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arXiv:1405.6071 · Physical Review A

Quantum simulation of superexchange magnetism in linear ion crystals

Peter A. Ivanov, Naoum Karchev, Nikolay V. Vitanov, Dimitris G. Angelakis

Published Jul 17, 2014• 3 citations
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Abstract

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 $\mathsf{V}$-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 control of the superexchange interactions by adjusting the trapping frequencies, the laser intensity, and the detuning.

DOI
10.1103/physreva.90.012325

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We present a system for the simulation of Heisenberg models with spins s=1/2s=1/2s=1/2 and s=1s=1s=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\mathsf{V}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 control of the superexchange interactions by adjusting the trapping frequencies, the laser intensity, and the detuning.
We present a system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tuning of the hopping frequency by adjusting the axial trapping frequency and the phonon-phonon repulsion via laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.
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The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.
We propose the realization of linear crystals of cold ions that contain different atomic species for investigating quantum phase transitions and frustration effects in spin systems beyond the commonly considered case of . Mutual spin–spin interactions between ions can be tailored via the Zeeman effect by applying oscillating magnetic fields with strong gradients. Further, collective vibrational modes in the mixed ion crystal can be used to enhance and to vary the strength of spin–spin interactions and even to switch the nature of the interacting forces from a ferro- to an antiferromagnetic character. We consider the behavior of the effective spin–spin couplings in an ion crystal of spin-1/2 ions doped with high-magnetic-moment ions with spin S = 3. We analyze the ground state phase diagram and find regions with different spin orders including ferrimagnetic states. In the most simple nontrivial example, we deal with a linear {Ca + ,Mn + ,Ca + } crystal with spins of . To demonstrate feasibility with current state-of-the-art experiments, we discuss how quantum phases might be detected using a collective Stern–Gerlach effect of the ion crystal and high-resolution spectroscopy. Here, the state-dependent laser-induced fluorescence of the indicator spin-1/2 ion, of species 40 Ca + , is used to reveal also the spin state of the simulator spin-3 ions, 50 Mn + , which does not possess suitable levels for optical excitation and detection.
Trapped atomic ion crystals are a leading platform for quantum simulations of spin systems, with programmable and long-range spin-spin interactions mediated by excitations of phonons in the crystal. We describe a complementary approach for quantum simulations of bosonic systems using phonons in trapped-ion crystals, here mediated by excitations of the trapped-ion spins. The scheme enables a high degree of programability across a dense graph of bosonic couplings, utilizing long-lived collective phonon modes in a trapped-ion chain. As such, it is well suited for tackling hard problems such as boson sampling and simulations of long-range bosonic and spin-boson Hamiltonians.
A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin–spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how the appropriate design of laser fields can provide for arbitrary multidimensional spin–spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently available trap technology and is scalable to levels where the classical methods of simulation are intractable.