Analytic theory for Bragg atom interferometry based on the adiabatic theorem

Abstract

High-fidelity Bragg pulses are an indispensable tool for state-of-the-art atom interferometry experiments. In this work, we introduce an analytic theory for such pulses. Our theory is based on the pivotal insight that the physics of Bragg pulses can be accurately described by the adiabatic theorem. We show that efficient Bragg diffraction is possible with any smooth and adiabatic pulse shape and that high-fidelity Gaussian pulses are exclusively adiabatic. Our results give strong evidence, that adiabaticity according to the adiabatic theorem is a necessary requirement for high-performance Bragg pulses. Our model provides an intuitive understanding of the Bragg condition, also referred to as condition on the "pulse area". It includes corrections to the adiabatic evolution due to Landau-Zener processes as well as the effects of a finite atomic velocity distribution. We verify our model by comparing it to an exact numerical integration of the Schrödinger equation for Gaussian pulses diffracting 4, 6, 8 and 10 photon recoils. Our formalism provides an analytic framework to study systematic effects as well as limitations to the accuracy of atom interferometers employing Bragg optics that arise due to the diffraction process.

Interacting quantum mixtures for precision atom interferometry

“…Especially in space missions with limited optical power, the beam waist, and consequently the ensemble size, needs to be kept small in order to reach sufficiently high Rabi frequencies. Moreover, beam splitters based on Bragg diffraction [13,[95][96][97] and Bloch oscillations [98,99] feature relatively long interrogation times, resulting in a sharp velocity acceptance such that the velocity width of the atomic distribution typically needs to be much smaller than the recoil velocity [100], equivalent to a few tens of nK. With DKC, these requirements are readily met as described in the previous sections of this paper as well as implemented in various experiments [45,[101][102][103][104].…”

Atomic Raman scattering: Third-order diffraction in a double geometry

“…Higher-order Bragg diffraction [1][2][3][4][5] in combination with sequential pulses [6,7] has become a standard tool for large-momentum-transfer (LMT) techniques to enhance the sensitivity of light-pulse atom interferometers [8,9]. However, with Raman diffraction [8,10,11], the the other main mechanism, only sequential pulses [12][13][14] have routinely been employed so far.…”

“…Bloch oscillations [18][19][20][21][22], higher-order diffraction [1][2][3][4][5], and sequential pulses [6,7,[12][13][14]23] are some of the most commonly used techniques used for LMT applications based on Bragg diffraction. They are complemented by double diffraction [2,6,[15][16][17], where an atom at rest diffracts from two counterpropagating light gratings in two opposite directions.…”