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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Bragg spectroscopy in optical lattices

Philipp T. Ernst, Sören Götze, Jasper Krauser, Karsten Pyka, K. Sengstock

Published Jun 1, 2009• 0 citations
Publisher

Abstract

Ultracold atoms with optical lattices provide an ideal model system. This paper presents measurement of a momentum-resolved excitation spectrum in such a quantum model system of a crystal by means of Bragg spectroscopy. For the first time, first and second bands were measured with high resolution along a slice through the whole Brillouin zone. Measurements were performed at several lattice depths and, furthermore, the density and pulse area dependence of the excitation energy were systematically studied.

DOI
10.1109/cleoe-eqec.2009.5192465

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Ultracold atoms with optical lattices provide an ideal model system. This paper presents measurement of a momentum-resolved excitation spectrum in such a quantum model system of a crystal by means of Bragg spectroscopy. For the first time, first and second bands were measured with high resolution along a slice through the whole Brillouin zone. Measurements were performed at several lattice depths and, furthermore, the density and pulse area dependence of the excitation energy were systematically studied.
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In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.
We report the first detection of the Higgs-type amplitude mode using Bragg spectroscopy in a strongly interacting condensate of ultracold atoms in an optical lattice. By the comparison of our experimental data with a spatially resolved, time-dependent bosonic Gutzwiller calculation, we obtain good quantitative agreement. This allows for a clear identification of the amplitude mode, showing that it can be detected with full momentum resolution by going beyond the linear response regime. A systematic shift of the sound and amplitude modes' resonance frequencies due to the finite Bragg beam intensity is observed.
We report the observation of quantum dynamical oscillations of ultracold atomic gases in the FFF and DDD bands of an ordinary optical lattice. We are able to control the Bragg reflections at the Brillouin-zone edge up to the third order. As a result, we can switch the quantum dynamics from oscillations across both the FFF and DDD bands to oscillations only within the FFF band. Our capability to observe these oscillations comes from a nonadiabatic technique which allows us to load ultracold atoms efficiently to the GGG band of an optical lattice.
Bragg spectroscopy is used to measure the excitations of a trapped, quantum-degenerate gas of 87 Rb atoms in a three-dimensional (3D) optical lattice. The measurements are carried out over a range of optical lattice depths in the superfluid phase of the Bose–Hubbard model. For a fixed wavevector, the resonant frequency of the excitation is found to decrease with increasing lattice depth. A numerical calculation of the resonant frequencies based on Bogoliubov theory shows a less steep rate of decrease than the measurements.