Robust Nuclear Spin Entanglement via Dipolar Interactions in Polar Molecules

Timur V. Tscherbul, Jun Ye, and Ana Maria Rey

Phys. Rev. Lett. 130, 143002 – Published 6 April 2023

Abstract

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold ${}^{1}Σ$ and ${}^{2}Σ$ polar molecules using electric dipolar interactions. By encoding a spin- $1 / 2$ degree of freedom in a combined set of spin and rotational molecular levels, we theoretically demonstrate the emergence of effective spin-spin interactions of the Ising and XXZ forms, enabled by efficient magnetic control over electric dipolar interactions. We show how to use these interactions to create long-lived cluster and squeezed spin states.

Received 30 April 2022
Accepted 13 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.143002

Physics Subject Headings (PhySH)

Cold and ultracold molecules Cold gases in optical lattices Dipolar gases Entanglement in quantum gases

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Timur V. Tscherbul ¹, Jun Ye ², and Ana Maria Rey ²

¹Department of Physics, University of Nevada, Reno, Nevada 89557, USA
²JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

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Issue

Vol. 130, Iss. 14 — 7 April 2023

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Images

Figure 1
(a) Experimental setup for nuclear spin entanglement generation consisting of ${}^{1}Σ$ molecules in superpositions of spin-rotational states trapped in an optical lattice on a 2D plane. Molecular spins (arrows) interact via the long-range Ising interaction (wavy line), creating cluster-state entanglement represented by the yellow shaded area. (b) Same as (a) but in the presence of a $B$ field and the spin-rotation interaction (red wavy lines) near an avoided crossing in ${}^{2}Σ$ molecules. The blue shaded area represents entanglement of the XXZ type leading to the generation of spin-squeezed states.
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Figure 2
(a) Zeeman energy levels of a typical bialkali molecule (here, ${}^{40}K {}^{87}{Rb}$ ). Our effective spin- $1 / 2$ states $| ↑ ⟩ = | \tilde{0} 0, M ⟩$ and $| ↓ ⟩ = | \tilde{1} 0, M^{'} ⟩$ are marked by arrows. (b) Expectation values of the EDM $d_{↑}$ (top curve) and $d_{↓}$ (bottom curve) and the Ising coupling constant $J_{z}$ (bottom panel) as a function of the reduced $E$ -field strength $β_{E} = d E / B_{e}$ [40]. (c) Protocol for creating long-lived nuclear spin cluster states of polar molecules via ED interactions.
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Figure 3
(a) Energy levels of ${}^{40}K {}^{87}{Rb}$ used in our entanglement generation protocol plotted vs $E$ field at $B = 400 G$ and $M_{F} = M_{N} + M_{I_{K}} + M_{I_{Rb}} = - 7 / 2$ . The initial coherent superposition of the $\tilde{N} = 0$ nuclear spin states is marked with a blue circle. The mw transition used to excite the initial coherent superposition $| + ⟩$ is marked with a green arrow. The competing mw transition is marked by the gray arrow. The differential Stark shift (b) and the NN Ising constant (c) plotted vs $E$ field for ${}^{40}K {}^{87}{Rb}$ molecules at the lattice spacing of 500 nm.
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Figure 4
(a) Zeeman energy levels of YO at $E = 5 kV / cm$ . The ALC between the levels $| \tilde{0} 0, 1 / 2 M_{I} ⟩$ and $| \tilde{1} 1, - 1 / 2 M_{I} ⟩$ is marked with a circle. Energy levels (b), EDM matrix elements (c), and NN spin coupling constants $J_{i, i + 1}^{z}$ and $J_{i, i + 1}^{⊥}$ (d) plotted as a function of $B$ field near the ALC at the NN spacing of 500 nm. (e) Experimental protocol for creating long-lived spin-squeezed states of YO molecules.
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Figure 5
(a) Mw-dressed states $| \pm, M ⟩$ (red bars) of ${}^{40}K {}^{87}{Rb}$ for $M_{F} = 7 / 2$ obtained by driving the mw transition (vertical arrow, $Ω / 2 π = 2.1 MHz$ ) between the bare levels $| \tilde{0} 0, - 2, - 3 / 2 ⟩$ and $| \tilde{1} 0, - 2, - 3 / 2 ⟩$ . The effective spin- $1 / 2$ is encoded into the mw-dressed state $| -, M ⟩$ and the bare state $| \tilde{1} - 1, - 4, 3 / 2 ⟩$ (blue bar), which are coupled by the electric quadrupole interaction (wavy line). $B$ -field dependence of the effective spin- $1 / 2$ energy levels (b), EDM matrix elements (c), and NN XXZ spin coupling constants $J_{i, i + 1}^{⊥}$ and $J_{i, i + 1}^{z}$ (d) near the ALC.
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