One- and Two-Axis Squeezing via Laser Coupling in an Atomic Fermi-Hubbard Model

T. Hernández Yanes, M. Płodzień, M. Mackoit Sinkevičienė, G. Žlabys, G. Juzeliūnas, and E. Witkowska

Phys. Rev. Lett. 129, 090403 – Published 24 August 2022

Abstract

Generation, storage, and utilization of correlated many-body quantum states are crucial objectives of future quantum technologies and metrology. Such states can be generated by the spin-squeezing protocols, i.e., one-axis twisting and two-axis countertwisting. In this Letter, we show activation of these two squeezing mechanisms in a system composed of ultracold atomic fermions in the Mott insulating phase by a position-dependent laser coupling of atomic internal states. Realization of both the squeezing protocols is feasible in the current state-of-the-art experiments.

Received 14 April 2022
Revised 5 July 2022
Accepted 28 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.090403

Physics Subject Headings (PhySH)

Cold gases in optical lattices Entanglement in quantum gases Fermionic condensates Spin-orbit coupling

Perturbation theory

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

T. Hernández Yanes ¹, M. Płodzień ², M. Mackoit Sinkevičienė ³, G. Žlabys ³, G. Juzeliūnas ³, and E. Witkowska ¹

¹Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
²ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
³Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257, Vilnius, Lithuania

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Issue

Vol. 129, Iss. 9 — 26 August 2022

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Images

Figure 1
(a) FHM for atoms in optical lattices with nearest-neighbor tunneling rate $J$ , on site interaction $U$ , and additional coupling between atomic internal degrees of freedom with position-dependent strength $Ω e^{i ϕ j}$ realized with one or two off resonant laser beams. (b) The coupling causes the transition between the $D_{N / 2}$ and $D_{N / 2 - 1}$ spin manifolds (see main text). In the weakly coupling regime, the projection of the Hamiltonian onto the Dicke manifold $D_{N / 2}$ leads to the OAT (single beam) and TACT (two beams) models. (c) The Ramsey-type spectroscopy for the spin-squeezing generation: (i) preparation of the initial spin coherent state in the $D_{N / 2}$ manifold, (ii) unitary evolution with the FHM and nonzero coupling reduces the value of $ξ^{2}$ , (iii) storing the spin squeezed state in the Mott phase for zero atom-light coupling.
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Figure 2
Temporal dependence of the spin-squeezing parameter $ξ^{2}$ for the initial state $| θ = π / 2, φ = π / 2 ⟩$ evolved with the FHM [Eq. (1)] (green dotted lines), the spin Hamiltonian [Eq. (5)] (orange circles), and the effective OAT model [Eq. (10)] (blue lines) under PBC for $N = 10$ , $J / U = 0.04$ , $J_{SE} = 0.0032 E_{R}$ , $J_{↑ ↓} / J_{SE} = 0.04$ (for $U = 0.5 E_{R}$ , $J = 0.02 E_{R}$ where $E_{R} = ℏ^{2} (2 π)^{2} / (2 m λ_{latt}^{2})$ is the recoil energy), and (a) $ϕ = π / 5$ , $J_{↑ ↓} / E_{ϕ} \approx 0.21$ , (b) $ϕ = 2 π / 5$ , $J_{↑ ↓} / E_{ϕ} \approx 0.06$ , (c) $ϕ = 3 π / 5$ , $J_{↑ ↓} / E_{ϕ} \approx 0.03$ , and (d) $ϕ = 4 π / 5$ , $J_{↑ ↓} / E_{ϕ} \approx 0.02$ . The results for the OBC are shown for the same parameters with the FHM (red squares) and the spin Hamiltonian (violet dashed lines). The panels (e) and (f) represent the best squeezing $ξ_{best}^{2}$ and the best squeezing time $t_{best}$ , respectively, versus the number of atoms $N$ for the spin (orange circles) and OAT (blue line) models for $ϕ = π + 2 π / N$ . Results for the OBC (red squares) are shown for comparison.
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Figure 3
Spin-squeezing parameter $ξ^{2}$ in time when the system is coupled by two laser beams to simulate TACT from the initial state $| θ = π / 2, φ = π / 2 ⟩$ . The evolution with the FHM [Eq. (1)] (marked by green squares), the spin Hamiltonian [Eq. (5)] (orange circles), and the effective TACT model [Eq. (12)] (blue line) under PBC is shown for $ϕ_{0} = π$ , $J_{↑ ↓}^{(1)} / J_{S E} = 0.04$ , and (a) $ϕ_{1} = π / 5$ , (b) $ϕ_{1} = 2 π / 5$ , (c) $ϕ_{1} = 3 π / 5$ , and (d) $ϕ_{1} = 4 π / 5$ . The results for OBC are shown for the same parameters using the FHM (red squares) and the spin Hamiltonian (violet dashed lines). The best squeezing $ξ_{best}^{2}$ (e) and the best squeezing time $t_{best}$ (f) are shown versus the number of atoms $N$ for the spin (orange circles for PBC and red squares for OBC) and TACT (blue line) models for $ϕ_{1} = π + 2 π / N$ . Other parameters are the same as in Fig. 2.
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