002919381 001__ 2919381
002919381 005__ 20250430100215.0
002919381 0248_ $$aoai:cds.cern.ch:2919381$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002919381 0247_ $$2DOI$$9arXiv$$a10.22331/q-2025-04-01-1683$$qpublication
002919381 037__ $$9arXiv$$aarXiv:2410.06655$$ccond-mat.quant-gas
002919381 035__ $$9arXiv$$aoai:arXiv.org:2410.06655
002919381 035__ $$9Inspire$$aoai:inspirehep.net:2838542$$d2025-04-23T16:20:57Z$$h2025-04-24T02:00:08Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002919381 035__ $$9Inspire$$a2838542
002919381 041__ $$aeng
002919381 100__ $$aBiswas, Sourav$$uDonostia Intl. Phys. Ctr., San Sebastian$$vDIPC - Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain
002919381 245__ $$9arXiv$$aRing-exchange physics in a chain of three-level ions
002919381 269__ $$c2024-10-09
002919381 260__ $$c2025-04-01
002919381 300__ $$a13 p
002919381 500__ $$9arXiv$$a13 pages, 9 figures
002919381 520__ $$9Verein zur Foerderung des Open Access Publizierens in den Quantenwissenschaften$$aIn the presence of ring exchange interactions, bosons in a ladder-like lattice may form the bosonic analogon of a correlated metal, known as the d-wave Bose liquid (DBL). In this paper, we show that a chain of trapped ions with three internal levels can mimic a ladder-like system constrained to a maximum occupation of one boson per rung. The setup enables tunable ring exchange interactions, transitioning between a polarized regime with all bosons confined to one leg and the DBL regime. The latter state is characterized by a splitting of the peak in the momentum distribution and an oscillating pair correlation function.
002919381 520__ $$9arXiv$$aIn the presence of ring exchange interactions, bosons in a ladder-like lattice may form the bosonic analogon of a correlated metal, known as the d-wave Bose liquid (DBL). In this paper, we show that a chain of trapped ions with three internal levels can mimic a ladder-like system constrained to a maximum occupation of one boson per rung. The setup enables tunable ring exchange interactions, transitioning between a polarized regime with all bosons confined to one leg and the DBL regime. The latter state is characterized by a splitting of the peak in the momentum distribution and an oscillating pair correlation function.
002919381 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002919381 540__ $$3publication$$aCC BY 4.0$$fOther$$uhttp://creativecommons.org/licenses/by/4.0/
002919381 542__ $$3publication$$dThe author(s)$$g2025
002919381 65017 $$2arXiv$$aquant-ph
002919381 65017 $$2SzGeCERN$$aGeneral Theoretical Physics
002919381 65017 $$2arXiv$$acond-mat.str-el
002919381 65017 $$2arXiv$$acond-mat.quant-gas
002919381 690C_ $$aCERN
002919381 690C_ $$aARTICLE
002919381 700__ $$aRico, E.$$uDonostia Intl. Phys. Ctr., San Sebastian$$uBasque U., Bilbao$$uCERN$$vDIPC - Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain$$vEHU Quantum Center and Department of Physical Chemistry, University of the Basque Country UPV/EHU, P.O. Box 644, 48080 Bilbao, Spain$$vEuropean Organization for Nuclear Research (CERN), Geneva 1211, Switzerland$$vIKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
002919381 700__ $$aGrass, Tobias$$uDonostia Intl. Phys. Ctr., San Sebastian$$uBasque U., Bilbao$$vDIPC - Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain$$vIKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
002919381 773__ $$c1683$$mpublication$$pQuantum$$v9$$xQuantum 9, 1683 (2025)$$y2025
002919381 8564_ $$82695108$$s906144$$uhttp://cds.cern.ch/record/2919381/files/ion_ladder_scheme.png$$y00000 (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.
002919381 8564_ $$82695109$$s50933$$uhttp://cds.cern.ch/record/2919381/files/Ens_t12K12_ED_L16_E0Gap.png$$y00001 Eigen-energies, computed using ED (for $L=16$), are shown as a function of $K$. Panel (a) depicts the lowest energies for various polarization sectors. In the inset, we zoom into the transition point, noting that the order of the different polarization sectors is altered. Panel (b) shows the energy difference between different lowest-lying energies in $\mathcal{P}$=0. For intermediate values of $K$, a degeneracy is observed, which is lifted when the system enters the DBL phase at large $K$. The degeneracy is also lifted at $K \to 0$, where the system becomes superfluid \cite{Sheng_2008}.
002919381 8564_ $$82695110$$s1083511$$uhttp://cds.cern.ch/record/2919381/files/2410.06655.pdf$$yFulltext
002919381 8564_ $$82695111$$s14867$$uhttp://cds.cern.ch/record/2919381/files/P2.png$$y00005 The $P_2 (\Delta x)$ for parallel diagonals: $Dia-Para$ ($\gamma =1, \eta=2 $ ) and perpendicular diagonals: $Dia-Perp$ ($\gamma =2, \eta=1 $ ) are opposite in sign and oscillate with a period $1/n_f$. In (a), we show the convention used for calculating the pair correlation, and in (b) and (c), results for different fillings are depicted. We observe changing $n_f$ changes the modulation in $P_2$ which is consistent with the shifting of peaks in FIG.~\eqref{fig:DBL}.
