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arXiv:0905.2593 · Physical Review A

Simulation of a quantum phase transition of polaritons with trapped ions

Peter A. Ivanov, Svetoslav S. Ivanov, Nikolay V. Vitanov, Alexander Mering, Michael Fleischhauer, Kilian Singer

Published Dec 3, 2009• 66 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.80.060301

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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.
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 report an experimental realization of the Jaynes-Cummings-Hubbard model using the internal and radial phonon states of two trapped ions. An adiabatic transfer corresponding to a quantum phase transition from a localized insulator ground state to a delocalized superfluid (SF) ground state is demonstrated. The SF phase of polaritonic excitations characteristic of the interconnected Jaynes-Cummings (JC) system is experimentally explored, where a polaritonic excitation refers to a combination of an atomic excitation and a phonon interchanged via a JC coupling.
Abstract We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband (BSB) transition, we realize the anti-Jaynes–Cummings–Hubbard (JCH) model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton–polariton interaction induced by the nonlinearity of the anti-Jaynes–Cummings (JC) interaction, thereby realizing the blockade of polariton hopping in the anti-JCH model with trapped ions. Our work is a step towards the development of a trapped-ion based quantum simulator for strongly interacting polaritonic systems.
We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.
Abstract We demonstrate the site-dependent control of polaritons in the Jaynes–Cummings–Hubbard (JCH) model with trapped ions. In a linear ioncrystal under illumination by optical beams nearly resonant to the red-sideband (RSB) transition for the radial vibrational direction, quasi-particles called polaritonic excitations or polaritons, each being a superposition of one internal excitation and one vibrational quantum(phonon), can exist as conserved particles. Polaritons can freely hop between ion sites in a homogeneous configuration, while their motioncan be externally controlled by modifying the parameters for the optical beams site-dependently. We demonstrate the blockade of polariton hop-ping in a system of two ions by the individual control of the frequency of the optical beams illuminating each ion. A JCH system consisting ofpolaritons in a large number of ion sites can be considered an artificialmany-body system of interacting particles, and the technique intro-duced here can be used to exert fine local control over such a system,enabling detailed studies of both its quasi-static and dynamic properties.