Two interacting electrons in a harmonic trap

Thomas Busch, Berthold‐Georg Englert, Kazimierz Rza̧żewski +1 more

Pablo Guillermo Carmona Rufo, Anupam Mazumdar, Carlos Sabín

We study the dynamics of quantum entanglement between two harmonically trapped electrons interacting via the electromagnetic force. Starting from two-mode Gaussian states at thermal equilibrium, we make use of the covariance matrix formalism in order to compute the logarithmic negativity of the evolved state as a quantitative measure of entanglement. We analyze two initial configurations: thermal single-mode and two-mode squeezed states, and describe the time evolution of entanglement in the system for different values of squeezing and temperature, while identifying the parameter regimes accessible to current and near-future single-electron trap experiments.

Ronen M. Kroeze, Jom Luiten, S. J. J. M. F. Kokkelmans

A full strength Coulomb interaction between trapped electrons can be felt only in absence of a neutralizing background. In order to study quantum degenerate electrons without such a background, an external trap is needed to compensate for the strong electronic repulsion. As a basic model for such a system, we study a trapped electron pair in a harmonic trap with an explicit inclusion of its Coulomb interaction. We find the eigenenergy of the ground state, confirming earlier work in the context of harmonium. We extend this to a complete set of properly scaled energies for any value of the trapping strength, including the excited states. The problem is solved either numerically or by making harmonic approximations to the potential. As function of the trapping strength a crossover can be made from the strongly to the weakly-coupled regime, and we show that in both regimes perturbative methods based on a pair-wise electron description would be effective for a many-particle trapped electron system, which resembles a Wigner crystal in the ground state of the strongly coupled limit.

Pooja Nadkarni Singh, Yuri V. Rostovtsev

J. Pitteloud, Thomas Pattard, Xiao‐Min Tong +1 more

April Cridland Mathad, John H. Lacy, Jonathan Pinder +4 more

We theoretically investigate the coupling of a single electron in a planar Penning trap with a remote superconducting microwave (MW) cavity. Coupling frequencies around Ω=2π·1 MHz can be reached with resonators with a loaded quality factor of Q=105, allowing for the strong coupling regime. The electron and the cavity form a system of two coupled quantum harmonic oscillators. This is a hybrid and linear microwave quantum network. We show that the coherent interaction can be sustained over distances of a few mm up to several cm. Similar to classical linear MW circuits, the coherent quantum exchange of photons is ruled by the impedances of the electron and the cavity. As one concrete application, we discuss the entanglement of the cyclotron motions of two electrons located in two separate traps.