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arXiv:2401.09688 · Optics Letters

Controlling atom-photon bound states in a coupled resonator array with a two-level quantum emitter

Zhongling Lu, Jing Li, Jing Lü, Lan Zhou

Published Jan 2, 2024• 8 citations
arXivHTMLPDF

Abstract

We consider a one-dimensional (1D) coupled-resonator array (CRA), where a two-level quantum emitter (2LE) is electric-dipole coupled to the modes of two adjacent resonators. We investigate the energy spectrum, the photon probability distribution of the bound states, and the emission process of the 2LE into the CRA vacuum. A quantum phase transition is found which is characterized by the change of the number of the out-of-band discrete levels. The condition for this change is also presented. The photon wave functions of bound states are found to be asymmetry around the position of the 2LE when the coupling strengths between the 2LE and the resonator are not equal, and they have the same preferred directions which are primarily determined by the larger one among the coupling strengths. The presence of the atom-photon bound states is manifested in the form of a stationary oscillation or a non-vanishing constant in the long enough time.

DOI
10.1364/ol.513907

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We study the bound states in the continuum for a system of nnn two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases n=3n=3n=3 and n=4n=4n=4 emitters.
Controlling the interaction between photons is one of the important technologies applied to quantum information processing at the few-photon level. We investigate the two-photon interaction via a Ξ-type atom, where one atomic transition is coupled to a one-dimensional waveguide, and the other transition is coupled to a cavity field. Whether the cavity is initially in the vacuum state or not, determines the effective configuration of the quantum emitter. When the cavity is in the vacuum state, only one bound state appears. We further found that the joint probability of transmitted photons oscillates with their spatial separation due to the coexistence of two bound states, if the cavity is in fock state |n〉 (n ≠ 0). With the incoming wave function consists entirely of plane waves, we present the exact out-state function that exhibit the bunching and antibunching behaviors. And, we discuss in detail with the behaviors of varying both the photon pair energy(E) and the energy difference between the two photons (Δ). Moreover, the spatial attraction and repulsion between the two transmitted photons can be controlled by the parameters of the cavity.