Algebraic localization and accelerated light-cones in left-handed waveguide-QED

Waveguide-QED plays a central role in applications such as remote entanglement generation and

analog quantum simulation. Here, we discuss a novel waveguide-QED system comprising a

single emitter coupled to a left-handed transmission line (LHTL). In sharp contrast to standard

waveguide-QED, this system exhibits extended bound states with an algebraic fall off with

distance from the emitter along with a crossover to exponential localization at a well-defined

length scale. The scattered photons, concomitantly, show a crossover from accelerated light

cones to standard constant-velocity light cones at the same length scale. By mapping the LHTL

to an extended tight-binding model, we connect these crossovers to the emergence of a critical

length, over which the line exhibits long-range couplings that decay only logarithmically with

distance. Moreover, this critical length is entirely set by an interplay of UV and IR frequency

scales of the LHTL independent of the properties of the emitter. These results motivate how

metamaterial-inspired waveguide engineering can be a powerful platform for simulating

collective quantum phenomena in the presence of complex structured environments, and for

realizing new mechanisms for multi-qubit information processing with tunable-range

interactions.