arXiv : Ring-exchange physics in a chain of three-level ions

Biswas, Sourav; Grass, Tobias; Rico, E.

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Preprint
Report number	arXiv:2410.06655
Title	Ring-exchange physics in a chain of three-level ions
Author(s)	Biswas, Sourav (Donostia Intl. Phys. Ctr., San Sebastian) ; Rico, E. (Donostia Intl. Phys. Ctr., San Sebastian ; Basque U., Bilbao ; CERN) ; Grass, Tobias (Donostia Intl. Phys. Ctr., San Sebastian ; Basque U., Bilbao)
Document contact	Contact: arXiv
Imprint	2024-10-09
Number of pages	7
Note	7 pages, 6 figures
Subject category	quant-ph ; General Theoretical Physics ; cond-mat.str-el ; cond-mat.quant-gas
Abstract	In the presence of ring exchange interactions, bosons in a ladder-like lattice may form the bosonic analogon of a correlated metal, known as the d-wave Bose liquid (DBL). In this Letter, we show that a chain of trapped ions with three internal levels can be used to mimic a ladder-like system constrained to a maximum occupation of one boson per rung. The setup enables tunable ring exchange interactions, giving rise to a transition between a polarized regime with all bosons confined to one leg and the DBL regime. The latter state is characterized by a splitting of the peak in the momentum distribution and an oscillating pair correlation function.
Other source	Inspire
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$(a) Mapping between the two-leg ladder and chain of three-level ions. (b,c) Implementation of intra-leg hopping and ring exchange via Raman transitions following the level diagram of $^{171}{\rm Yb}^+$ shown in (b). As illustrated in (c), the pairs drawn in red couple to the longitudinal phonon direction, and are equipped with two beat notes, tuned to the $\tau_{-0}$ transition and the $\tau_{0+}$ transition, with different detunings $\delta_{l,-}$ and $\delta_{l-,+}$ from the longitudinal center-of-mass mode at frequency $\omega_{{\rm com},l}$, as indicated in the box. The pairs drawn in red couple to transverse phonon modes, and are equipped with one beat-note tuned to the $\tau_{-+}$ transition with a detuning $\delta_t$ from the transerved center-of-mass mode at frequency $\omega_{{\rm com},t}$. Both couplings operate on a single side-band.$ $Eigen-energies, computed using ED (for $L=16$), are shown as a function of $K$. (a) depicts the lowest energies for various polarization sectors. (b) shows the energy difference between different lowest-lying energies in $\mathcal{P}$=0.$ $(a) The correlation $C_{zz}(1, L)$ is plotted as a function of $K$ using ED ($L=16$) at ${\cal P}=0$. The system passes from an ordered phase to a phase without long-range order. This transition persists with varying $L$, as observed from DMRG (in the insets). (b) The correlator $C_{zz}(1,j)$ behaves differently in these two phases (i.e. $K<K_c$ and $K>K_c$).$ Show more plots

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Record created 2024-12-11, last modified 2024-12-12

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