Memory effects in spontaneous emission processes

Abstract

We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective twolevel system with a vacuum decay rate Γ0 and transition angular frequency ωA. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the dimensionless lifetime τ = tΓ0 of spontaneous emission, we obtain deviations from exponential decay of the form O(1/τ ) for the decay amplitude as well as the previously obtained asymptotic behaviors of the form O(1/τ 2 ) or O(1/τ ln 2 τ ) for τ ≫ 1. The actual asymptotic behavior depends on the adopted regularization procedure as well as on the physical parameters at hand. We show that for any reasonable range of τ and for a sufficiently large value of the required angular frequency cut-off ωc of the electro-magnetic fluctuations, i.e. ωc ≫ ωA, one obtains either a O(1/τ ) or a O(1/τ 2 ) dependence. In the presence of physical boundaries, which can change the decay rate with many orders of magnitude, the conclusions remains the same after a suitable rescaling of parameters.

Dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media

“…In this strategy a noise current is added phenomenologically to Maxwell's equation in order to preserve unitarity of the full evolution and in particular the constancy of all conjugate canonical variables commutator with time [58]. The Green function strategy has been intensively used in the literature in the recent years [59][60][61][62][63][64][65][66][67] and applied to several problems including dielectric or magnetic materials, and coupling of light with atoms in the regime of weak or strong coupling in presence of plasmonic nanoparticles [68][69][70][71][72][73][74][75][76]. Despite its success the Langevin noise method applied to macroscopic electrodynamics (unlike for atomic physics in vacuum [55]) lacks a neat and clear quantum foundation that, like the Huttner-Barnett model [39], could be justified using an Hamiltonian description.…”

Spontaneous light emission by atomic hydrogen: Fermi's golden rule without cheating

“…4. In a recent paper [15] devoted to the decay of magnetic dipoles, similar questions were raised, and the Compton frequency was proposed as a cutoff. With this cutoff, Grimsmo et al proposed a regularisation of their problem following the lines of Bethe's mass renormalisation.…”

“…and then shall take the limit τ → 0 at the end to retrieve the desired integral (15). In this limit, some terms inf (τ, t) become ill-defined, a consequence of the fact that f (·, t) is not summable.…”

Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

“…This result is naturally obtained in the standard DLN approach [29,40] and therefore constitutes another illustration of the powerfulness of the DLN methodology (see refs. [37][38][39][40][41][42][43][44][45] for more on this topics in connection with Bloch equations and the DLN formalism). Moreover, in the present article we showed how to give a clean foundation to the DLN approach by including dipolar sources located far away from the dipole µ 1,2 and its local environment and acting effectively as the pure photon field required in the generalized Huttner-Barnett formalism [71,72] (see also [17]).…”

“…Instead, fluctuating currents are phenomenologically added to deal with the problem of dissipation and dispersion. This approach was intensively used in the literature [27][28][29][30][31][32][33][34][35][36], e. g., for describing optical Bloch equations in the weak or strong optical coupling in QNP [37][38][39][40][41][42][43][44][45], Casimir interactions, quantum frictions and thermal fluctuating forces [46][47][48][49][50], and more recently for modeling quantum optical non-linearities such as spontaneous down conversion of photon pairs [51,52]. It is central to observe that the DLN approach is a direct development of the historical works by Rytov and others [53][54][55][56] which, based on some considerations about the standard fluctuation dissipation theorem for electric currents [57], was used for justifying Casimir and thermal forces (for recent developments of such phenomenological 'fluctuational electrodynamics' techniques in the context of nanotechnology see [58][59][60][61][62][63]).…”