Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: A fractional calculus approach

Abstract

Spontaneous emission (SE) from a two-level atom in a photonic crystal (PC) with anisotropic oneband model is investigated using the fractional calculus. Analytically solving the kinetic equation in terms of the fractional exponential function, the dynamical discrepancy of SE between the anisotropic and isotropic systems is discussed on the basis of different photon density of states (DOS) and the existence of incoherent diffusion field that becomes even more clearly as the atomic transition frequency lies close to the band edge. With the same atom-field coupling strength and detuning in the forbidden gap, the photon-atom bound states in the isotropic system turn into the unbound ones in the anisotropic system that is consistent with the experimental observation in P hys. Rev. Lett. 96, 243902 (2006). Dynamics along different wavevectors with various curvatures of dispersion is also addressed with the changes of the photon DOS and the appearance of the diffusion fields.

Spontaneous emission with a cascaded driving field in the same transition channel

“…The spontaneous emission can be significantly suppressed or enhanced for excited atoms in cavities. Since an effective high-Q cavity [6] can be obtained by using photonic band gap material [7][8][9][10][11][12], the spontaneous emission near the edge of a photonic-band-gap has attracted substantial attention in the literature [13][14][15][16].…”

Fractional Langevin Equation in Quantum Systems with Memory Effect

“…Here the atomic operators ω from the band edge frequency c ω [7]. With this special form of memory kernel, the kinetic equation of the excited amplitude ( ) As the inverse Laplace transform is applied to these partial-fractional forms of ( ) C s  with fractional powers of the variables s , we use the formulas of ( ) ( ) …”

“…Recently, the fractional time derivative is given a physical interpretation by Iomin which describes an effective interaction of a quantum system with its environment [6]. Here we will introduce the practical quantum system with long-time memory effect [7].…”

“…Many novel methods have been proposed to generate controllable qubit states through the environment of the qubits [8]- [10]. When a qubit made of a twolevel atom is embedded inside a structured reservoir with memory effect, the correlation between the qubit and environment will affect the dynamics of the qubit [7] [11] [12]. In this case, the effective interaction of the qubit with the photon modes of the environment is expressed as a memory kernel.…”

Lévy Transport in Slab Geometry of Inhomogeneous Media

“…As shown in [13,14], the FSE is an effective way to describe the dynamics of a quantum system interacting with the environment. In this case, fractional time derivative is an effect of the interaction of the quantum system with the environment, where part of the quantum information is lost [14,15]. Therefore, in the paper we consider a physical example of a fractional (both in space and time) Schrödinger equation, which appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media.…”