth single ion magnets (Acc. Chem. Res., 2016, 49, 2381; Angew. Chem. Int. Ed.2010, 122, 7610), and pioneered the development of organometallic single ion magnets (J. Am. Chem. Soc.2011, 133, 4730).

Theoretically, we developed a crystal field method to predict the quantization axis of low-symmetric rare （）earth ions (Inorg. Chem. Front.2015, 2, 613). Experimentally, he developed angular resolved magnetic susceptibility determination method on the single crystal sample of coordination molecules (Struct. Bond., 2014, 164, 111; J. Am. Chem. Soc.2015, 137, 12923). Moreover, together with the collaborators, we have also directly observed the aspheric electron cloud shape of the 4f elements for the first time (Nat. Chem.2020, 12, 213), and also determined the molecular magnetic principal axis via polarized neutron diffraction (Chem.-Eur. J., 2018, 24, 16576). We have also built the frequency- and field- domain high field/frequency EPR spectrometers, with which the spin Hamiltonian parameters could be precisely determined. We have reported the direct observation of the largest zero field splitting with D = 45 cm-1 in a mononuclear Ni2+ complex (J. Am. Chem. Soc.2015, 137, 12923)

Figure 1. Methods and related publications in magnetic axes prediction and determination.

（2）Enhancement of quantum coherence and scalability of magnetic molecules

On the basis of deep understanding of molecular electronic structures, the magnetic molecules can be applied to perform the quantum information processing. The prerequisite of the quantum computation is to define the quantum bit (qubit) that processes long quantum coherence time and possibility of scalability. We proposed to protect the high spin molecules in the cage-shape structure such as fullerene, which are nonmagnetic and lack of nuclear spins. This enables the spin carriers isolated from the environmental electron and nuclear spins as well as the phonon, affording largely enhanced quantum coherence time, and the high spin nature of the molecule can scale the Hilbert space up.

We have demonstrated the above idea by encapsulating an organic radical together with three Sc³⁺ ions in a C₈₀ cage (Sc₃C₂@C₈₀), elongating the coherence time up to 70 μs at 5 K (Chem. Sci.2018, 9, 457). By encapsulating two Gd3+ ions in an azafullerene (Gd₂@C₇₉N), the molecule is stabilized in a high spin ground state S =15/2 (J. Am. Chem. Soc.2018, 10, 1123). This high spin quantum system turns out to cohere with the longest time up to 5 μs among each pair of allowed transition. More importantly, all of these observed transitions are possible to generate arbitrary quantum superposition states by diverse Rabi cycles. This is by far the highest spin system with multiple Rabi cycles. The Hilbert space dimension of 16 scales 1 qubit to 4 within one molecule and is a prominent candidate to realize Grover’s algorithm. The deep understanding of this sort of anisotropic Rabi oscillation in a high spin molecule is further demonstrated on a single crystal sample of Gd³⁺ complex with strict C₄ axis (Inorg. Chem. Front.2020,7, 3875).

Figure 2. Enhancement of quantum coherence time by cage protection protocol and the discovery of highest spin molecule with quantum coherence properties.

We have also investigated the chemical substitution effects on the quantum coherence behavior in endohedral fullerene molecules (Chem. Sci. 2020, 11, 10737). By substituting odd numbers of morpholine groups on Gd@C82, the free radical on the cage is quenched, which is able to largely enhance the quantum coherence behavior of the encapsulated Gd3+ ions as much as 50 times. It is also revealed that the spin-lattice relaxation time of the molecule is also enhanced by increasing the substitution numbers.

（3）Quantum coherent manipulations of magnetic molecules

To realize efficient, precise and high-fidelity quantum coherent manipulation on magnetic molecules, it is necessary to employ laser, electric field and microwave as the physical stimulations. It is also important to solve the quantum state initialization, scalability and high efficient manipulation problems.

Electric field manipulation of electron spin has significant advantages in terms of spatial resolution, energy consumption, and device structure complexity, but the electric-spin coupling (10^-4 Hz/(Vꞏm^-1)) is much lower than the magnetic-spin interaction (10¹⁰ Hz/T), it is difficult to achieve efficient control of the spin by the electric field. We proposed that the spin-orbit coupling (Natl. Sci. Rev., 2020, 7, 1557) and the ferroelectricity (J. Am. Chem. Soc.2022, 144, 8605) can amplify the interaction between the electron spin and the external electric field, thereby achieving low-voltage control of the spin. In Ce:YAG, we increased the electric-spin coupling by 4 orders (1 Hz/(Vꞏm-1)), and successfully realized an efficient and controllable quantum phase shift gate, the quantum bang-bang control, quantum Zeno effect and the Deutsch-Jozsa quantum algorithm.

Figure 3. Electric-field coherent manipulation of electron spin

We also initialized the excited triplet spin state of C₇₀ by laser via intersystem crossing, and the three-eigenstate superposition state of the molecular system was prepared for the first time (npj Quant. Infor., 2021, 7, 32). The density matrices of this superposition state were determined by tomography approach, and the fidelity was determined to be 89.0%. More interestingly, the quantum phase interference behavior was also demonstrated for the first time. It is worth noting that this interference can only be observed in high spin system, where there is more than one quantum phase. This illustrates that the high spin molecules have much richer connotations than those of traditional physical systems.

Figure 4. Discovery of quantum phase interference in the excited state of C₇₀.

To further demonstrate the power of high spin molecular qudits, We have recently demonstrated the multilevel quantum coherence manipulation in ⁴S_3/2 N@C₆₀ molecules (Angew. Chem. Int. Ed.2022, 61, e202115263). The original molecule is of Ih symmetry and the zero-field splitting vanishes. By modifying the carbon cage, a small anisotropy is introduced and the molecule can be well aligned in the liquid crystal, enabling the distinctive electron transition selectivity. Based on the above chemical engineering, the spinor behavior as well as the Berry phase of the electron is fully demonstrated in the molecular system for the first time.

Figure 5. Electronic structure and spin manipulation in N@C₆₀.

Since the N@C₆₀ molecules have four electronic energy levels, and each one are further divided into three sublevels by hyperfine interaction. Therefore, the electronic levels are divided into three groups by hyperfine, and each group can play a role as one of the quantum computing core. We can process identical or different tasks in these cores(Angew. Chem. Int. Ed.2023, 62, e202212939). If the tasks are identical, this is the idea of quantum error correction, if the tasks are different, this is the muti-task. The quantum error correction was demonstrated with the Deutsch Jozsa algorithm, and the multi-task was achieved with applying the X-gate and Z-gate simultaneously from different channels.