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

Journal of Physics A Mathematical and Theoretical

Fractional relaxations in photonic crystals

Filippo Giraldi, Francesco Petruccione

Published Sep 16, 2014• 5 citations
Publisher

Abstract

A quantum dot interacting with the radiation field of a photonic crystal is considered. An analytical description of the dynamics and the coherence between the two states of the quantum dot is provided. Besides the well-known trapping, a fractional nature of the dynamics appears via relaxations of the Mittag–Leffler type. Furthermore, coherence exhibits a transition from the decay to if the transition frequency of the quantum dot is exactly in the middle of the band gap. Similarly, the population of the excited level undergoes a transition from the relaxation to . These resonances and transitions belong also to the context of matter-wave emissions in optical lattices.

DOI
10.1088/1751-8113/47/39/395304

Related papers

Characteristics of the coherent excitation of an impurity atom in a photonic crystal

Ashat M. Basharov

It is shown that when an optically allowed transition is coherently excited in an impurity atom in a photonic crystal under conditions where one of the normal relaxation channels is suppressed by the spectral characteristics of the photonic crystal, new relaxation mechanisms are activated involving a coherent field quantum. These mechanisms substantially alter the dynamics of the atomic system, leading to filling of levels of the impurity atom which do not belong to the coherently excited atomic transition. Under certain conditions this leads to population inversion as a result of an optically allowed transition which does not interact with the coherent pump and at a frequency where no photonic band gaps can exist.

Journal of Experimental and Theoretical Physics•Dec 1, 1999•3 citations

Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal

Jing-Nuo Wu, Wen–Feng Hsieh, Hsin-Chien Huang +1 more

An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.

Advances in Condensed Matter Physics•Jan 1, 2013•0 citations

On the dominant role of two-photon relaxation in photonic crystals in external fields

Ashat M. Basharov

It is shown that resonant interaction of a coherent wave with impurity atoms leads to filling of levels of an impurity atom that lie in the gap in the photon density of states and do not belong to resonant transitions, while the interaction of impurity atoms with a nonresonant coherent wave results in effective deactivation of the indicated levels. The main mechanism determining the pumping and decay of an impurity level in a gap are two-photon radiative relaxation processes previously investigated by the present author (Zh. Éksp. Teor. Fiz. 102 , 1126 (1992) [Sov. Phys. JETP 75 , 611 (1992)]).

Journal of Experimental and Theoretical Physics Letters•Oct 1, 1999•4 citations

Quantum dynamics of two quantum dots in the vicinity of a photonic band edge: role of structured reservoirs and phonons

C. Roy

We study the population and disentanglement dynamics of two identical quantum dots placed inside the structured electromagnetic reservoir of a photonic crystal and coupled to an independent bath of thermal phonons. A formalism based on the method of generalized-Laplace transforms is developed to study the population and disentanglement dynamics. The effect of resonant dipole dipole interaction between the two quantum dots on the population dynamics in the presence of phonons and shows that the two two-level atoms can have a residual population at long times in the structured reservoir of a photonic crystal due to the formation of a photon-atom bound state. The disentanglement dynamics of the two quantum dots (assumed to be initially entangled) is studied using concurrence as a measure and is computed from the reduced two two-level system density matrix using the method of generalized-Laplace transforms. We show that partial disentanglement results from the interaction of the two quantum dots with the electromagnetic and phonon reservoirs. However, substantial entanglement is preserved in the fractionalized steady state formed if the transition frequency of two the quantum dots lies in the vicinity of the photonic band edge. We also discuss in detail the role of acoustic phonons on the population and disentanglement dynamics and the long time residual entanglement.

