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European Quantum Electronics Conference (EQEC)

Spatial quantum noise interferometry in expanding ultracold atom clouds

S. Filling, Fabrice Gerbier, Artur Widera, Olaf Mandel, Tatjana Gericke, Immanuel Bloch

Published Jan 18, 2006• 10 citations
Publisher

Abstract

The paper reports on measurement on a Mott insulator released from an optical lattice trap. We show that strong periodic quantum correlations exist at the atomic shot noise level between density fluctuations in the expanding atom cloud, reflecting the underlying spatial ordering in the lattice. These spatial correlations find a natural interpretation in terms of a multiple wave HBT interference effect, and provide a unique tool to identify novel quantum phases of ultracold bosonic or fermionic atoms.

DOI
10.1109/eqec.2005.1567398

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The paper reports on measurement on a Mott insulator released from an optical lattice trap. We show that strong periodic quantum correlations exist at the atomic shot noise level between density fluctuations in the expanding atom cloud, reflecting the underlying spatial ordering in the lattice. These spatial correlations find a natural interpretation in terms of a multiple wave HBT interference effect, and provide a unique tool to identify novel quantum phases of ultracold bosonic or fermionic atoms.
Ultracold bosonic and fermionic quantum gases in optical lattices can be used as versatile model systems for the investigation of fundamental condensed matter physics hamiltonians. We report on two novel detection techniques, which have allowed us to reveal e.g. the in trap density profile of strongly correlated bosonic quantum gases in the lattice. Thereby we have been able to observe the formation of spatial shell structures in the density of the trapped atom cloud across the superfluid to Mott insulator transition. In addition we use quantum noise correlations in expanding bosonic and fermionic atom clouds released from the lattice to observe quantum statistical Hanbury‐Brown and Twiss type hunching and antibunching of the atoms and show that this can be used to reveal the ordering of the particles in the lattice.
Atoms in the Mott insulator state trapped in an optical lattice are incoherence matter wave source. It is not the first-order, but the second-order interference effect (density correlation) that will appear for this incoherence wave source after being released. A density correlation function of the freely expanding ultracold gases is obtained theoretically, which presents sharp peaks of interference, and the stripes structure is similar to the diffraction gratings. It is further pointed out that the peak structure of the density correlation function depends on the relative position between two detectors. The phenomenon of subwavelength interference of matter waves is also proposed in this paper.
The time-correlation function of ultracold atomic gas is theoretically investigated. Atoms are initially confined in an optical lattice and in a Mott insulator regime. We consider the effect of gravity on the time correlation among atomic wave functions when the atomic cloud is released from the optical lattice. The time-correlation function in this process displays sharp peaks, a feature that is analogous to the spatial-normalized correlation observed in recent experiments. The origin and properties of the interference pattern are theoretically investigated in detail. Similar to the spatial correlation, the time correlation in expanding atomic clouds reveals the ordering of indistinguishable particles in an optical lattice. Experimental detection scheme and its potential use in the measurement of gravitational acceleration are briefly discussed.
Density-density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density-density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density-density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density-density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density-density correlation spectra agreed with our experimental observations.
We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the noise correlations contain full information on the most important fluctuations present in the system. We point out the importance of the sum rules fulfilled by the noise correlations and show that they yield nonsingular structures beyond the predictions of bosonization approaches. Noise correlations can thus serve as a universal probe of order and can be used to characterize the many-body states of cold atoms in optical lattices.
This thesis describes experiments which investigate ultracold atom \nensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state.\nThe tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.\n