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. Quantum simulations allow us to study the properties of many-body quantum systems that are hard to investigate with classical computers. A promising platform for realizing quantum simulations is a system of trapped ions. Trapped ions have advantages over other systems from such perspectives as ease of preparation and control, and we can address individual particles with little perturbation to neighboring particles. TheJaynes-Cummings (JC) model describes the atom-field interaction in a combined system of a two-level atom and a quantized electric-field mode. An interconnected array of two-level atoms interacting with quantized wave modes is known as the Jaynes-Cummings-Hubbard (JCH) model, and related systems of coupled cavity arrays have been extensively investigated. The JCH model can be realized with arrays of cavity QED systems and of circuit QED systems, as well as systems of trapped ions. These systems can be flexibly controlled with sets of system parameters.Therefore, they can be considered to be attractive systems for studying quantum many-body phenomena. In the JCH model, quasiparticles called polaritons play an essential role. Each polariton is represented as the superposition of an internal excitation and a photon or a motional excitation (phonon). Polaritons are well-defined particles in the JCH model and their total number is conserved.
The implications for understanding the JCH model are apparent in the quantum phase transition of a JCH system between the Mott -insulator (MI) and superfluid (SF) phases, which are characterized by a drastic change in the polariton-number variance per site.
In conclusion, we proposed a scalable scheme for the simultaneous determination of internal and motional states in trapped ions based on conditional measurements. The scheme was applied to a system of polaritons in the JCH model, and a phase crossover was studied by evaluating the quantities such as the variance for the total excitation number (polariton number) per site. The scheme proposed here can be applied to larger JCH systems where steeper phase crossovers and transitions as well as non-equilibriumbehaviors reflecting interactions are expected. In addition, the scheme can also be applied to other subjects in quantum simulations with trapped ions where both the internal and motional degrees of freedom are fully exploited as the simulation resources.
|Presenter name||Silpa Muralidharan|
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