arXiv:2504.02358

Interference trapping of populations in a semi-infinite coupled-resonator waveguide

Fu, Qinglian, Jing Li, Jing Zhou Lu, Zhihui Peng, Lan Zhou

Published Apr 3, 2025• 0 citations

Abstract

We study the energy structure and dynamics of a two-level emitter (2LE) locally coupled to a semi-infinite one-dimensional (1D) coupled-resonator array (CRA). The energy spectrum in the single-excitation subspace features a continuous band with scattering states, discrete levels with bound states, and a quantum phase transition characterized by the change of the number of bound states. The number of bound states is revealed by the behavior of the excited-state population at long times with quantum beat, residual oscillation, a constant with either non-zero or zero.

DOI: 10.48550/arxiv.2504.02358

Related papers

Quantum phase transition and interference trapping of populations in a coupled-resonator waveguide

Lei Qiao, Ya‐Ju Song, Chang-Pu Sun

We study the energy structure and dynamics of a V-type three-level emitter embedded in a one-dimensional waveguide with model dispersion. Due to the presence of two different couplings between the upper levels and the waveguide modes, we find that the bound states in this system are quite different from the case of a two-level emitter. The energy structure is dependent on the relative position of the emitter's transition frequencies from the band with finite width. We obtain the phase diagrams through numerical analysis. The dynamics of spontaneous emission of the system is calculated exactly in the general case by means of the Green's function approach. The emitted photon is characterized by two components: a localized part and a traveling part, and the average frequency of the traveling part is different from that for resonant scattering. Through the quantum interference between the emitter's two transitions, it is found that the total excitation number of the localized photon and emitter can be greatly enhanced in some case in the spontaneous-emission process.

Physical Review AJul 15, 201925 citations

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

Zhongling Lu, Jing Li, Jing Lü +1 more

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.

arXiv:2401.09688Optics LettersJan 2, 20248 citations

Atom-photon bound states and non-Markovian cooperative dynamics in coupled-resonator waveguides

Lei Qiao, Chang-Pu Sun

We study the properties of atom-photon bound states and single-photon cooperative dynamics in a waveguide system which consists of a finite-bandwidth channel with model dispersion and an ensemble of two-level atoms whose size is ignorable when compared with the lattice constant. The bound states are formed by all atoms and a localized photonic excitation. We find that the effect of atomic collection is equivalent to the case of one atom by rescaling the coupling strength with the square root of the atom number, as far as the eigenenergy equation is concerned. Besides, it is found there is a quantum phase transition when more than one type of atom are present. The characteristic lengths and wave functions are analyzed near the phase transition point. The exact analytical results for the cooperative dynamics at the single excitation level are obtained and we point out the dark state in this system leads to a universal population trapping in the time evolution process. This type of trapping obeys a simple law that is only associated with the atom number. A direct conclusion that results from the trapping law is that the single-photon cooperative emission is suppressed when the number of atoms is large enough.

Physical Review ADec 4, 201914 citations

Phase Control of Single‐Photon States in 1D Coupled‐Resonator Waveguide

Jing Li, Jing Lu, Lan Xu +1 more

Abstract A system consisting of a two‐level system (TLS) coupled to the modes of two adjacent resonators in 1D coupled‐resonator waveguide (CRW) is studied. The single‐photon energy spectrum, transmission spectrum, and the spontaneous emission process of the TLS are considered. The focus is on the influence of the phase difference of the coupling strength. It is found that the phase difference controls the number of the bound states outside the continuous, deciding whether the occupation of the TLS's excited state at long times is residual oscillatory or non‐zero constant with one excitation initial in the TLS and the CRW in the vacuum state. The transport behavior of a single photon within a continuous spectrum is also investigated and discovered that the phase difference controls the crossover between reciprocal and nonreciprocal photon transmission when the dissipation of the TLS is present as well as the position of the transmission dip. These results provide new insights for applications in quantum information processing and quantum optics.

Advanced Quantum TechnologiesJun 22, 20253 citations

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

Yao-Lung L. Fang, Harold U. Baranger

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.

arXiv:1502.03803Physical Review AMay 22, 2015129 citations

Waveguide QED: Two Photons, Many Qubits, and a Mirror

Yao-Lung L. Fang, Harold U. Baranger

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.

Feb 12, 20151 citation