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# Waveguide QED

Conventional waveguide quantum electrodynamics (waveguide QED) studies collective interaction of quantum emitters in the presence of a one-dimensional (1D) radiation channel. This channel is an ideal non-trivial reservoir for dissipation engineering protocols. The hallmark of collective effects in such systems is the formation of super- and sub-radiant states in the spontaneous emission of an ensemble of atoms, as first described by Dicke. While super(sub)-radiance deals with exchange of real photons between atoms within an electromagnetic reservoir, collective effects can also be achieved by exchange of virtual photons. A virtual photon emitted by an atom can be reabsorbed by another identical atom, giving rise to an effective photon-mediated interaction between a pair of resonant atoms. Although such interactions have been identified via a collective level shift in the spectrum (i.e., the collective Lamb shift), direct signatures of such interactions have not been observed until recently due to the presence of the much stronger radiative decay.

Motivated by previous studies, and with a desire to experimentally study the coherent interactions amongst collections of qubits coupled to a common 1D electromagnetic reservoir, the Painter group recently created and measured a chain of several transmon qubits, acting as artificial atoms, coupled to a coplanar microwave waveguide (this work is in collaboration with the theory groups of Darrick Chang at ICFO and Ana Asenjo-Garcia at Columbia University). Utilizing a magic cavity' qubit layout (see Fig. to the right), coherent dynamics associated with the interaction of a designated probe (or atom') qubit with the qubit chain has been observed in recent work by the Painter group. In this scenario, cancellation of radiative decay is achieved by means of precise control of the phase separation between the mirror qubits, resulting in a form of high-finesse atomic cavity' along the waveguide. The synthetic qubit-cavity system achieves a large cooperativety of C=170 due to the collective enhancement of waveguide-mediated interactions amongst qubits, entering the strong coupling regime. This experiment demonstrates a crucial first step towards realizing a scalable platform for studying many-body physics of quantum spin chains with superconducting qubits: long-range connectivity is achieved by means of the waveguide acting as an open quantum system, while simultaneous cancellation of radiative decay is achieved by encoding quantum information in a decoherence-free subspace of the qubits.

As the qubit number and physical extent of the waveguide is increased, one is naturally forced to deal with non-Markovian effects resulting from the extended nature of the dissipative waveguide reservoir. A central goal of our research is to explore exactly such driven-dissipative quantum systems, where the dissipation is non-Markovian, meaning that the influence of the dissipative environment on the principle system degrees of freedom (the qubits) is not purely local in time (i.e. the bath has a `memory"). The motivation for this is to attempt to harness non-Markovian dissipative environments, which represent a new kind of potentially powerful form of engineered dissipation, for the engineering of quantum states (this work is in collaboration with the theory group of Aash Clerk at the University of Chicago).

"Magic Cavity" qubit chain geometry