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

2008; American Physical Society; Volume: 77; Issue: 2 Linguagem: Inglês

10.1103/physreva.77.023609

1538-4446

Holger Müller, Sheng‐wey Chiow, Steven Chu,

Quantum Information and Cryptography

We present an analytic theory of the diffraction of (matter) waves by a lattice in the ``quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and ``channeling'' regimes and the short-interaction Raman-Nath regime. The Schr\"odinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and reinserting the result into the Schr\"odinger equation to yield a second-order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.