Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Iranian Journal of Physics Research

Geometric phase of a two-level atom near a dissipative and dispersive dielectric slab

Somaye Mohamadi Abdhvand, Ehsan Amooghorban, Ali Mahdifar

Published Jul 1, 2020• 1 citation
Publisher

Abstract

In this paper, we study the geometric phase of a two-level atom near a dielectric slab. For this purpose, by applying the Von-Neumann equation, we obtain eigenvalues and eigenvectors of the reduced density operator of the atomic system. Then, we obtain the Lamb shift and transition rates of the atomic system in term of the electromagnetic Green tensor. Finally, by calculating the electromagnetic Green tensor of the system and making use of the kinematic approach, we study the geometric phase of the atomic system near the dielectric slab. We show that the geometric phase can be used as a sensitive probe to the surface-phonon polariton waves.

DOI
10.47176/ijpr.20.2.12065

Related papers

Quantum electrodynamics of an atom in front of a dielectric slab

Reyes Contreras, Ana María

Quantum electrodynamic theory (QED) in the vicinity of macroscopic structures has achieved new importance due to its applicability, particularly in nanotechnology. There are many powerful methods for studying QED near media with diverse properties and geometries. However, applying them to a particular problem generally necessitates extensive numerical calculations. This is not the case for simple systems of high symmetry, in which the electromagnetic field can be quantised by explicit mode expansion, allowing exact analytic calculations. In the present thesis, we calculate the energy-level shift of a ground state atom near a non-dispersive and non-dissipative dielectric slab. The shift is due to the interaction of the atom with electromagnetic field fluctuations, which in turn are affected by the presence of the slab. Thus, a quantisation of the electromagnetic field in the presence of a layered system is required. We derive the field modes, which comprise of a continuous set of travelling modes (with incident, reflected and transmitted parts) and trapped modes, subject to repeated total internal reflection and emerge as an evanescent field outside the slab, they only exist at certain discrete frequencies. The shift is obtained by means of second-order perturbation theory. It splits up naturally into two contributions, due to the different nature of the modes, and a problem arises when we have to add them all. We have come up with a convenient method of summing over all modes, and its validity has been demonstrated by proving the completeness. The calculation of the shift follows as an application of our method. The result is analysed asymptotically for various regions, reducing to simple formulas that can be utilised in recent experiments, in which the thickness of the substrate matters.

•Feb 1, 2009•0 citations

Topological Berry phase of a pumped three-level atom in the presence of dispersing and absorbing dielectric bodies: application to a half-space dielectric surface

M. S. Ateto

Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped $Λ$-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are compared with that of an atom in free space. We expect, the additional noise due to presence of the dielectric will modify, in a unified way, the behavior and values measured of the phase shift between the wavefunction evolution and its original state. It is shown that for small separation distance between atom and the dielectric surface, the angle separation between the wavefunction evolution and the original state reduced noticeably that is of strong applications in construction of the universal quantum logic gates. Further, the study opens routes for new challenging applications of atomically systems as various sources of coherent light emitted by pumped atoms in dielectric surroundings.

arXiv:1109.0339•Sep 2, 2011•0 citations

Geometric phase of a two-level atom near a dielectric nanosphere out of thermal equilibrium

Ehsan Amooghorban, S. Shahidani, Somaye Mohamadi Abdhvand

We study the geometric phase (GP) of a two-level atom coupled to an environment composed of free space and a dielectric nanosphere in thermal and out of thermal equilibrium. We analytically and numerically analyze the optical properties and loss of the dielectric medium, along with the nonequilibrium effects of the environment on the GP. In the weak coupling limit, we find that the correction to the GP depends on the partial local density of photonic states at the atom position, and an effective parameter that emerges out of the nonequilibrium configuration of the system. The GP exhibits a significant enhancement due to the excitation of evanescent surface waves at its resonance frequency. It is shown that the GP acquired by the atomic system out of thermal equilibrium is always bounded between the thermal-equilibrium counterparts. Furthermore, the temperature difference between the nanosphere and free space can play an important role in the GP only at moderate atomic distances from the nanosphere. Our results elegantly demonstrate properties of the GP near material media that can support phononic modes and pave the way for further research of GP as a resource for quantum computation.

