Pulse Electrical Current Resonance: Classical and Quantum Echoes

Abstract

We discuss the theoretical basis of a recent proposal for a new experimental technique in Solid State Physics: Electrical Current Resonance (ECR); continuous wave (CW) and pulsed. In the first part of the paper we show that the Bloch equations for magnetic moments in magnetic fields are formally identical to the Drude equation of motion for the electrical current in electric and magnetic fields. Then, applying a matrix method to solve the current equation of motion, we explore the consequences of this similarity. First we consider continuous magnetic fields; various examples of applications are worked out. In the pulsed case we deduce expressions for the current echoes and free current decays, transient effects similar to spin echoes and free induction decays in the magnetic case. We briefly discuss the application of the technique to the study of electron scattering rates and ECR spectroscopy. On the second part we show that the quantum problem of a charged particle in a oscillating magnetic field has an exact solution, both for continuous and pulsed fields. In the continuous case we show that the particle energy states in the field (the Landau tubes) are turned by 90° as the resonance frequency is approached. In the pulsed case we calculate the expected value of the particle momentum [Formula: see text] after a sequence of one and two magnetic pulses, and show that this quantity corresponds to the free current decay and current echo, deduced classically.