Polariton Mott insulator with trapped ions or circuit QED

M. Hohenadler, M. Aichhorn, L. Pollet, and S. Schmidt

Phys. Rev. A 85, 013810 – Published 9 January 2012

Abstract

We consider variants of the Jaynes-Cummings-Hubbard model of lattice polaritons, taking into account next-nearest-neighbor, diagonal, and long-range photon hopping in one and two dimensions. These models are relevant for potential experimental realizations of polariton Mott insulators based on trapped ions or microwave stripline resonators. We obtain the Mott-superfluid phase boundary and calculate excitation spectra in the Mott phase using numerical and analytical methods. Including the additional hopping terms leads to a larger Mott phase in the case of trapped ions, and to a smaller Mott phase in the case of stripline resonators, compared to the original model with nearest-neighbor hopping only. The critical hopping for the transition changes by up to about 50 percent in one dimension and by up to about 20 percent in two dimensions. In contrast, the excitation spectra remain largely unaffected.

Received 14 October 2011

DOI:https://doi.org/10.1103/PhysRevA.85.013810

Authors & Affiliations

M. Hohenadler^1,*, M. Aichhorn², L. Pollet³, and S. Schmidt³

¹Institut für Theoretische Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, Germany
²Institut für Theoretische Physik–Computational Physics, TU Graz, A-8010 Graz, Austria
³Institut für Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland

^*martin.hohenadler@physik.uni-wuerzburg.de

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Vol. 85, Iss. 1 — January 2012

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Images

Figure 1
Circuit-QED realization of the JCHM on a 2D square lattice. A filled circle indicates a lattice site, defined by the position of a qubit. Each qubit is located inside a resonator represented by a rectangle. The capacitive coupling between resonators gives rise to photon hopping across the lattice. Two different couplings occur: nearest-neighbor hopping, with amplitude $t$ along the lattice axes; and diagonal next-nearest-neighbor hopping, in every other plaquette with amplitude $t^{'}$ .Reuse & Permissions
Figure 2
Zero-temperature Mott lobe with density $n = 1$ of the 1D JCHM, showing the effect of (a) long-range hopping defined by Eq. (4) and (b) sign-alternating long-range hopping defined by Eq. (3), as appropriate for an experimental realization based on trapped ions. Case (a) can be investigated by QMC simulations (symbols), and the phase boundary is compared to the VCA (lines; for a cluster size $L = 8$ ). For reference, we also show the exact result for the original JCHM with nearest-neighbor hopping only [7] (shaded regions). Case (b) is not accessible for QMC, and we rely on the VCA for the phase diagram.Reuse & Permissions
Figure 3
Zero-temperature Mott lobe with density $n = 1$ of the 2D JCHM, showing the effect of (a) next-nearest-neighbor hopping $t^{''} = t / 8$ (see Sec. 2) and (b) diagonal next-nearest-neighbor hopping $t^{'} = t / 2$ as appropriate for an experimental realization based on stripline resonators (see Fig. 1 and Sec. 2). We show results from QMC simulations (symbols), the VCA (lines; $L = 8$ ), the mean-field theory (RPA), and the one-loop approximation. For reference, we also include the $t^{'} = t^{'} = 0$ QMC results for the original 2D JCHM model (shaded regions; taken from [9]).Reuse & Permissions
Figure 4
Zero-temperature excitation spectra of the 1D JCHM at zero detuning with (a) nearest-neighbor hopping $t$ and (b) sign-alternating long-range hopping $t_{i j}$ , relevant for trapped ions Eq. (3). Results are from the VCA with cluster size $L = 8$ and using $t / g = 0.1$ , $μ / g = 0.15$ [see Fig. 2b].Reuse & Permissions
Figure 5
Zero-temperature excitation spectra for the 2D JCHM at zero detuning with $t^{'} = 0$ (solid lines) or $t^{'} / t = 1 / 2$ [dashed lines and intensity plot in (a)], as appropriate for a circuit-QED setup (see Fig. 1 and Sec. 2). (a) Parameters deep in the Mott lobe, using $t / g = 0.02$ , $μ / g = 0.22$ . (b) Parameters exactly at the Mott lobe tip, using $t / g = 0.04$ (for $t^{'} = 0$ ) respectively $t / g = 0.032$ (for $t^{'} / t = 1 / 2$ ) and $μ / g = 0.22$ [see Fig. 3b]. Lines are RPA results for the particle/hole dispersion. The density plot in (a) shows VCA results based on a $2 \times 2$ cluster.Reuse & Permissions

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