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

Abstract

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 "channelling" regimes and the short-interaction Raman-Nath regime. The Schrödinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and re-inserting the result into the Schrödinger 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.

Squeezed-light-enhanced atom interferometry below the standard quantum limit

“…(10) apply to other coherent beamsplitting techniques, such as Bragg pulses [61,62] and Bloch oscillations [63]. Indeed, given that inertial sensors based on Bose-condensed sources and large momentum transfer beamsplitters offer a promising alternative route to improved sensitivity [46,64,65], incorporating such interferometers within the squeezed-light-enhanced schemes outlined below is a most attractive prospect.…”

Noise-Immune Conjugate Large-Area Atom Interferometers

“…As beam splitters, we use multiphoton Bragg diffraction of matter waves at an optical lattice [11,[18][19][20]. The optical lattice is formed by two counterpropagating laser beams that we may call the top and bottom beam (Fig.…”

“…2) is to satisfy δφ L = 0 as well as technically possible. Moreover, our laser system is optimized for driving LMT beam splitters based on high-order Bragg diffraction [11,20], which requires laser pulses having smooth envelope functions with an optimized duration and high power.…”

Low-phase noise and high-power laser for Bragg atom interferometer

“…The laser power required for Bragg transitions sharply increases with the diffraction order. 20,21 These high power lasers can be prepared by the secondharmonic generation (SHG) method. [22][23][24][25] The frequency difference between the two Bragg beams needs to be chirped to compensate for the Doppler shift occurring because of the free fall of the atoms.…”