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arXiv:1310.8409 · Physical Review A

Enhanced resonant force between two entangled identical atoms in a photonic crystal

Roberta Incardone, Taku Fukuta, Satoshi Tanaka, Tomio Yamakoshi Petrosky, Lucia Rizzuto, Roberto Passante

Published Jun 27, 2014• 27 citations
arXivHTMLPDF

Abstract

We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation as their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models of photonic crystal considered are discussed in detail, as well as a comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.

DOI
10.1103/physreva.89.062117

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We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation as their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models of photonic crystal considered are discussed in detail, as well as a comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.
Abstract We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involves both an isotropic three-dimensional model and the one-dimensional case. The resonance interaction asymptotically decays faster with distance compared to the free-space case, specifically as 1/r2 compared to the 1/r free-space dependence in the three-dimensional case, and as 1/r compared to the oscillatory dependence in free space for the one-dimensional case. Nonetheless, the interaction energy remains significant and much stronger than dispersion interactions between atoms. On the other hand, spontaneous emission is strongly suppressed by the environment and the correlated state is thus preserved by the spontaneous-decay decoherence effects. We conclude that our configuration is suitable for observing the elusive quantum resonance interaction between entangled atoms.
Radiative coupling between identical atoms sharing an excitation is studied in media where dispersion creates photonic band gaps, i.e., forbidden bands of light propagation for all directions and polarizations. Photonic band gaps can exist in media whose dielectric index exhibits strong three-dimensionally periodic modulations (``photonic crystals'') or in bands of polaritonic media. It is shown that the resonant dipole-dipole interaction as well as cooperative fluorescence of two-atom systems can be strongly enhanced or suppressed, to the extent of being essentially eliminated, by one of the following mechanisms: (a) dependence on location of the atoms within a unit cell of a photonic crystal, i.e., sensitivity to the spatial variation of the field normal modes; (b) dependence on the density of normal modes in allowed bands and on the density of virtual (evanescent) modes in band gaps. The ability to suppress the dipole-dipole interactions at interatomic separations characterizing quasimolecules would have far-reaching implications on their dissociative or collisional dynamics, spectroscopy, and rates of energy transfer.
We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC's band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of the band edge relative to the lower excited state.
We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC's band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of themore » band edge relative to the lower excited state.« less
We present a comprehensive investigation of entanglement dynamics in multi-level V-type atomic systems embedded within photonic crystals. We mainly focus on the synergistic roles of resonant dipole-dipole interactions and quantum interference through analytical modeling and numerical simulations using the Schrodinger equation. Key findings reveal that resonant interaction dominates when the interatomic distance is comparable to the localization length of photon-atom bound states lying in the bandgap region. For atoms with anti-parallel dipole orientations, both initially entangled and separable states exhibit robust entanglement preservation due to strong collective interactions. Conversely, when dipoles are oriented orthogonally, initially entangled states exhibit unique oscillatory patterns in their entanglement dynamics. This effect arises from the formation of dark states due to destructive interference within the structured photonic environment, with resonant dipole-dipole interactions sustaining non-Markovian dynamics. We further demonstrate that positioning the atomic excited states deeper within the photonic bandgap accelerates the decay of entanglement oscillations due to the exponential suppression of resonant energy exchange mediated by evanescent modes. Our analysis establishes resonant dipole-dipole interactions and quantum interference as potential tools for tailoring entanglement dynamics, paving the way for controlled quantum coherence in photonic crystal platforms.
Quantum electrodynamics of two identical two-level atoms placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied within the framework of the dipole resonance (rotating-wave) approximation. For finite interatomic distances a polariton-atom bound state lying within the polaritonic gap is shown to be split into a doublet due to an effective atom-atom interaction. Evaluating the splitting as a function of the interatomic separation, we estimate a width of a polariton-impurity band when a system of spatially correlated atoms is present. The results obtained for the case of two atoms are then generalized to the case of an atomic chain (a one-dimensional atomic lattice). The equations describing a propagation of a band polariton are derived and the expressions for the band polariton spectrum and its effective mass are obtained. The model under consideration has quite a general structure and is applied to the case of photonic-band-gap materials as well. Numerical calculations are presented for SiC semiconductors.