Journal of Modern Optics•Apr 10, 2010•0 citations

Dynamics of relaxation, decoherence and entropy of a qubit in anisotropic photonic crystals

Jing-Nuo Wu, Chen, Hung-Kuang, Wen–Feng Hsieh +1 more

We study the quantum dynamics of relaxation, decoherence and entropy of a qubit embedded in an anisotropic photonic crystal (PhC) through fractional calculus. These quantum measurements are investigated by analytically solving the fractional Langevin equation. The qubit with frequency lying inside the photonic band gap (PBG) exhibits the preserving behavior of energy, coherence and information amount through the steady values of excited-state probability, polarization oscillation and von Neumann entropy. This preservation does not exist in the Markovian system with qubit frequency lying outside the PBG region. These accurate results are based on the appropriate mathematical method of fractional calculus and reasonable inference of physical phenomena.

arXiv:1207.0395•Jul 2, 2012•0 citations

Quantum Theory of Phonon-Mediated Decoherence and Relaxation of Two-Level Systems in a Structured Electromagnetic Reservoir

C. Roy

In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.

•Jan 1, 2009•1 citation
A quantum dot interacting with the radiation field of a photonic crystal is considered. An analytical description of the dynamics and the coherence between the two states of the quantum dot is provided. Besides the well-known trapping, a fractional nature of the dynamics appears via relaxations of the Mittag–Leffler type. Furthermore, coherence exhibits a transition from the decay to if the transition frequency of the quantum dot is exactly in the middle of the band gap. Similarly, the population of the excited level undergoes a transition from the relaxation to . These resonances and transitions belong also to the context of matter-wave emissions in optical lattices.
It is shown that when an optically allowed transition is coherently excited in an impurity atom in a photonic crystal under conditions where one of the normal relaxation channels is suppressed by the spectral characteristics of the photonic crystal, new relaxation mechanisms are activated involving a coherent field quantum. These mechanisms substantially alter the dynamics of the atomic system, leading to filling of levels of the impurity atom which do not belong to the coherently excited atomic transition. Under certain conditions this leads to population inversion as a result of an optically allowed transition which does not interact with the coherent pump and at a frequency where no photonic band gaps can exist.
An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.
It is shown that resonant interaction of a coherent wave with impurity atoms leads to filling of levels of an impurity atom that lie in the gap in the photon density of states and do not belong to resonant transitions, while the interaction of impurity atoms with a nonresonant coherent wave results in effective deactivation of the indicated levels. The main mechanism determining the pumping and decay of an impurity level in a gap are two-photon radiative relaxation processes previously investigated by the present author (Zh. Éksp. Teor. Fiz. 102 , 1126 (1992) [Sov. Phys. JETP 75 , 611 (1992)]).
We study the population and disentanglement dynamics of two identical quantum dots placed inside the structured electromagnetic reservoir of a photonic crystal and coupled to an independent bath of thermal phonons. A formalism based on the method of generalized-Laplace transforms is developed to study the population and disentanglement dynamics. The effect of resonant dipole dipole interaction between the two quantum dots on the population dynamics in the presence of phonons and shows that the two two-level atoms can have a residual population at long times in the structured reservoir of a photonic crystal due to the formation of a photon-atom bound state. The disentanglement dynamics of the two quantum dots (assumed to be initially entangled) is studied using concurrence as a measure and is computed from the reduced two two-level system density matrix using the method of generalized-Laplace transforms. We show that partial disentanglement results from the interaction of the two quantum dots with the electromagnetic and phonon reservoirs. However, substantial entanglement is preserved in the fractionalized steady state formed if the transition frequency of two the quantum dots lies in the vicinity of the photonic band edge. We also discuss in detail the role of acoustic phonons on the population and disentanglement dynamics and the long time residual entanglement.
We study the quantum dynamics of relaxation, decoherence and entropy of a qubit embedded in an anisotropic photonic crystal (PhC) through fractional calculus. These quantum measurements are investigated by analytically solving the fractional Langevin equation. The qubit with frequency lying inside the photonic band gap (PBG) exhibits the preserving behavior of energy, coherence and information amount through the steady values of excited-state probability, polarization oscillation and von Neumann entropy. This preservation does not exist in the Markovian system with qubit frequency lying outside the PBG region. These accurate results are based on the appropriate mathematical method of fractional calculus and reasonable inference of physical phenomena.
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.