Collective Lamb Shift due to 1D Dipole-dipole Interaction with Artificial Atoms

Kuan-Ting Lin^1*, Io-Chun Hoi³, Guin-Dar Lin^1,2

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Center of Quantum Science and Engineering, Taipei, Taiwan
³Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Kuan-Ting Lin, email:alex968.tw@gmail.com

We investigate the dipole-dipole interaction between two artificial atoms in a 1D geometry, implemented by two transmon qubits coupled through transmission lines. In this work, we effectively set one end of the transmission line to be a mirror, in front of which two qubits are placed. We calculate the reflected field as the separation between two qubits changes, thus probing the dipole-dipole shift and linewidth in terms of the reflective spectrum. We observe that, even when one qubit is located in the node of the resonant mode, which is thought to be decoupled from the pumping field, energy shift can be observed. Such shift comes from the dipole-dipole interaction by exchanging virtual photons, leading to the so-called collective Lamb shift. We also generalize our calculation to multi-atom cases and discuss how these effects scale with the qubit number. Our calculation also applies to the optical cavity systems with real atoms.

Keywords: dipole-dipole interaction, Collective Lamb shift, Superradiance and Subradiance