Quantum Magnetism and Topological Ordering via Rydberg Dressing near F\"orster Resonances

Quantum Magnetism and Topological Ordering via Rydberg Dressing near Förster Resonances

R. M. W. van Bijnen and T. Pohl

Phys. Rev. Lett. 114, 243002 – Published 17 June 2015

Abstract

We devise a cold-atom approach to realizing a broad range of bilinear quantum magnets. Our scheme is based on off-resonant single-photon excitation of Rydberg $P$ states (Rydberg dressing), whose strong interactions are shown to yield controllable $X Y Z$ interactions between effective spins, represented by different atomic ground states. The distinctive features of Förster-resonant Rydberg atom interactions are exploited to enhance the effectiveness of Rydberg dressing and, thereby, yield large spin interactions that greatly exceed the corresponding decoherence rates. We illustrate the concept on a spin-1 chain implemented with cold rubidium atoms, and demonstrate that this permits the dynamical preparation of topological magnetic phases. Generally, the described approach provides a viable route to exploring quantum magnetism with dynamically tunable (an)isotropic interactions as well as variable space and spin dimensions in cold-atom experiments.

Received 12 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.243002

Authors & Affiliations

R. M. W. van Bijnen and T. Pohl

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany

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Vol. 114, Iss. 24 — 19 June 2015

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Figure 1
(a) A one-dimensional lattice of ultracold Rubidium atoms realizes an effective spin-1 chain, encoded in the $m_{F} = 0, \pm 1$ Zeeman states of the $F = 1$ hyperfine manifold, as illustrated in panel (b). An elliptically polarized beam admixes excited states of a $n P_{3 / 2}$ Rydberg manifold with a detuning $Δ$ and Rabi frequency $Ω ≪ | Δ |$ . The strong Rydberg interactions, shown in (c) for $n = 43$ , thereby induce effective interactions between the dressed ground states. Exciting close to the minima of the interaction potential yields drastically enhanced interactions and permits to tune the relative strength of different interaction terms by selective coupling to molecular states with total angular momenta of $M = 0$ or $M = \pm 1$ . The color coding indicates the fraction, $f_{p}$ , of optically coupled Rydberg-pair states for each molecular eigenstate [23].
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Figure 2
Pair potentials for optical excitation to (a),(b) $32 P_{3 / 2}$ and (c),(d) $43 P_{3 / 2}$ Rydberg states by $σ_{+}$ -polarized light with $Ω = 10$ and $Δ = - 226 MHz$ . In both cases the maximum decay rate is $\bar{γ} / γ = 5.5 \times 10^{- 3}$ , while the effective ground state interactions close to a Förster resonance (d) are strongly enhanced compared to purely repulsive interactions (b). The colors indicate the potentials of 2-atom ground states ( $| g g ⟩$ ) as well as singly ( $| e g ⟩$ ) and doubly ( $| e e ⟩$ ) excited states. Panels (b),(d) show the detailed interaction energy for pairs of $| g ⟩ = | ↓ ⟩ \equiv | 5 S_{1 / 2} m_{J} = - 1 / 2 ⟩$ fine structure ground states.
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Figure 3
Examples of virtual four-photon processes leading to state-changing interactions between the fine structure ground states. The combination of $σ_{+}$ - and $σ_{-}$ -polarized components opens up different interaction channels between (a): $| ↑ ↓ ⟩$ and $| ↓ ↑ ⟩$ , and (b): $| ↑ ↑ ⟩$ and $| ↓ ↓ ⟩$ , depending on the total angular momentum $M$ of the doubly excited Rydberg state.
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Figure 4
Strengths of dressing-induced interactions between (a) fine and (b) hyperfine ground states, scaled by the corresponding decoherence rate $\bar{γ}$ . Rydberg $43 P_{3 / 2}$ states are excited with $Ω = 10 MHz$ for an atomic distance $R = 1.2 μ m$ . The interactions are obtained from 4th order perturbation theory, which is accurate well outside of the gray-shaded regions corresponding to $| δ | < Ω^{2} / (2 | Δ |)$ .
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Figure 5
$ε$ dependence of the interaction strengths and effective magnetic field for two atoms separated by $R = 1.2 μ m$ coupled to the $43 P_{3 / 2}$ Rydberg manifold with $Ω = 10$ and $Δ = - 163 MHz$ .
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Figure 6
(a) Time evolution of $D$ and $Ω$ used to steer the ground state of a 12-atom chain with a lattice constant of $1.2 μ m$ , coupled to $43 P_{3 / 2}$ Rydberg states with $Δ = - 163 MHz$ and $ε = 1$ . (b) The large ground state fidelity indicates the high degree of adiabaticity for a short evolution time $τ \approx 0.4 ms$ . (c) $τ$ dependence of the final ground state fidelity. (d),(e) Short-range Neél-order and long-range string-order correlations, $O_{N, z}^{(i, j)}$ (c) and $O_{s, z}^{(i, j)}$ (d) of the final state, characteristic for the targeted Haldane phase.
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Physical Review Letters

Quantum Magnetism and Topological Ordering via Rydberg Dressing near Förster Resonances

R. M. W. van Bijnen and T. Pohl

Phys. Rev. Lett. 114, 243002 – Published 17 June 2015

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