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arXiv:1903.04011 · Physical Review A

Lattice-depth measurement using continuous grating atom diffraction

Benjamin T. Beswick, Ifan G. Hughes, S. A. Gardiner

Published Dec 16, 2019• 1 citation
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Abstract

We propose an approach to characterizing the depths of optical lattices, in which either an atomic gas is given a finite initial momentum or, alternatively, a corresponding ``walking'' configuration is applied to the optical lattice itself. This leads to high-amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally, we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth and the initial temperature of the atomic gas from a single common data set.

DOI
10.1103/physreva.100.063629

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We propose an approach to characterizing the depths of optical lattices, in which either an atomic gas is given a finite initial momentum or, alternatively, a corresponding ``walking'' configuration is applied to the optical lattice itself. This leads to high-amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally, we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth and the initial temperature of the atomic gas from a single common data set.
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.
In this thesis we investigate the diffraction of cold atomic gases by optical lattices. Of particular interest to atom interferometry is the implementation of a high momentum-transfer ``beam-splitter,'' which may be achieved by inducing quantum resonance in such an atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration, and demonstrate that an ϵ\epsilonϵ-pseudoclassical model for the dynamics of the gas atoms reproduces quantum resonant behavior for both zero-temperature and finite-temperature non-interacting gases. We show that this model agrees well with the fully quantum treatment of the system over a timescale set by the choice of experimental parameters. In similar setups, the depth of a laser lattice may be measured by exposing an atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the population found in each of the allowed momentum states. We present an 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 at zero and finite temperature. We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, leading to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a zero-temperature analytic formula describing such oscillations, extend it to include atoms with initial momenta detuned from our chosen initial value, and analyze the full finite-temperature response.
We report on a method to calibrate the depth of an optical lattice. It consists of triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the interband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates the oscillation of the zeroth and first orders of the interference pattern observed after a sufficiently long time of flight. The method is robust against atom-atom interactions and the exact value of the extra weak external confinement superimposed to the optical lattice.
We use a coherent Bragg diffraction method to impart an external momentum to ultracold bosonic atoms trapped in a one-dimensional optical lattice. This method is based on the application of a single light pulse, with conditions where scattering of photons can be resonantly amplified by atomic density grating. An oscillatory behavior of the momentum distribution resulting from the time evolution in the lattice potential is then observed. By measuring the oscillating frequencies, we extract multiband energy structures of single-particle excitations with zero pseudomomentum transfer for a wide range of lattice depths. The excitation energy structures reveal the interaction effect through the whole range of lattice depths.
We study light scattering from atoms in optical lattices at finite temperature. We examine the light scattered by fermions in the noninteracting regime and by bosons in the superfluid and Mott insulating regimes. We extend previous theoretical studies to include the full band structure of the optical lattice. We find that light scattering that excites atoms out of the lowest band leads to an increase in light scattering away from the classical diffraction peaks and is largely temperature independent. This additional light scattering leads to lower efficiency of temperature measurements based on photon counting.
The precise calibration of optical lattice depth is an important step in the experiments of ultracold atoms in optical lattices. The Raman-Nath diffraction method, as the most commonly used method of calibrating optical lattice depth, has a limited range of validity and the calibration accuracy is not high enough. Based on multiple pulses Kapitza-Dirac diffraction, we propose and demonstrate a new calibration method by measuring the fully transfer fidelity of the first diffraction order. The high sensitivity of the transfer fidelity to the lattice depth ensures the highly precision calibration of the optical lattice depth. For each lattice depth measured, the calibration uncertainty is further reduced to less than 0.6% by applying the Back-Propagation Neural Network Algorithm. The accuracy of this method is almost one order of magnitude higher than that of the Raman-Nath diffraction method, and it has a wide range of validity applicable to both shallow lattices and deep lattices.