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Oscillating bound states for a giant atom

Guo, L., Frisk Kockum, A., Marquardt, F., Johannson, G.

Published Oct 2, 2020• 127 citations
OpenAlex

Abstract

We investigate the relaxation dynamics of a single artificial atom interacting, via multiple coupling points, with a continuum of bosonic modes (photons or phonons) in a one-dimensional waveguide. In the non-Markovian regime, where the traveling time of a photon or phonon between the coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the atom, we find that a boson can be trapped and form a stable bound state. As a key discovery, we further find that a persistently oscillating bound state can appear inside the continuous spectrum of the waveguide if the number of coupling points is more than two since such a setup enables multiple bound modes to coexist. This opens up prospects for storing and manipulating quantum information in larger Hilbert spaces than available in previously known bound states.

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We investigate the relaxation dynamics of a single artificial atom interacting, via multiple coupling points, with a continuum of bosonic modes (photons or phonons) in a one-dimensional waveguide. In the non-Markovian regime, where the traveling time of a photon or phonon between the coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the atom, we find that a boson can be trapped and form a stable bound state. As a key discovery, we further find that a persistently oscillating bound state can appear inside the continuous spectrum of the waveguide if the number of coupling points is more than two since such a setup enables multiple bound modes to coexist. This opens up prospects for storing and manipulating quantum information in larger Hilbert spaces than available in previously known bound states.
It is known that the superposition of two bound states in the continuum (BICs) leads to the phenomenon of an oscillating bound state, where excitations mediated by the continuum modes oscillate persistently. We perform exact calculations for the oscillating BICs in a one-dimensional photonic lattice coupled to a ``giant atom'' at multiple points. Our work is significantly distinct from previous proposals of oscillating BICs in continuous waveguide systems due to the presence of a finite energy band contributing band-edge effects. In particular, we show that the bound states outside the energy band are detrimental to the oscillating BIC phenomenon, and can be suppressed by increasing either the number of coupling points or the separation between each coupling point. Crucially, non-Markovianity is necessary for the existence of oscillating BICs, and the oscillation amplitude increases with the characteristic delay time of the giant atom interactions. We also propose an initialization scheme in the BIC subspace. Our work be experimentally implemented on current photonic waveguide array platforms and opens up prospects in utilizing reservoir engineering for the storage of quantum information in photonic lattices.
We study the non-Markovian dynamics of a two-level giant atom interacting with a one-dimensional semi-infinite waveguide through multiple coupling points, where a perfect mirror is located at the endpoint of the waveguide. The system enters a non-Markovian process when the travel time of the photon between adjacent coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. The photon released by the spontaneous emission of the atom transfers between multiple coupling points through the waveguide or is reabsorbed by the atom with the photon emitted via the atom having completed the round trip after reflection of the mirror, which leads to the photon being trapped and forming bound states. We find that three different types of bound states can be formed in the system, containing the static bound states with no inversion of population, the periodic equal amplitude oscillation with two bound states, and the periodic nonequal amplitude oscillation with three bound states. The physical origins of the three bound states' formation are revealed. Moreover, we consider the influences of the dissipation of unwanted modes and dephasing on the bound states. Finally, we extend the system to a more general case involving many giant atoms coupled into a one-dimensional semi-infinite waveguide. The obtained set of delay differential equations for the giant atoms might open a way to better understand the non-Markovian dynamics of many giant atoms coupled to a semi-infinite waveguide.
Abstract We investigate the dynamics of two two-level giant atoms coupled to a one-dimensional waveguide in separate and braided configurations. Using the resolvent method, the quantum dynamics are determined by the poles of the Green’s function. We identify conditions under which three real poles with distinct eigenfrequencies emerge, corresponding to three bound states in the continuum (BICs). Their superposition gives rise to oscillating BICs. In this regime, the atomic excitation oscillates between the two atoms, while the photon field remains confined between the coupling points and exhibits persistent oscillations. The maxima of the photon field distribution coincide with those of the atomic excitations, reflecting the atom-photon bound-state nature. The revival of the photon distribution reveals the coherent interaction between the two giant atoms mediated by the BICs. This work broadens the fields of quantum information storage and manipulation by leveraging larger Hilbert spaces enabled by multiple nonradiative BICs.
Quantum optics with giant atoms provides a new approach for implementing optical memory devices at the atomic scale. Here, we theoretically investigate the relaxation dynamics of a single driven three-level atom interacting with a one-dimensional waveguide via two coupling points. Under certain conditions, after long-time dynamics, we find that the population of the giant atom can either remain stable or exhibit regular periodic oscillations, while photons are trapped within the region of the giant atom. This phenomenon cannot be realized using a two-level atom configured with two coupling points. It is noteworthy that the atomic excitation probability of a stable bound state is a constant value, which is determined by the size of the atom. Importantly, the size of the atom, defined as the distance between the two coupling points, is significantly larger than the wavelength of the light field, which is a necessary condition for the existence of oscillating bound states.
Coherent Control of Spontaneous Emission for a giant driven ΛΛΛ-type three-level atom
Quantum optics with giant atoms provides a new approach for implementing optical memory devices at the atomic scale. Here, we theoretically study the relaxation dynamics of a single driven three-level atom interacting with a one-dimensional waveguide, via two coupling points. Under certain conditions, after the long-time dynamics, we found that the population of giant atom can either maintain stable values or exhibit regular periodic oscillation behavior, while photons can be trapped in the region of giant atoms. This phenomenon is not achievable using a two-level atom with two legs. It is worth noting that the atomic excitation probability of a stable bound state is a constant value, which is determined by the size of the atom. Crucially, the size of the atom (the distance between the two coupling points) is much larger than the wavelength of the light field, which is a necessary condition for the existence of oscillating bound states.
We study the bound states in the continuum (BIC) in a system of two identical two-level giant atoms coupled to a one-dimensional waveguide. By deriving general dark-state conditions, we clarify how coupling configurations and atomic parameters influence decay suppression. Through analysis of the long-time dynamical behaviors of atoms and bound photons, we carry out a detailed classification of bound states and explore the connections between these dynamical behaviors and the system's intrinsic light-matter interactions. The system supports static bound states with persistent atomic excitations, and oscillating bound states with periodic atom-photon or atom-atom excitation exchange. Under certain conditions, oscillating bound states can contain more harmonic components owing to the emergence of additional quasi-dark modes, rendering them promising platforms for high-capacity quantum information processing. These findings advance the understanding of BIC in waveguide quantum electrodynamics with multiple giant atoms and reveal their prospective applications in quantum technologies.