Disentangling Pauli Blocking of Atomic Decay from Cooperative Radiation and Atomic Motion in a 2D Fermi Gas

Thomas Bilitewski, Asier Piñeiro Orioli, Christian Sanner, Lindsay Sonderhouse, Ross B. Hutson, Lingfeng Yan, William R. Milner, Jun Ye, and Ana Maria Rey

Phys. Rev. Lett. 128, 093001 – Published 4 March 2022

Abstract

The observation of Pauli blocking of atomic spontaneous decay via direct measurements of the atomic population requires the use of long-lived atomic gases where quantum statistics, atom recoil, and cooperative radiative processes are all relevant. We develop a theoretical framework capable of simultaneously accounting for all these effects in the many-body quantum degenerate regime. We apply it to atoms in a single 2D pancake or arrays of pancakes featuring an effective $Λ$ level structure (one excited and two degenerate ground states). We identify a parameter window in which a factor of 2 extension in the atomic lifetime clearly attributable to Pauli blocking should be experimentally observable in deeply degenerate gases with $\sim 10^{3}$ atoms. We experimentally observe a suppressed excited-state decay rate, fully consistent with the theory prediction of an enhanced excited-state lifetime, on the ${}^{1}{S_{0}} - {}^{3}{P_{1}}$ transition in ${}^{87}{Sr}$ atoms.

Received 10 August 2021
Accepted 17 February 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.093001

Physics Subject Headings (PhySH)

Cold gases in optical lattices Fermi gases Light-matter interaction Spontaneous emission

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Thomas Bilitewski ^1,2, Asier Piñeiro Orioli^1,2, Christian Sanner¹, Lindsay Sonderhouse ¹, Ross B. Hutson¹, Lingfeng Yan¹, William R. Milner¹, Jun Ye ¹, and Ana Maria Rey ^1,2

¹JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
²Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA

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Vol. 128, Iss. 9 — 4 March 2022

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Images

Figure 1
(a) A 2D cloud of atoms is optically excited by a laser pulse with Rabi frequency $Ω_{L}$ and wave vector $k_{L}$ propagating perpendicularly to the 2D plane and linearly polarized ( $n_{L}$ ) along $x$ . (b) Internal level structure ( $Λ$ system), with one excited state $e$ and two ground states $g_{α}$ . The single-particle decay rate for $e \to g_{α}$ is $Γ_{α α}$ . (c) Protocol: after state preparation, atoms evolve freely and decay during a dark time $t$ , followed by population measurement. (d) In plane momentum space $(k_{x}, k_{y})$ with two Fermi seas (red and blue circles). Filled circles denote occupied states. Interaction processes involving virtual exchange of photons between atoms at $k$ and $q$ are depicted as a wiggly line; single-particle spontaneous decay proportional to $Γ$ are illustrated as the circular region (blue shading) around $k^{'}$ . (e) Processes included in the master equation. Top: dipolar exchange between atoms in momenta $k$ and $q$ . Bottom: spontaneous decay from $k^{'}$ to $q^{'}$ .
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Figure 2
Pauli blocking of spontaneous emission for noninteracting atoms. Decay rate $γ_{eff}^{nonint} / Γ$ vs $T / T_{F}$ comparing 3D (dashed) to 2D (solid) for $N_{0} = N_{1}$ and $θ = π$ . $N_{2 D} = 100$ , 200, 400, 800 for the colored lines (top to bottom), corresponding to $k_{0} / k_{F} = 1.51$ , 1.26, 1.07, 0.90. $N_{3 D}$ is chosen such that $k_{0} / k_{F}^{3 D} = k_{0} / k_{F}^{2 D}$ at these atom numbers. Inset: illustration of the initial state before and after laser excitation in 2D and 3D. Colored circles denote Fermi seas of different atomic levels and striped areas denote an overlap of two Fermi seas. Blue circles of radius $k_{0}$ labeled $Γ$ show the states reachable by a spontaneous decay process.
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Figure 3
Interplay of dipolar interactions and Pauli blocking in 2D. (a) $γ_{eff} (θ) / γ_{eff}^{nonint} (π)$ comparing the full ME (solid) to the noninteracting part (dashed) at $T / T_{F} = 0.1$ for different $N = N_{0} = N_{1}$ . (b) Decay rate $γ_{eff} / Γ$ at $θ = π / 2$ vs $N$ at different temperatures comparing the full ME (solid) to the frozen atom approximation (dash-dotted lines). (c) Decay rate $γ_{eff}^{nonint} (π)$ vs $N_{0}$ and $N_{1}$ . (d) Interaction effects quantified by $γ_{eff} / γ_{eff}^{nonint}$ for $θ \to 0$ vs $N_{0}$ , $N_{1}$ . (c),(d) In thermal equilibrium for $T_{0} = T_{1}$ and $T / T_{F, 1} = 0.1$ .
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Figure 4
Decay rates in stacked pancakes geometry. (a) Scaling of the decay rate $γ_{eff}$ with $N$ comparing the balanced case (dotted), $N_{0} = N_{1} = N$ , to the highly imbalanced case (solid), $N_{0} = 200$ , $N_{1} = N$ , for a $θ = π$ pulse. The gray shading denotes the fixed $N = 1500$ used in (b) $γ_{eff} / Γ$ vs $θ$ . Temperatures indicated in the legend in (b), in the imbalanced case $T_{0} = T_{1}$ and $T / T_{F}$ given with respect to $T_{F, 1}$ . Points with error bars are experimental data taken under the same conditions as the solid green lines.
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