arXiv:2404.15216•Physical Review A•Sep 10, 2024•1 citation

Thermalization of a two-level atom in a planar dielectric system out of thermal equilibrium

Puxun Wu, Hongwei Yu

We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is nonabsorbing and nondispersive, out-of-thermal-equilibrium effects exist only when its thickness is infinite. In other words, no out-of-thermal-equilibrium effects appear for a real dielectric slab of a finite thickness $d$. Furthermore, a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\mathrm{Im}\ensuremath{\epsilon}$ behaves like a half-space dielectric substrate if $\frac{\mathrm{Im}\ensuremath{\epsilon}}{\sqrt{\mathrm{Re}\ensuremath{\epsilon}\ensuremath{-}1}}\frac{d}{{\ensuremath{\lambda}}_{0}}>1$ is satisfied, where ${\ensuremath{\lambda}}_{0}$ is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out-of-thermal-equilibrium fluctuations with a half-space (infinite thickness) dielectric.

arXiv:1510.04382•Physical Review A•Dec 16, 2015•1 citation

Casimir-Polder interaction between an atom and a dielectric slab

Ana M. Contreras-Reyes, Claudia Eberlein

We present an explicit analytic calculation of the energy-level shift of an atom in front of a nondispersive and nondissipative dielectric slab. We work with the fully quantized electromagnetic field, taking retardation into account. We give the shift as a two-dimensional integral and use asymptotic analysis to find expressions for it in various retarded and nonretarded limiting cases. The results can be used to estimate the energy shift of an atom close to layered microstructures.

arXiv:0907.2350•Physical Review A•Sep 16, 2009•23 citations

Spontaneous decay of a two-level atom near the left-handed slab

Jingping Xu, Yaping Yang, Qiang Lin +1 more

Spontaneous decay of a two-level atom near the left-handed material (LHM) slab is investigated. The contributions of the guided modes and the surface-plasmon polariton (SPP) modes supported by the LHM slab to the spontaneous decay are studied at length. We find that the atomic decay near a LHM slab is much different from that near a dielectric slab or metal slab. The first---the dielectric slab with arbitrary thickness---supports at least two guided modes (one for TE polarized and one for TM polarized), but LHM slab may support none of the guided mode for certain thickness. The second---the atom near the LHM slab---may decay through both TE- and TM-polarized SPP, but the atom near the metal slab can decay only through TM-polarized SPP. The third, when the LHM slab supports only TE-polarized SPP modes, the atom near such slab cannot couple to the SPP mode when its dipole moment is perpendicular to the interface. Even if LHM contains weak loss, above analysis is also valid, and the decay rate directly related to material's losses (defined by the decay through dissipation here) can be distinguished from the total decay rate. Most interesting, we find that the decay through SPP will be larger than the decay through dissipation when the atom is placed at an appropriate position. Our results will give constructive reference to the design and fabrication of the quantum device made of LHM.

