Atom-wave diffraction between the Raman-Nath and the Bragg regime: Effective Rabi frequency, losses, and phase shifts

摘要

We present an analytic theory of the diffraction of (matter) waves by alattice in the "quasi-Bragg" regime, by which we mean the transition regionbetween the long-interaction Bragg and "channelling" regimes and theshort-interaction Raman-Nath regime. The Schroedinger equation is solved byadiabatic expansion, using the conventional adiabatic approximation as astarting point, and re-inserting the result into the Schroedinger equation toyield a second order correction. Closed expressions for arbitrary pulse shapesand diffraction orders are obtained and the losses of the population to outputstates otherwise forbidden by the Bragg condition are derived. We consider thephase shift due to couplings of the desired output to these states that dependson the interaction strength and duration and show how these can be keptnegligible by a choice of smooth (e.g., Gaussian) envelope functions even insituations that substantially violate the adiabaticity condition. We also givean efficient method for calculating the effective Rabi frequency (which isrelated to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.