Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor

Tanaka, Satoshi; Passante, Roberto; Fukuta, Taku; Petrosky, Tomio

doi:10.1103/physreva.88.022518

Cited by 8 publications

(18 citation statements)

References 37 publications

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“…This gives a strong coupling with field modes with frequencies in the proximity of the gap. We will now consider two specific cases: a 1D case where we use relations (23), (24), (25) for a onedimensional crystal (we will discuss later on about validity and limits of the 1D approximation), and an isotropic 3D case where these relations are assumed valid for any direction of the wavevector k.…”

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

“…Following the same procedure and approximations used above for the isotropic case, using the 1D dispersion relation (24) in the effective mass approximation, the k integral in (18) after some algebra becomes…”

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

“…We shall therefore neglect them compared to modes just above the gap. All these considerations allow us to use k 0 and ∞ as, respectively, lower and upper limit of integration in (14), and to use the effective mass approximation (24). The fact that in this way we are also including modes with wavevector k well above k 0 , for which the effective mass approximation is not valid, does not introduce a significant error because they give a small contribution to the integral, due to the low density of states and/or the off-resonance condition for these field modes.…”

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

“…In Eq. (14), ω k is given by the dispersion relation (23) or (24) in the effective mass approximation, below and above the gap respectively. In evaluating the integral over k in (14), we must pay some attention to the validity of our approximations.…”

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

See 3 more Smart Citations

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

Passante¹,

Rizzuto²,

Petrosky

et al. 2014

Phys. Rev. A

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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 of 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 considered of photonic crystal are discussed in detail, as well as 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.

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Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

Section: Resonant Interatomic Force In the Photonic Crystalmentioning

confidence: 99%

See 2 more Smart Citations

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

Passante¹,

Rizzuto²,

Petrosky

et al. 2014

Phys. Rev. A

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“…We have applied this theory to open quantum systems to study dissipation processes of a discrete quantum state interacting with a continuum with a finite bandwidth. We have revealed that the decay is nonanalytically enhanced when the discrete state is located closely to the bandedge of the continuum, and, as a result, it shows a nonanalytic decay process [47][48][49][50]. Therefore, in order to describe the DCE of a hybrid quantum system, it is important to study the competition between the parametric amplification and the resonance instability which will be clarified only when we take into account the effect of the energy-dependent self-energy.…”

Section: Introductionmentioning

confidence: 99%

Dissipative dynamical Casimir effect in terms of the complex spectral analysis in the symplectic-Floquet space

Tanaka¹,

Kanki²

2020

Preprint

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Dynamical Casimir effect of the optomechanical cavity interacting with one-dimensional photonic crystal is theoretically investigated in terms of the complex spectral analysis of Floquet-Liouvillian in the symplectic-Floquet space. The quantum vacuum fluctuation of the intra-cavity mode is parametrically amplified by a periodic motion of the mirror boundary, and the amplified photons are spontaneously emitted to the photonic band. We have derived the non-Hermitian effective Floquet-Liouvillian from the total system Liouvillian with the use of the Brillouin-Wigner-Feshbach projection method in the symplectic-Floquet space. The microscopic dissipation process of the photon emission from the cavity has been taken into account by the energy-dependent self-energy. We have obtained the discrete eigenmodes of the total system by non-perturbatively solving the nonlinear complex eigenvalue problem of the effective Floquet-Liouvillian, where the eigenmodes are represented by the multimode Bogoliubov transformation. Based on the microscopic dynamics, the nonequilibrium stationary eigenmodes are identified as the eigenmodes with vanishing values of their imaginary parts due to the balance between the parametric amplification and dissipation effects. We have found that the nonlocal stationary eigenmode appears when the mixing between the cavity mode and the photonic band is caused by the indirect virtual transition, where the external field frequency to cause the DCE can be largely reduced by using the finite bandwidth photonic band.

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Resonance interaction energy between two entangled atoms in a photonic bandgap environment

Notararigo

Passante

Rizzuto

2018

Sci Rep

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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.

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Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor

Cited by 8 publications

References 37 publications

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

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

Dissipative dynamical Casimir effect in terms of the complex spectral analysis in the symplectic-Floquet space

Resonance interaction energy between two entangled atoms in a photonic bandgap environment

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