Simulation of a quantum phase transition of polaritons with trapped ions

We present a system for the simulation of Heisenberg models with spins s = 1 2 and s = 1 with a linear crystal of trapped ions. We show that the laser-ion interaction induces a Jaynes-Cummings-Hubbard interaction between the atomic V-type level structure and the two phonon species. In the strong-coupling regime the collective atom and phonon excitations become localized at each lattice site and form an effective spin system with varying length. We show that the quantum-mechanical superexchange interaction caused by the second-order phonon hopping processes creates a Heisenberg-type coupling between the individual spins. Trapped ions allow to control the superexchange interactions by adjusting the trapping frequencies, the laser intensity, and the detuning.

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“…Assuming that the radial trapping potential is much larger than the Coulomb interaction we arrive at [12,23] …”

Section: Phonon Hamiltonianmentioning

confidence: 99%

Quantum simulation of superexchange magnetism in linear ion crystals

et al. 2014

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“…The competition between strong photon-qubit coupling, giving rise to an effective photonic repulsion (localization), and the photon hopping between cavities (delocalization) leads to a phase diagram featuring Mott lobes reminiscent of those of ultracold atoms in optical lattices as described by the BHM. The realization of the JCHM has been proposed in various solid-state or quantum-optical systems, e.g., with nitrogen-vacancy (NV) centers in diamond [7][8][9], quantum dot excitons [17], superconducting qubits [13], and trapped ions [18]. Device integration, high tunability, and individual addressability of each cavity make wide parameter regimes easily accessible.…”

Section: Introductionmentioning

confidence: 99%

Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

et al. 2011

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An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott insulator transition of lattice polaritons. From mean-field and strong coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid density and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the 3D XY universality class, analogous to the Bose-Hubbard model.Comment: 4 pages, 4 figures. To appear as a Rapid Communication in Phys. Rev.

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“…At this point, let us compare our model to the Jaynes-Cummings and Rabi lattice models, which arise in coupled-cavity arrays [15,16], or trapped-ion crystals [17,18], and may be considered as particular instances of cooperative Jahn-Teller models [19]. In these models, spins only interact locally with the bosonic modes, which are in turn coupled among themselves.…”

Section: The Model: Definition and Backgroundmentioning

confidence: 99%

The interspersed spin boson lattice model

Kurcz

García-Ripoll

Bermúdez

2015

Eur. Phys. J. Spec. Top.

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We describe a family of lattice models that support a new class of quantum magnetism characterized by correlated spin and bosonic ordering [Phys. Rev. Lett. 112, 180405 (2014)]. We explore the full phase diagram of the model using Matrix-Product-State methods. Guided by these numerical results, we describe a modified variational ansatz to improve our analytic description of the groundstate at low boson frequencies. Additionally, we introduce an experimental protocol capable of inferring the low-energy excitations of the system by means of Fano scattering spectroscopy. Finally, we discuss the implementation and characterization of this model with current circuit-QED technology.

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Simulation of a quantum phase transition of polaritons with trapped ions

Cited by 73 publications

References 37 publications

Quantum simulation of superexchange magnetism in linear ion crystals

Quantum simulation of superexchange magnetism in linear ion crystals

Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

The interspersed spin boson lattice model

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