In Situ Thermometry of Fermionic Cold-Atom Quantum Wires

Clément De Daniloff, Marin Tharrault, Cédric Enesa, Christophe Salomon, Frédéric Chevy, Thomas Reimann, and Julian Struck

Phys. Rev. Lett. 127, 113602 – Published 9 September 2021

Abstract

We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature $T / T_{F}$ at nearly constant entropy per particle $S / N k_{B}$ . The ability to probe individual atomic wires in situ paves the way to quantitatively study equilibrium and transport properties of strongly interacting 1D Fermi gases.

Received 1 February 2021
Accepted 2 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.113602

Physics Subject Headings (PhySH)

Atom & ion trapping & guiding Cold gases in optical lattices Fermi gases Thermodynamics

1-dimensional systems Ultracold gases

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Clément De Daniloff , Marin Tharrault , Cédric Enesa , Christophe Salomon, Frédéric Chevy, Thomas Reimann, and Julian Struck ^*

Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France

^*[email protected]

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Vol. 127, Iss. 11 — 10 September 2021

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Images

Figure 1
Individually resolved fermionic quantum wires. (a) Array of tube traps created by superimposing two optical lattices along the $x$ and $y$ directions. The optical lattices are formed by the pairwise interference of the beams under small angles ( $∡ (k_{1}, k_{3}) \approx ∡ (k_{2}, k_{4}) \approx 24 °$ ), resulting in a lattice spacing of $d \approx 2.6 μ m$ . Here, $k_{i}$ denotes the wave vector of the $i$ th beam. Only a single row of tube traps is populated with atoms. (b) 32 averaged in situ absorption images of Fermi gases in the 1D regime. Shown is the optical density (OD). (c) Central region of interest of (b) and the corresponding integrated line profile. For a single absorption image see the Supplemental Material [41].
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Figure 2
Lattice loading procedure. (a) (I) First, the gas (red) is strongly compressed along the $y$ direction by a repulsive ${TEM}_{01}$ -like optical potential (green). (II) Second, the optical lattice is ramped up, populating only a single row of the array of tube traps. (III) Finally, the compression potential is removed. (b) Center of mass (CoM) of the atoms in the lattice as a function of the compression beam center along the $y$ axis in units of the lattice constant $d$ . The solid line is a guide to the eye. The top inset shows the intensity profile of the compression beam. The insets on the right represent characteristic images for single- and double-row loading.
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Figure 3
(a) Averaged 1D density profiles for individual tubes with a total atom number $N$ per spin state. The solid lines represent fits of the noninteracting equation of state, with $T$ (from top to bottom): $0.51 (1) μ K$ , $0.44 (2) μ K$ , $0.31 (2) μ K$ , $0.41 (2) μ K$ , $0.29 (2) μ K$ , $0.27 (2) μ K$ , and $0.25 (3) μ K$ . (b) Reconstructed axial potential for $a = - 40 a_{0}$ (orange dashed-dotted line) and $a = + 40 a_{0}$ (blue solid line). The harmonic part (gray dashed line) of the potential has been independently measured (Supplemental Material [41]). (c) Relative difference $δ V_{\pm 40 a_{0}} (z) = (V_{∥, - 40 a_{0}} (z) - V_{∥, + 40 a_{0}} (z)) / V_{∥, - 40 a_{0}} (z)$ between the reconstructed potentials for attractive and repulsive interactions.
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Figure 4
Thermodynamics of the 1D-3D crossover. The data points in (b), (c), and (d) correspond to the center of each tube trap ( $z = 0$ ), where the Fermi energy is the highest. Green, orange, and blue colors represent a selection of three characteristic tubes whose indices are indicated in (d). Tube trap indices label the 18 selected central tubes from left to right along the $x$ axis. (a) The temperature of individual atomic wires normalized by the transverse frequency $k_{B} T / ℏ ω_{⊥}$ and (b) the reduced temperature $T / T_{F}$ . The gray gradient in (a) depicts the 1D limit. The solid lines in (b) that emanate from the data points represent the continuous change in $T / T_{F}$ and $E_{F} / (ℏ ω_{⊥})$ within each atomic wire according to the local density approximation. (c) The entropy per particle $S / N k_{B}$ . (d) Mean value of the entropy per particle obtained by averaging the data of (c) for the green, orange, and blue points. The gray points represent the other 15 tubes traps, which were omitted in (a), (b), and (c).
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