Correlations among photons are typically very weak: because photons do not interact with each other, the position of one photon does not depend on the position of another photon. However, if 'matter' is present with which the photons strongly interact, the matter mediates an effective interaction between the photons-- the first photon strongly affects the matter which then affects the second photon-- that then leads to photon-photon correlation. The matter can take a wide variety of forms, such as atoms, quantum dots, or superconducting qubits. Interactions in one dimension (1D) are particularly interesting since the photons cannot miss each other which often leads to enhanced correlations. Interest in these quantum optics phenomena in one dimension, dubbed 'waveguide Quantum Electrodynamics (QED)', or "waveguide QED",, has rapidly grown in recent years, driven notably by the fact that several such experimental systems can now be made with relatively strong interactions. Examples include tapered fibers coupled to atoms, microwave transmission lines coupled to superconducting qubits, and semiconductor dielectric waveguides coupled to quantum dots. Photon correlations in multi-qubit waveguide systems will be studied. Theoretically much is now known about a single atom or qubit interacting with 1D photons, and so the time is ripe for considering photonic waveguide systems with more complex matter. First, situations in which a few two-level-systems (qubits or atoms, say) interact with 1D light will be studied with the aim of describing the specifically quantum properties of the light that can be produced (non-classical light). Then, the case of many qubits (a large amount of matter) will be considered with the idea that new phases of the light/matter system may be possible. Phase transitions in driven systems, called dynamical phase transitions, are receiving increasing attention; the waveguide QED system may be a way to realize different kinds of dynamical phases. The research in this project connects to several other broad fields. First, nanophotonic devices often involve two-level systems and 1D modes as building blocks. The new physical effects studied here will lead to a better understanding of such elements and may lead to qualitatively new devices. Second, the proposed structures in their superconducting qubit/microwave version constitute quantum meta-materials, a rapidly developing offshoot of the enormous interest in meta-materials generally in recent years. Third, quantum networks for quantum information purposes involve elements that look exactly like the waveguide QED systems studied here.
The subject of this research is the correlations among photons in a waveguide caused by their interaction with discrete quantum objects, such as atoms, quantum dots, or qubits. Photon correlations caused by strong light-matter interaction have been studied extensively in the context of relatively closed cavities. In contrast, one-dimensional (1D) waveguides are quantum open systems, in some of which, nevertheless, it may soon be possible to achieve strong coupling to atoms or qubits. In this theoretical work photon correlations in multi-qubit waveguide systems will be investigated. Specifically, three areas will be studied. First, nonclassical light and time delay for few qubit systems will be studied. The photon correlations (coherences) will be calculated for several few qubit situations involving up to 10 two-level or three-level systems. An immediate result will be the change in the properties of the non-classical light generated as a function of number of qubits - non-classical features are expected to be enhanced, though the interplay with interference effects may be complicated. Three-level systems introduce a new aspect: time-delay. The use of this for enhancing interaction or interference effects (interferometry) will be evaluated. Second, for many qubit systems, the question of whether dynamical phase transitions can produce new states of light will be studied. An infinite system with sparse periodic, disordered, or dense atoms or qubits brings in the possibility of a new state of light. Since the system is necessarily driven, this would involve a dynamical phase transition. Whether such a transition can take place in a waveguide QED system will be evaluated. Finally, quantum optics phenomena with DC electrical transport will be studied. Electromagnetic radiation along a chain of Josephson junctions coupled to a superconducting qubit is a new waveguide QED system. If time permits, the possibility of probing the system by electrical transport through a weakly coupled probe junction, thus revealing the quantum optics properties, will be investigated. Several methods will be used to tackle these problems. Tasks 1 and 3 can be started with exact methods that were developed previously, and then will be continued with numerical propagation of pulses. Both the few and many qubit problems will be approached with a slave-boson mean field theory and Keldysh quantum field theory. The comparison with the exact methods in the few qubit cases will provide an important cross-check.
