Nuclear magnetic resonance (NMR) studies of sintering effects on the lithium ion dynamics in Li1.5Al0.5Ti1.5(PO4)3

Various nuclear magnetic resonance (NMR) methods are combined to study the structure and dynamics of Li1.5Al0.5Ti1.5(PO4)3 (LATP) samples, which were obtained from sintering at various temperatures between 650 and 900 °C. 6Li, 27Al, and 31P magic angle spinning (MAS) NMR spectra show that LATP crystallites are better defined for higher calcination temperatures. Analysis of 7Li spin-lattice relaxation and line-shape changes indicates the existence of two species of lithium ions with clearly distinguishable jump dynamics, which can be attributed to crystalline and amorphous sample regions, respectively. An increase of the sintering temperature leads to higher fractions of the fast lithium species with respect to the slow one, but hardly affects the jump dynamics in either of the phases. Specifically, the fast and slow lithium ions show jumps in the nanoseconds regime near 300 and 700 K, respectively. The activation energy of the hopping motion in the LATP crystallites amounts to ca. 0.26 eV. 7Li field-gradient diffusometry reveals that the long-range ion migration is limited by the sample regions featuring slow transport. The high spatial resolution available from the high static field gradients of our setup allows the observation of the lithium ion diffusion inside the small (<100 nm) LATP crystallites, yielding a high self-diffusion coefficient of D = 2 × 10−12 m2/s at room temperature.

Quantum Zeno Jumps in a Resonantly Driven Qubit under Frequent Measurements

In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.