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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 off-resonant 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.
Highlights
Precision measurement of optical lattice [1] depths is important for a broad range of fields in atomic and molecular physics [2,3], most notably in atom interferometry [4,5], many-body quantum physics [6,7], accurate determination of transition matrix elements [8,9,10,11,12], and, by extension, ultraprecise atomic clocks [13,14]
The most commonly used scheme is Kapitza-Dirac scattering [18], where an ultracold atomic gas is exposed to a pulsed laser standing wave and theoretical predictions for the fraction of atoms found in each of the allowed momentum states are fitted to time of flight measurements [7,19,20,21]
We display the variation of A and of φ versus Veff in Fig. 26; φ initially increases approximately linearly with Veff, meaning that over a sufficiently small range of lattice depths, we should expect to see an approximate universality in the population dynamics when the time axis is scaled by Veff
Summary
Precision measurement of optical lattice [1] depths is important for a broad range of fields in atomic and molecular physics [2,3], most notably in atom interferometry [4,5], many-body quantum physics [6,7], accurate determination of transition matrix elements [8,9,10,11,12], and, by extension, ultraprecise atomic clocks [13,14]. The most commonly used scheme is Kapitza-Dirac scattering [18], where an ultracold atomic gas is exposed to a pulsed laser standing wave and theoretical predictions for the fraction of atoms found in each of the allowed momentum states are fitted to time of flight measurements [7,19,20,21]. When determining the matrix elements of weak atomic transitions, the lattice depths involved are correspondingly small (V 0.01ER for any atom, here V is the lattice depth and ER is the laser recoil energy), such that signal-to-noise considerations become an issue [22].
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