Lattice-depth measurement using multipulse atom diffraction in and beyond the weakly diffracting limit

Abstract

Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry and for the accurate determination of transition matrix elements.In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of offresonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time of flight measurement, after some number of pulses. We present a full analytic model for the time evolution of the atomic populations of the lowest momentum-states, which is sufficient for a "weak" lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature. * b.t.beswick@durham.ac.uk † i.g.hughes@durham.ac.uk ‡ s.a.gardiner@durham.ac.uk 1 In practice, this additive effect is only maintained for a certain number of pulses set by the lattice depth, as we discuss in section IV. 2 The quantum degeneracy is not important in our analysis, as the requirement is simply for a very narrow initial momentum spread. 3 It is conventional to define the lattice depth with respect to a potential of the form U 0 sin 2 (K x/2). In this work we refer to the lattice depth as V = −U 0 /2 = − Ω 2 /8∆ for a laser Rabi frequency Ω and detuning ∆ ≡ ω L −ω 0 .

Lattice-depth measurement using continuous grating atom diffraction

“…In previous work we have presented improved models for the expected multipulse diffraction patterns for a given lattice depth. We have also noted that when considering a gas with initial momentum K/2, the functional form of these models is markedly simpler and therefore easier to fit to data to make an accurate measurement of the lattice depth [23].…”

“…The initial momentum p = K/2 is chosen with a view to creating population oscillations between the zeroth and first diffraction orders with a strong sinusoidal character, as suggested in[23].…”