Physical Review A•Apr 14, 2009•33 citations
In this paper, we study the geometric phase of a two-level atom near a dielectric slab. For this purpose, by applying the Von-Neumann equation, we obtain eigenvalues and eigenvectors of the reduced density operator of the atomic system. Then, we obtain the Lamb shift and transition rates of the atomic system in term of the electromagnetic Green tensor. Finally, by calculating the electromagnetic Green tensor of the system and making use of the kinematic approach, we study the geometric phase of the atomic system near the dielectric slab. We show that the geometric phase can be used as a sensitive probe to the surface-phonon polariton waves.
Quantum electrodynamic theory (QED) in the vicinity of macroscopic structures has achieved new importance due to its applicability, particularly in nanotechnology. There are many powerful methods for studying QED near media with diverse properties and geometries. However, applying them to a particular problem generally necessitates extensive numerical calculations. This is not the case for simple systems of high symmetry, in which the electromagnetic field can be quantised by explicit mode expansion, allowing exact analytic calculations. In the present thesis, we calculate the energy-level shift of a ground state atom near a non-dispersive and non-dissipative dielectric slab. The shift is due to the interaction of the atom with electromagnetic field fluctuations, which in turn are affected by the presence of the slab. Thus, a quantisation of the electromagnetic field in the presence of a layered system is required. We derive the field modes, which comprise of a continuous set of travelling modes (with incident, reflected and transmitted parts) and trapped modes, subject to repeated total internal reflection and emerge as an evanescent field outside the slab, they only exist at certain discrete frequencies. The shift is obtained by means of second-order perturbation theory. It splits up naturally into two contributions, due to the different nature of the modes, and a problem arises when we have to add them all. We have come up with a convenient method of summing over all modes, and its validity has been demonstrated by proving the completeness. The calculation of the shift follows as an application of our method. The result is analysed asymptotically for various regions, reducing to simple formulas that can be utilised in recent experiments, in which the thickness of the substrate matters.
Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped ΛΛΛ-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are compared with that of an atom in free space. We expect, the additional noise due to presence of the dielectric will modify, in a unified way, the behavior and values measured of the phase shift between the wavefunction evolution and its original state. It is shown that for small separation distance between atom and the dielectric surface, the angle separation between the wavefunction evolution and the original state reduced noticeably that is of strong applications in construction of the universal quantum logic gates. Further, the study opens routes for new challenging applications of atomically systems as various sources of coherent light emitted by pumped atoms in dielectric surroundings.
We study the geometric phase (GP) of a two-level atom coupled to an environment composed of free space and a dielectric nanosphere in thermal and out of thermal equilibrium. We analytically and numerically analyze the optical properties and loss of the dielectric medium, along with the nonequilibrium effects of the environment on the GP. In the weak coupling limit, we find that the correction to the GP depends on the partial local density of photonic states at the atom position, and an effective parameter that emerges out of the nonequilibrium configuration of the system. The GP exhibits a significant enhancement due to the excitation of evanescent surface waves at its resonance frequency. It is shown that the GP acquired by the atomic system out of thermal equilibrium is always bounded between the thermal-equilibrium counterparts. Furthermore, the temperature difference between the nanosphere and free space can play an important role in the GP only at moderate atomic distances from the nanosphere. Our results elegantly demonstrate properties of the GP near material media that can support phononic modes and pave the way for further research of GP as a resource for quantum computation.
We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is nonabsorbing and nondispersive, out-of-thermal-equilibrium effects exist only when its thickness is infinite. In other words, no out-of-thermal-equilibrium effects appear for a real dielectric slab of a finite thickness ddd. Furthermore, a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\mathrm{Im}\ensuremath{\epsilon}$ behaves like a half-space dielectric substrate if $\frac{\mathrm{Im}\ensuremath{\epsilon}}{\sqrt{\mathrm{Re}\ensuremath{\epsilon}\ensuremath{-}1}}\frac{d}{{\ensuremath{\lambda}}_{0}}>1$ is satisfied, where ${\ensuremath{\lambda}}_{0}$ is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out-of-thermal-equilibrium fluctuations with a half-space (infinite thickness) dielectric.
Spontaneous decay of a two-level atom near the left-handed material (LHM) slab is investigated. The contributions of the guided modes and the surface-plasmon polariton (SPP) modes supported by the LHM slab to the spontaneous decay are studied at length. We find that the atomic decay near a LHM slab is much different from that near a dielectric slab or metal slab. The first---the dielectric slab with arbitrary thickness---supports at least two guided modes (one for TE polarized and one for TM polarized), but LHM slab may support none of the guided mode for certain thickness. The second---the atom near the LHM slab---may decay through both TE- and TM-polarized SPP, but the atom near the metal slab can decay only through TM-polarized SPP. The third, when the LHM slab supports only TE-polarized SPP modes, the atom near such slab cannot couple to the SPP mode when its dipole moment is perpendicular to the interface. Even if LHM contains weak loss, above analysis is also valid, and the decay rate directly related to material's losses (defined by the decay through dissipation here) can be distinguished from the total decay rate. Most interesting, we find that the decay through SPP will be larger than the decay through dissipation when the atom is placed at an appropriate position. Our results will give constructive reference to the design and fabrication of the quantum device made of LHM.