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Confinement and retrieval of local phonons in a trapped-ion chain

Ryutaro Ohira, Shota Kume, Kyoichi Takayama, Silpa Muralidharan, Hiroki Takahashi, Kenji Toyoda

Published Mar 9, 2020• 1 citation
OpenAlex

Abstract

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.

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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 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.
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 propose and demonstrate phonon-number-resolving detection of the multiple local phonon modes in a trapped-ion chain. To mitigate the effect of phonon hopping during the detection process, the probability amplitude of each local phonon mode is mapped to the auxiliary long-lived motional ground states. Sequential state-dependent fluorescence detection is then performed. In the experiment, we have successfully observed the time evolution of two local phonon modes in two ions, including the phonon-number correlation between the two modes.
Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 μμμm on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.
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.