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arXiv:0802.3158 · Physical Review A

Probing ultracold Fermi atoms with a single ion

Yu. B. Sherkunov, B. A. Muzykantskiǐ, N. d’Ambrumenil, Benjamin D. Simons

Published Feb 4, 2009• 24 citations
arXivHTMLPDF

Abstract

We show that the recently proposed ionic microscope setup [Kollath et al., Phys. Rev. A 76, 063602 (2007)] could be adapted to measure the local single-particle energy distribution of a degenerate Fermi gas in situ with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photoassociation rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photoassociation rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.

DOI
10.1103/physreva.79.023604

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We show that the recently proposed ionic microscope setup [Kollath et al., Phys. Rev. A 76, 063602 (2007)] could be adapted to measure the local single-particle energy distribution of a degenerate Fermi gas in situ with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photoassociation rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photoassociation rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.
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The binding energy of Feshbach molecules from a two-component Fermi gas of 40{}^{40}40K atoms has been experimentally measured with the momentum-resolved Raman spectroscopy. Comparing with the radio-frequency spectroscopy, in the present experiment the signal of unpaired (free atoms) and the bound molecules can be directly observed and the binding energy can be simultaneously determined in a single running experiment. The energy-momentum dispersion spectra of the ultracold Fermi gas in the BEC side are also measured and reconstructed. The present experimental technology of the momentum-resolved Raman spectroscopy can be easily extended to perform spatially momentum-resolved Raman spectroscopy and to obtain the response spectra of a homogeneous system in the local density approximation.
Abstract. We report on the local probing and preparation of an ultracold Fermi gas on the length scale of one micrometer, i.e. of the order of the Fermi wavelength. The essential tool of our experimental setup is a pair of identical, high-resolution microscope objectives. One of the microscope objectives allows local imaging of the trapped Fermi gas of 6Li atoms with a maximum resolution of 660 nm, while the other enables the generation of arbitrary optical dipole potentials on the same length scale. Employing a 2D acousto-optical deflector, we demonstrate the formation of several trapping geometries including a tightly focussed single optical dipole trap, a 4x4-site two-dimensional optical lattice and a 8-site ring lattice configuration. Furthermore, we show the ability to load and detect a small number of atoms in these trapping potentials. A site separation of down to one micrometer in combination with the low mass of 6Li results in tunneling rates which are sufficiently large for the implementation of Hubbard-models with the designed geometries. ∗ These authors contributed equally to the presented work. † Author to whom any correspondence should be addressed. ar
We propose a versatile experimental probe for cold atomic gases analogous to the scanning tunneling microscope (STM) in condensed matter. This probe uses the coherent coupling of a single particle to the system. Depending on the measurement sequence, our probe allows us to obtain either the local density and spatial density correlations, with a resolution on the nanometer scale, or the single particle correlation function in real time. We discuss applications of this scheme to the various possible phases for a two dimensional Hubbard system of fermions in an optical lattice.
We propose a new technique for the detection of single atoms in ultracold quantum gases. The technique is based on scanning electron microscopy and employs the electron impact ionization of trapped atoms with a focused electron probe. Subsequent detection of the resulting ions allows for the reconstruction of the atom's position. This technique is expected to achieve a much better spatial resolution compared to any optical detection method. In combination with the sensitivity to single atoms, it makes new in situ measurements of atomic correlations possible. The detection principle is also well suited for the addressing of individual sites in optical lattices.
Hybrid atom-ion systems combine the precise control of a single radio-frequency-trapped atomic ion with the rich few- to many-body phenomena of ultracold degenerate quantum gases trapped in light fields. The associated long-range interaction enables studies of impurity physics and the implementation of a single-particle quantum gas microscope, sensitive to quantities beyond the atomic density, including energy distributions, atom-atom couplings, and many-body exchange symmetry. This perspective requires atom-ion coupling, which can be tuned through resonantly enhanced scattering. While atom-ion Feshbach resonances have recently become experimentally accessible, the role of quantum statistics in resonantly enhanced three-body recombination remains largely unexplored. This thesis investigates the role of fermionic quantum statistics in atom-atom-ion three-body recombination. The experiment employs a single 138Ba+ ion immersed in an ultracold two-component Fermi gas of 6Li. An atom-ion Feshbach resonance enables resonantly enhanced recombination for one spin component, while the other component acts as a non-resonant spectating collision partner. This allows a direct comparison between recombination processes involving identical and distinguishable fermions. Experimentally, recombination rates are extracted from bath polarization-dependent ion-loss spectroscopy. Expressing the results as relative rate constants largely detaches them from the total atomic density and results in suppression of recombination in the identical fermion channel. Additional measurements of two-body reactive collisions are combined with simulations of the Fermi gas, demonstrating that density modifications arising from Fermi-Dirac statistics or mutual atom-atom attraction are insufficient to explain the observed recombination behavior. To interpret the measurements, an extension of the conventional two-step model is developed. Using a hyperspherical treatment that includes all pairwise interactions and fermionic exchange symmetry, effective relaxation rates for the loosely-bound atom-ion complex are obtained. The calculations predict a suppression of recombination involving identical fermions relative to distinguishable collision partners. The experimental observations are consistent with this prediction and provide evidence that fermionic exchange symmetry significantly affects resonantly enhanced atom-atom-ion recombination. These results establish three-body recombination as a sensitive probe of short-range quantum correlations in degenerate gases and demonstrate that a single trapped ion can be employed as a localized sensor of many-body quantum statistics.