**Quantum electrodynamics in lineland**

Quantum electrodynamic phenomena, such as spontaneous emission from an atom or coupling between two dipoles, sensitively depend on the dimension of the surrounding space. The intrigue of dimensional dependence is whimsically related in Abbott’s story about a Square living in two-dimensional Flatland [1]. The Square tries to comprehend three-dimensional Spaceland from a visiting Sphere, and, in a separate tale, the Square tries to explain the second dimension to the Points inhabiting one-dimensional Lineland.
Superconducting circuits with inbuilt artificial atoms, based on using Josephson junctions to realize nonlinear oscillators with quantized energy levels, enable us to realize Quantum Electrodynamics in Lineland. Lineland turns out to be a technological wonderland, with easy access to strong dipole coupling, excellent mode matching and non-abating dipole-dipole coupling over long distances. In particular we explore coherent and collective effects of artificial atoms in Lineland and their technological implications [2-5].
[1] Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions (1884).
[2] J. Joo, J. Bourassa, A. Blais and B. C. Sanders, Electromagnetically-induced transparency with amplification in superconducting circuits, Physical Review Letters 105(7): 073601 (2010).
[3] P. M. Leung and B. C. Sanders, Coherent control of microwave pulse storage in superconducting circuits , Physical Review Letters 109(25): 253603 (2012).
[4] K. Lalumière, B. C. Sanders, A. F. Van Loo, A. Fedorov, A. Wallraff and A. Blais, Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms, Physical Review A 88(4): 043806 (2013).
[5] A. F. Van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais and A. Wallraff, Photon-mediated interactions between distant artificial atoms, Science 342(6165), 1494-1496 (2013).