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arXiv:2206.09565 · Annalen der Physik

Retardation Effect and Dark State in a Waveguide QED Setup With Rectangle Cross Section

Xue Yang, Zhihai Wang

Published Mar 10, 2023• 2 citations
arXivHTMLPDF

Abstract

Abstract This paper investigates the dynamics of two two‐level atoms, which simultaneously couple to a quasi‐1D waveguide with rectangular cross section. The waveguide modes serve as environment, which induces the interaction and collective dissipation between the two distant atoms. When both of the two atoms are located in the middle of the waveguide, a retardation effect is observed, which can be broken by moving one of the atoms away from the center of the waveguide. To preserve the complete dissipation of the system via dark state mechanism, a scheme where the connection of the atoms is perpendicular to the axis of the waveguide is proposed.

DOI
10.1002/andp.202200458

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EPJ Web of Conferences•Jan 1, 2015•0 citations
Abstract This paper investigates the dynamics of two two‐level atoms, which simultaneously couple to a quasi‐1D waveguide with rectangular cross section. The waveguide modes serve as environment, which induces the interaction and collective dissipation between the two distant atoms. When both of the two atoms are located in the middle of the waveguide, a retardation effect is observed, which can be broken by moving one of the atoms away from the center of the waveguide. To preserve the complete dissipation of the system via dark state mechanism, a scheme where the connection of the atoms is perpendicular to the axis of the waveguide is proposed.
Abstract We study a quantum electrodynamics (QED) system made of a two-level atom and a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one end. The spatial dependence of the atomic spontaneous emission has been included in the coupling strength relevant to the eigenmodes of the waveguide. The role of retardation is studied for the atomic transition frequency far away from the cutoff frequencies. The atom-mirror distance introduces different phases and retardation times into the dynamics of the atom interacting resonantly with the corresponding transverse modes. It is found that the upper state population decreases from its initial as long as the atom-mirror distance does not vanish, and is lowered and lowered when more and more transverse modes are resonant with the atom. The atomic spontaneous emission can be either suppressed or enhanced by adjusting the atomic location for short retardation time. There are partial revivals and collapses due to the photon reabsorbed and re-emitted by the atom for long retardation time.
We study a quantum electrodynamics (QED) system made of an two-level atom and a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one end. The spatial dependence of the atomic spontaneous emission has been included in the coupling strength relevant to the eigenmodes of the waveguide. The role of retardation is studied for the atomic transition frequency far away from the cutoff frequencies. The atom-mirror distance introduces different phases and retardation times into the dynamics of the atom interacting resonantly with the corresponding transverse modes. It is found that the upper state population decreases from its initial as long as the atom-mirror distance does not vanish, and is lowered and lowered when more and more transverse modes are resonant with the atom. The atomic spontaneous emission can be either suppressed or enhanced by adjusting the atomic location for short retardation time. There are partial revivals and collapses due to the photon reabsorbed and re-emitted by the atom for long retardation time.
Quantum emitters coupled to a waveguide are a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use antisymmetric states of atomic dimers---a pair of closely spaced atoms---as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide-mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.
Waveguides allow for direct coupling of emitters separated by large distances, offering a path to connect remote quantum systems. However, when facing the distances needed for practical applications, retardation effects due to the finite speed of light are often overlooked. Previous works studied the non-Markovian dynamics of emitters with retardation, but the properties of the radiated field remain mostly unexplored. By considering a toy model of two distant two-level atoms coupled through a waveguide, we study the spectrum of the radiated field that exhibits non-Markovian features such as linewidth broadening beyond standard superradiance, or narrow Fano-resonance-like peaks. We also observe modifications to the energy-exchange dynamics in the presence of retardation. We discuss a proof-of-concept implementation of our results in a superconducting circuit platform.
We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM mn ) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity N 1 can be found as the atom–mirror distance is large enough, however, the asymptotic value of N 2 of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that N 1 is a constant, and the analytical expression for N 2 is related to the parameters associated with the modes, which is related to the interference of the two modes.
The light-matter interaction effects are especially important in one-dimentional (1D) systems, where there is no spatial spreading of emitted radiation. We study Such metastable states of a singly excited pair of resonant atoms arise when the distance between the atoms takes special values We have calculated their decay rate when the interatomic distance deviates from the special values or when the transition frequencies of the two atoms do not coincide (inhomogeneous detuning). Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay, but with a finite probability can evolve to one of the metastable singly-excited states. Dark states of pairs of qubits may serve as memory elements or sensitive detectors of external perturbations.