Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy

TL;DR

The paper introduces atom-resolved microscopy in the continuum to directly measure interparticle correlations in $^{23}$Na Bose and $^6$Li Fermi gases, freezing atomic positions with a pinning lattice and collecting fluorescence via Raman sideband cooling. Using this real-space microscope, they observe Bose enhancement in $g^{(2)}$ for thermal bosons and a Fermi hole for fermions, and in the strongly interacting 2D Fermi gas they reveal non-local pairing across the BEC-BCS crossover. From the short-range structure of the measured pair correlations, they extract the pairing gap $\Delta$, an effective pair size $b$, and the short-range contact $c$, providing a microscopic view of pairing in the continuum. Fluctuation-dissipation thermometry is demonstrated for in situ temperature calibration, and the work establishes atom-resolved, continuum quantum-gas imaging as a versatile platform for studying strongly correlated bosons, fermions, and mixtures.

Abstract

We demonstrate atom-resolved detection of itinerant bosonic $^{23}$Na and fermionic $^6$Li quantum gases, enabling the direct in situ measurement of interparticle correlations. In contrast to prior work on lattice-trapped gases, here we realize microscopy of quantum gases in the continuum. We reveal Bose-Einstein condensation with single-atom resolution, measure the enhancement of two-particle $g^{(2)}$ correlations of thermal bosons, and observe the suppression of $g^{(2)}$ for fermions; the Fermi or exchange hole. For strongly interacting Fermi gases confined to two dimensions, we directly observe non-local fermion pairs in the BEC-BCS crossover. We obtain the pairing gap, the pair size, and the short-range contact directly from the pair correlations. In situ thermometry is enabled via the fluctuation-dissipation theorem. Our technique opens the door to the atom-resolved study of strongly correlated quantum gases of bosons, fermions, and their mixtures.

Figures (7)

• Figure 1: Atom-resolved microscopy of quantum gases in the continuum. (a) Itinerant atoms in an atom trap (red) are suddenly frozen in place via an applied optical lattice and imaged via Raman sideband cooling Cheuk2015. (b) Microscope images of bosonic $^{23}$Na forming a Bose-Einstein condensate (left), of a single spin state in a weakly interacting $^{6}$Li Fermi mixture (middle), and of both spin states of a strongly interacting Fermi mixture, directly revealing pair formation (right).
• Figure 2: Pair correlation function of a thermal Bose gas (top) and a non-interacting Fermi gas (bottom). The red curve (top) is a fit giving a thermal de Broglie wavelength of $\lambda_{\rm dB}{=}4.4\,\rm \mu m$ and a temperature $T{=}6.9(3)$ nK. The blue curve (bottom) is the $T{=}0$ pair correlation for a 2D non-interacting Fermi gas at our interparticle spacing $n^{-1/2}{=}3.6\,\rm \mu m$, without free parameters. The insets show exemplary microscope images for the Bose and Fermi gas. Black dashed lines indicate $g^{(2)}{=}1$.
• Figure 3: Pair correlations of the 2D strongly interacting Fermi gas in the BEC-BCS crossover. (a) Fermi gas microscope images of both spin states from the BEC to the BCS regime ($\eta=\log(k_{\rm F} a_{\rm 2D}){=}0.2$, 1.2, and 4.2 from left to right). The thin ellipses show closely spaced pairs of fermions, as expected in the BEC-BCS crossover. (b) The density-density correlation map $g_{nn}^{(2)}(\vec{r})$, showing how the pair size increases from the BEC to the BCS regime. (c) Microscope images with one spin component removed. (d) The $\uparrow\uparrow$ correlation map for a single spin component. The Fermi hole grows towards the BCS limit.
• Figure 4: a) Pair correlation functions for total density $g_{nn}^{(2)}$ (red circle) and equal spin $g_{\uparrow\uparrow}^{(2)}$ (blue square) in the BEC-BCS crossover. From left to right $\eta=\log(k_{\rm F} a_{\rm 2D})=0.2$, $1.2$ and $4.2$. The red and blue solid curves are fits to Eqs. \ref{['eq:correlations']}. Black dashed curve: correlation function for ideal Fermi gas at $T=0$. b) Derived unequal spin correlation function $g_{\uparrow\downarrow}^{(2)} = 2 g_{nn}^{(2)} - g_{\uparrow\uparrow}^{(2)}$.
• Figure 5: Characterization of pairing in the BEC-BCS crossover. a) Contact, b) effective pair size as obtained from fits to correlation functions Eqs. \ref{['eq:correlations']}. In a), black solid line: Monte Carlo result Shi2015. black dashed line: mean field result. Blue solid line: Fermi liquid contact Shi2015. In b) black solid line: mean-field result $k_{\rm F} a_{\rm 2D}e^{\gamma}/2$.