Yao-Lung L. Fang

Waveguide QED: Power spectra and correlations of two photons scattered off multiple distant qubits and a mirror

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.

One-dimensional waveguide coupled to multiple qubits: photon-photon correlations

For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation L. We study the correlations by calculating the second-order correlation function g2(t) in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function g2(t) including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation L could be readily explored with our approach.

Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubits dynamical map. Tools of open quantum systems theory allow us then to discuss the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.

Multiple emitters in a waveguide: Nonreciprocity and correlated photons at perfect elastic transmission

We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven {\Lambda}-type three-level system (3LS) in both the single- and two- photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted photons completely uncorrelated. Slightly away from this separation, we find that the inelastic scattering (fluorescence) is large, leading to nonlinear effects such as non-reciprocity (rectification). We connect this non-reciprocity to inelastic scattering caused by driving a dark pole and so derive a condition for maximum rectification. Finally, by placing a true 3LS midway between the two 2LS, we show that elastic scattering produces only transmission, but inelastic scattering nevertheless occurs (the fluorescence is not quenched) causing substantial photon correlations.