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arXiv:2105.04772 · Physical Review A

Evaluating states in trapped ions with local correlation between internal and motional degrees of freedom

Silpa Muralidharan, Ryutaro Ohira, Shota Kume, Kenji Toyoda

Published Dec 6, 2021• 2 citations
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Abstract

We propose and demonstrate a scalable scheme for the simultaneous determination of internal and motional states in trapped ions with single-site resolution. The scheme is applied to the study of polaritonic excitations in the Jaynes-Cummings-Hubbard model with trapped ions, in which the internal and motional states of the ions are strongly correlated. We observe quantum phase crossovers of polaritonic excitations in two ions by directly evaluating their variances per ion site. Our work establishes an essential technological method for large-scale quantum simulations of polaritonic systems.

DOI
10.1103/physreva.104.062410

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We propose and demonstrate a scalable scheme for the simultaneous determination of internal and motional states in trapped ions with single-site resolution. The scheme is applied to the study of polaritonic excitations in the Jaynes-Cummings-Hubbard model with trapped ions, in which the internal and motional states of the ions are strongly correlated. We observe quantum phase crossovers of polaritonic excitations in two ions by directly evaluating their variances per ion site. Our work establishes an essential technological method for large-scale quantum simulations of polaritonic systems.
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 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 experimental results of using trapped ions for the study of energy transport and quantum correlations in many-body systems. We investigate energy propagation by locally exciting one end of an ion chain and then observing the subsequent dynamics. The experimental results agree with the presented normal mode model of ion motion, and signify the first steps towards realizing theoretical proposals of studying many-body physics with the motional degree of freedom of trapped ions. Additionally, we present a method for detecting correlations between an open quantum system and its environment by acting only locally on the open system. We implement this method using a single trapped ion and discuss our current work towards extending the results to larger systems. Lastly, we demonstrate how the presented method for local detection of quantum correlations can be used for detection of quantum phase transitions.
Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.
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.