Electron Spin Echo Envelope Modulation at Clock Transitions in Molecular Spin Qubits

Clock transitions (CTs) have been shown to protect qubits against various sources of decoherence. Here, we present a joint experimental and theoretical investigation of the decoupling of a central electron spin qubit from the surrounding nuclear spin bath by studying the so-called Electron Spin Echo Envelope Modulation (ESEEM) effect in the vicinity of a magnetic CT. Experimentally, ESEEM spectra are collected for a HoW$_{10}$ molecular spin qubit, and suppression of the modulation at a CT is clearly demonstrated. The effect is then simulated theoretically by exact quantum time evolution using a simple model Hamiltonian of a central electron spin with an avoided Zeeman crossing coupled to a finite number of nuclear bath spins. The results reproduce key experimental observations and reveal that, due to the quadratic energy dependence on magnetic field at the avoided crossing, fluctuations of the nuclear spin bath that couple linearly to the central spin do not affect its quantum dynamics at the CT. Consequently, hyperfine coupling effectively vanishes, leading to a complete suppression of ESEEM and electron-nuclear decoherence at the CT.