002919381 8564_ $$82695112$$s9949$$uhttp://cds.cern.ch/record/2919381/files/SFq_DMRG_t12K12_R0.2K0.3.png$$y00006 $\mathcal{S}_z(q)$ computed using DMRG. At $K=0.3$, a comparison between $L=16,48$ shows the persistence of sharp peaks with $\Delta q_L$ wave vector. In the inset, we see data for $L=48$ at $K=0.6$. The smoothness of $\mathcal{S}_z$ suggests an absence of any true long-range order. This is a characteristic of the DBL phase.
002919381 8564_ $$82695113$$s4984$$uhttp://cds.cern.ch/record/2919381/files/Nq.png$$y00004 $n(q)$ is plotted for $K=0.6$, using DMRG for $L=60$. The absence of zero momenta peak and the presence of peaks at $k_s=\pi n_f$ are also consistent with the known features of such a phase. We see that changing $n_f $ from $1/4$ to $1/3$ shifts the peaks.
002919381 8564_ $$82695114$$s20690$$uhttp://cds.cern.ch/record/2919381/files/Transition_ED_DMRG_Rf0.2_t12K12.png$$y00002 (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 a state with a domain wall (DW) to a state without any local order (DBL). This transition persists with varying $L$, as observed from DMRG, as shown in (b) and (c). We demarcate separate phases on the plot to ease the visual representation of different phases.
002919381 8564_ $$82722879$$s7996$$uhttp://cds.cern.ch/record/2919381/files/Sz_Bulk_Scaling_DMRG_Rf0.2_t12K12.png$$y00007 Both the panels are plotted with $L=48$, where for DBL we use $K=0.6$ and for the DW we use $K=0.3$. In (a) we show the local magnetization. It is evident that for DBL there is no local order. However, for DW there is a finite local order. In (b) we plot the decay of the connected correlator in the bulk, using a $\log-\log$ scale. The $C_{zz}^{conn}$ decays faster following an exponential behavior for the DW, whereas it is a power law for DBL.
002919381 8564_ $$82722880$$s4079$$uhttp://cds.cern.ch/record/2919381/files/Scaling_Sz1L_DMRG_Rf0.2_t12K12.png$$y00003 The correlator $C_{zz}(1,j)$ behaves differently in these two phases (i.e. $K<K_c$ and $K>K_c$). In the DW phase (red), positive correlations for $j \leq 8$ indicate that these rungs are polarized on the same leg as the first rung, whereas negative values for $j>8$ indicate opposite polarization, establishing a domain wall at $j=8$.
002919381 8564_ $$82722881$$s5824$$uhttp://cds.cern.ch/record/2919381/files/ED_Split_Nq.png$$y00008 (a) The quantity $\Delta n =n(0) - {\rm max}(n(q))$ is plotted vs. $K$ to identify DBL formation through the characteristic features of $n(q)$, using ED for a chain with $L=16$. The zero value of the quantity implies that the maximum of $n(q)$ corresponds to $q=0$. A finite negative value, with increasing $K$, denotes the appearance of a momenta peak at a non-zero value, indicating peak splitting which is typical of the DBL phase. We plot the same function for different $\alpha$. For $\alpha \geq 2$, the DBL transition is observed, whereas for $\alpha =1.5$ it is not. We have also shown the $\Delta n$, corresponding to the data set of Fig. 2 of the main text, for the sake of completeness. (b) We show $n(q)$ for $\alpha=2$, to illustrate the splitting of peaks at sufficiently large ring exchange ($K=3.0$, red dashed-dotted line), in contrast to a single peak for sufficiently small ring exchange ($K=1.0$, blue dashed line).
002919381 8564_ $$82722882$$s130623$$uhttp://cds.cern.ch/record/2919381/files/scheme.png$$y00000 (a) Mapping between the two-leg ladder and chain of three-level ions: Each rung of the ladder is represented by an ion. A hopping process $t_{i,i+1}$ on the lower leg of the ladder (green solid line) maps onto the combined transition of two ions, from $\ket{-}$ to $\ket{0}$ on ion $i$, and from $\ket{0}$ to $\ket{-}$ on ion $i+1$. Similarly, hopping on the upper leg (green dashed line) translates into transitions between $\ket{+}$ to $\ket{0}$. The ring exchange interaction describes correlated hopping processes of two particles on opposite corners of a plaquette (yellow lines). These processes translate into transitions between $\ket{-}$ to $\ket{+}$ on two neighboring ions. (b,c) Implementation of 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 green couple to the longitudinal phonons, and are equipped with two beat notes, tuned to the $\tau_{0-}$ transition and the $\tau_{0+}$ transition, with different detunings $\delta_{0-}^{\mathsf{lcom}}$ and $\delta_{0+}^{\mathsf{lcom}}$ from the longitudinal center-of-mass mode at frequency $\omega_{\mathsf{lcom}}$, as indicated in the box. The pairs drawn in yellow couple to transverse phonon modes, and are equipped with one beat-note tuned to the $\tau_{-+}$ transition with a detuning $\delta_{-+}^{\mathsf{tcom}}$ from the transverse center-of-mass mode at frequency $\omega_{\mathsf{tcom}}$. Both couplings operate on the blue sideband.
002919381 8564_ $$82728506$$s1087933$$uhttp://cds.cern.ch/record/2919381/files/document.pdf$$yFulltext
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002919381 980__ $$aARTICLE