[en] In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical and asymptotic regime, the radiation force experienced by a two-level atom interacting with any number of plane waves with arbitrary intensities, frequencies, phases, and propagation directions [J. Opt. Soc. Am. B 35, 127 (2018)]. Here, we extend this treatment to the multilevel atom case, where degeneracy of the atomic levels is considered and polarization of light enters into play. A matrix formalism is developed to this aim.
Disciplines :
Physics
Author, co-author :
Podlecki, Lionel ; Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Martin, John ; Université de Liège - ULiège > Département de physique > Optique quantique
Bastin, Thierry ; Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Language :
English
Title :
Radiation pressure on single atoms: generalization of an exact analytical approach to multilevel atoms
Publication date :
06 October 2021
Journal title :
Journal of the Optical Society of America. B, Optical Physics
ISSN :
0740-3224
Publisher :
Optical Society of America, United States - District of Columbia
Volume :
38
Pages :
3244
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
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The system in Eq. (19) is only defined if all A(ξξn) + Bξξ(n,0) matrices are invertible, which is ensured if the periodic regime is unique. Otherwise, the following formalism does not apply. This is, for instance, the case for 1J = −1 and all waves with the same polarization εj (λm = 0 and det (A(ξξ0) + B(ξξ0,0)) = 0).
Such suitable matrices can be given by (see, e.g., Ref. [37]): Q(ξξn) = 0 if x(ξn) = 0; otherwise, Q(ξξn) = (eiθkx(ξn)k/kx(ξ0)k)1ξ if x(ξn)/kx(ξn)k = eiθ(x(ξ0)/kx(ξ0)k) (θ ∈ [0, 2π[); otherwise, Q(ξξn) = (kx(ξn)k/kx(ξ0)k)Uξξ(n). In the latter, Uξξ(n) is the unitary matrix eiφ(n)Vξξ(n), where φ(n) is the phase of the complex number x(ξ0)∗ · x(ξn), conventionally set to 0 if the complex number is zero, and where Vξξ(n) is the Householder matrix Vξξ(n) = 1ξ − (2/kz(ξn)k2)(z(ξn)z(ξn)†), with z(ξn) = eiφ(n)x(ξ0) − (kx(ξ0)k/kx(ξn)k)x(ξn). In particular, we have in that case Q(ξξ0) = 1ξ and Qξξ(−n) = Q(ξξn)∗
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Indeed, Eq. (22) can be expressed as a function of x(ξ0) according to (1 + W0)y0 = −W00 x(ξ0), where y0 is the y vector excluding the x(ξ0) component, W0 is the W matrix excluding the Wξξ(0,n0) and Wξξ(n,0) blocks, ∀n, n0, and W00 is the W matrix restricted to the only blocks Wξξ(n,0), ∀n6= 0. Under condition stated in [32], we have (1 + W0)−1 ' 1 + P+∞k=1 (−W0)k. This implies y0 ' −W00 x(ξ0), so that kx(ξn)k kx(ξ0)k, and thus Q(ξξn) ' 0ξξ, ∀n6= 0, i.e., sξξ,j ' sξξ,j.
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