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arXiv:2103.05253 · Quantum Science and Technology

Polariton blockade in the Jaynes–Cummings–Hubbard model with trapped ions

Ryutaro Ohira, Shota Kume, Hiroki Takahashi, Kenji Toyoda

Published Mar 26, 2021• 7 citations
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Abstract

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.

DOI
10.1088/2058-9565/abecd1

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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.
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.
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.
Driving an ion at a motional sideband transition induces the Jaynes--Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we report the confinement of multiple local phonons to a single ion site using this nonlinear quantum effect. By using phonon-number-resolving detection, we observe the dynamics of multiple phonons in an ion chain. In addition to simply confining local phonons, by turning the JC interaction on and off dynamically, we can confine a single local phonon to a single ion site and subsequently retrieve it out of the site. Our work establishes a key technological component for quantum simulation with multiple bosonic particles, which can simulate classically intractable problems.
The Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here, we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of 2^{77}, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our Letter demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems.