Resonance fluorescence of a trapped three-level atom

Abstract

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are Λ-shaped and driven at two-photon resonance by a pair of lasers, which cool the center-of-mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser-cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb-Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -the Stokes and anti-Stokes components of the scattered light -while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow-type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.

Factorization of Numbers with Physical Systems

“…This scheme is based on a simple substitution within the alphabet: Each letter of the plain text is replaced by the one which originates from a constant shift of the original letter. With this knowledge and Caesar's original shift of three letters the plain text can be decrypted by simple means 1 . Once new technologies had been developed they had immediate application in cryptography.…”

“…In this case the probability amplitude c e is proportional to the Gauss sum which involves purely quadratic phases. 1 In Appendix B we show that for a Gaussian weight factor distribution w n (π/2) with large ∆n the Gauss sum S N ′ (ℓ ′ ) is identical to the standard Gauss sum G(ℓ ′ , N ′ ). In section 2.3 we have analyzed in detail the factorizing property of the standard Gauss sum G(ℓ ′ , N ′ ).…”

Factorization of numbers with physical systems

“…This scheme is based on a simple substitution within the alphabet: Each letter of the plain text is replaced by the one which originates from a constant shift of the original letter. With this knowledge and Caesar's original shift of three letters the plain text can be decrypted by simple means 1 .…”

Quantum jumps induced by the center-of-mass motion of a trapped atom

“…with the density matrix ρ st defined for the internal degrees of freedom and obeying L I ρ st = 0, while µ st is the density matrix for the center-of-mass degrees of freedom, which solves the effective equation for laser cooling [22,23]. Projectors on the corresponding subspaces,…”

“…In a suitable setup their analysis can provide information on the dynamics and the state of the atomic center of mass degree of freedom. Information on the quantum state of the atoms can be also extracted by the spectrum of resonance fluorescence, which, when taken at the steady state of laser cooling, reveals the relevant scattering processes characterizing the dynamical steady state [19,20] and can provide a measurement of the cooling rate and steady state phonon number occupation [21][22][23][24][25].…”