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

Abstract

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 g 2 (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 g 2 (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.

Single-photon transport through an atomic chain coupled to a one-dimensional nanophotonic waveguide

“…In particular, a photon with frequency resonant to the two-level atom can be * zeyangliao@physics.tamu.edu † zubairy@physics.tamu.edu even completely reflected. Since then, this method has been generalized to the case for multilevel atom and multiphoton interactions [17][18][19][20][21][22]. In the stationary calculations, the photon is assumed to be a plane wave with single frequency.…”

Decay of metastable excited states of two qubits in a waveguide

“…There have been many investigations of the dynamics, entanglement, and emission of two TLAs coupled with an electromagnetic field in free space, in a cavity, and, in particular, in a one-dimensional (1D) waveguide (see the review in Refs. [11] and recent papers [12][13][14]). The latter 1D case is of special interest: on one hand, in contrast to the case of a higher dimension, there is no spatial spreading of the emitted radiation; on the other hand, the electromagnetic field in a thin 1D waveguide comprises an infinite number of modes for rightand left-moving photons of arbitrary frequencies.…”

“…Nevertheless, some particular problems can still be described explicitly. Among them is the problem of photon scattering by a system of few TLAs where the (inelastic) scattering matrix of several photons 063829-2 can be explicitly found [12,14,[22][23][24][25]. However, the problem of the spontaneous decay of an initially excited system of TLAs is more difficult because it requires describing the system in time rather than in the spectral domain, and the transition from one to another is quite sophisticated.…”

“…To describe the 1D propagation of an electromagnetic field in a waveguide we use the coordinate representation for "smooth" (envelope) field operators rather than the momentum representation. This widely implemented approach (see, for instance, [3,14,18,20,22,23,25]) is well suited for the nonperturbative treatment of multiple absorption-emission-reflection events in a system with spatially separated TLAs. The more traditional momentum representation is usually applied for configurations where there is no back-and-forth propagation of photons between the TLAs (e.g., for collocated TLAs [12], chiral waveguides [24], etc.…”

Few-photon scattering on Bose-Hubbard lattices

“…scattering theory [15][16][17][18][19], Lehmann-Symanzik-Zimmermann formalism [20], generalized master equations [21,22], SLH formalism [23,24], and input-output theory [19,25]. We here provide a generalization of the scattering theory methods to more complex local and quasi-local scatterers.…”