Statistics of interferograms in three-level systems

Abstract

We report on the high-frequency (HF) regime of a microwave (MW) pulse consisting of a superimposition of N harmonics acting transversally on a three-level system (ThLS) simultaneously driven in the longitudinal direction by a radio-frequency (RF) signal and in the presence of a zero-energy splitting term D(Sz)2 where D denotes the uniaxial anisotropy and Sz the projection of the spin-1 vector along the quantization direction. We carry out the study by numerical simulations of the Bloch equation (in the absence of relaxation) and present the associated interference patterns for various combinations of the system's parameters. We have established that at high frequencies, the MW opens 2N windows for replication of the action of the RF on the interferograms. The ThLS exhibits multiple (N successive) coherent destruction of tunneling (CDT) when the RF drives it to avoided level crossings where it undergoes Landau-Zener-Stückelberg-Majorana (LZSM) transitions. These CDT are centered at resonance points where D matches the characteristic frequencies of the counter-rotating and rotating terms in the MW pulse. The effects observed are explained by invoking the rotating wave approximation and the Floquet theory. Our analytical results are found in satisfactory agreement with numerics. We have equally observed an infinite multiplication of interferograms for a bichromatic RF pulse when the characteristic amplitude and frequency of the additional signal are large even in the absence of a periodic MW pulse.