High-Contrast Interference of Ultracold Fermions

Philipp M. Preiss, Jan Hendrik Becher, Ralf Klemt, Vincent Klinkhamer, Andrea Bergschneider, Nicolò Defenu, and Selim Jochim

Phys. Rev. Lett. 122, 143602 – Published 12 April 2019

Abstract

Many-body interference between indistinguishable particles can give rise to strong correlations rooted in quantum statistics. We study such Hanbury Brown–Twiss-type correlations for number states of ultracold massive fermions. Using deterministically prepared ${}^{6}{Li}$ atoms in optical tweezers, we measure momentum correlations using a single-atom sensitive time-of-flight imaging scheme. The experiment combines on-demand state preparation of highly indistinguishable particles with high-fidelity detection, giving access to two- and three-body correlations in fields of fixed fermionic particle number. We find that pairs of atoms interfere with a contrast close to 80%. We show that second-order density correlations arise from contributions from all two-particle pairs and detect intrinsic third-order correlations.

Received 30 November 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.143602

Physics Subject Headings (PhySH)

Atomic gases Fermionic condensates

Atom & ion trapping & guiding

Atomic, Molecular & Optical

Authors & Affiliations

Philipp M. Preiss^1,*, Jan Hendrik Becher¹, Ralf Klemt¹, Vincent Klinkhamer¹, Andrea Bergschneider^1,†, Nicolò Defenu^1,2, and Selim Jochim¹

¹Physics Institute, Heidelberg University, 69120 Heidelberg, Germany
²Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany

^*preiss@physi.uni-heidelberg.de
^†Present address: Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland.

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Vol. 122, Iss. 14 — 12 April 2019

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Images

Figure 1
Many-body interference of fermionic particles. (a) The coincidence events for two detectors monitoring single-particle sources are given by the available sets of many-body paths. For indistinguishable particles, the paths add coherently where the sign of their interference depends on quantum statistics. Two sources emitting indistinguishable fermions display suppressed coincidence counts. In a setting with more particles, correlations between detectors arise due to interference of all many-body paths. (b) We realize the thought experiment from Fig. 1 using ultracold fermions in optical tweezers. Time-of-flight expansion is performed in an optical dipole trap aligned with the $x$ axis connecting the tweezers, and particles are detected in free-space fluorescence imaging. (c) The probability distribution $| Ψ (x_{1}, x_{2}) |^{2}$ (plotted for the two-mode case) evolves from localized to delocalized states during time of flight but retains a node at $x_{1} = x_{2}$ due to fermionic antisymmetry.
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Figure 2
Interference of two fermions. (a) Measured momentum correlator $⟨ : {\hat{n}}_{k 1} {\hat{n}}_{k 2} : ⟩$ for two particles prepared in two optical tweezers, showing strong fermionic antibunching. The data are symmetric about the diagonal $k_{1} = k_{2}$ by construction, but we plot the full correlator for visual clarity. (b) The normalized correlator $C^{(2)} (d)$ shows a clear, almost full sinusoidal modulation in the relative momentum $d$ . We extract a contrast of 79(2)% by fitting a cosine to the data, excluding the grayed out points near the origin, for which coincidences cannot reliably be detected.
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Figure 3
Second-order correlations for three fermions. (a) Top: For an arbitrary configuration of single-fermion sources, each pair of particles contributes a sinusoidal oscillation to the correlation function $C^{(2)} (d)$ . The full correlator can exhibit complex patterns due to beat notes between all spatial frequencies. Bottom: Expected full correlation function for three regularly spaced sources. (b) Correlators for individual pairs of sources. (c) Three particles released from three equidistant tweezers exhibit correlations at the momentum scale $k_{lat}$ and its first harmonic, leading to a “superlattice” structure in $C^{(2)} (d)$ . The bottom row displays the measured $C^{(2)} (d)$ for three particles (data points), together with a prediction (red line) given by the weighted sum of fits to the two-particle contributions from Fig. 3. (d) For three tweezers with irregular spacing, three distinct spatial frequencies contribute to the full second-order correlator. The sharp dip at $k_{1} = k_{2}$ is partially due to our lack of sensitivity to coincidences at short distances.
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Figure 4
Third-order momentum correlations. Normalized correlation function $C^{(3)} (d_{1}, d_{2})$ for three fermions released from three wells with regular spacing ( $a_{23} = a_{12}$ , top row) and nonequal spacing ( $a_{23} = 1.5 a_{12}$ , bottom row). The left column shows the full measured correlations, and the central and right columns show the disconnected and connected parts of the correlation function, respectively. By construction, the function is symmetric under the transformation $(d_{1}, d_{2}) \Leftrightarrow (- d_{1}, - d_{2})$ . The connected part of the correlation function $C_{con}^{(3)}$ is scaled by a factor of two for better visibility. The measurement demonstrates the sensitivity to third-order correlations in the fermionic matter-wave field.
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