Rabi oscillations in two-level systems beyond the rotating-wave approximation

TL;DR

This paper investigates Rabi oscillations in two-level quantum systems beyond the rotating-wave approximation, revealing the Bloch-Siegert shift and proposing methods to achieve complete population inversion with short pulses.

Contribution

It introduces second-order perturbation techniques to analyze Rabi oscillations beyond RWA and proposes two methods to achieve population inversion despite the Bloch-Siegert shift.

Findings

Bloch-Siegert shift increases resonant frequency with field amplitude

Short $\pi$-pulses do not achieve complete inversion without correction

Chirping and pulse shaping methods effectively achieve population inversion

Abstract

Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant $\pi$-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short $\pi$-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.