Larmor time of a bound electron wave packet tunneling through a barrier

Abstract

The Larmor time of an incident wave packet has recently been measured experimentally [R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature (London) 583, 529 (2020)]. It differs essentially from previous well-studied free-particle cases, whereas the unique properties of wave packets are unrevealed in their theoretical analysis and state-of-the-art Larmor clock studies. In this paper, we study the Larmor time of a bound two-component electron wave packet and supplement the theoretical lack of wave-packet tunneling. We find that the spin shows a pure Larmor precession in the plane perpendicular to the field without a rotation parallel to the field. The Larmor time is defined in the limit of vanishing field where the precession angle is proportional to the field. For relatively weak fields, this precession angle will respond to the field approximately linearly. For the wave-packet tunneling case, we propose an effective scheme that utilizes the fidelity of the tunneled wave packets to calibrate an approximate linear-response region. Furthermore, we show that in the approximate linear-response region the change in the fidelity can be approximately regarded as the result of the accumulated displacement in phase space. This result reveals the inner mechanism of wave-packet tunneling. Our findings may have implications for future experiments of the Larmor clock.