Optical spectroscopy of trapped neutral atoms

Gabbanini, C.

doi:10.1007/bf02874558

Cited by 2 publications

(2 citation statements)

References 235 publications

(222 reference statements)

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“…The doubling of the peaks is caused by the presence of the strong trapping laser on the first step of the optical double resonance. The frequency splitting between the peaks depends on the Rabi frequency and the detuning of the trapping laser [1]; the amplitudes of the two peaks are different in the case of nonzero detuning. As the trapping laser is detuned about 1.5 linewidths from the D 2 F = 2-F = 3 87 Rb transition in the recording of figure 3, the amplitudes are strongly dissimilar and the Autler-Townes effect is evident just on the strongest hyperfine transition of the 5P 3/2 → 5D 5/2 F = 3-F manifold.…”

Section: Resultsmentioning

confidence: 99%

“…Over recent years the field of atomic spectroscopy has taken advantage of progress in laser cooling and trapping. Cold atoms, in fact, give the opportunity of performing highresolution measurements thanks to the dramatic reduction of the Doppler effect and other perturbations [1]. The use of cold atomic samples has developed into a new powerful tool to measure hyperfine structure splittings and constants [2][3][4][5][6][7], integrating traditional techniques like quantum beats and level crossings [8].…”

Section: Introductionmentioning

confidence: 99%

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Resonance-enhanced ionization spectroscopy of laser-cooled rubidium atoms

Gabbanini¹,

Ceccherini²,

Gozzini³

et al. 1999

Meas. Sci. Technol.

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We report the utilization of resonance-enhanced ionization to perform high-resolution spectroscopy on laser-cooled atoms. The technique is applied to the 5S1/25P3/25DJ (J = (3/2), (5/2)) optical double resonances of rubidium atoms in a magneto-optical trap. Ions generated when atoms in the double excited state absorb a single photon are detected, together with the induced fluorescence. The two detection channels are compared for this class of high-resolution spectroscopy experiment.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resonance-enhanced ionization spectroscopy of laser-cooled rubidium atoms

Gabbanini¹,

Ceccherini²,

Gozzini³

et al. 1999

Meas. Sci. Technol.

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The general boson normal ordering problem

2003

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We solve the boson normal ordering problem for F (a † ) r a s , with r, s positive integers, a, a † = 1, i.e. we provide exact and explicit expressions for its normal form N F (a † ) r a s , where in N (F ) all a's are to the right. The solution involves integer sequences of numbers which are generalizations of the conventional Bell and Stirling numbers whose values they assume for r = s = 1. A comprehensive theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski -type formulas) and generating functions. These last are special expectation values in boson coherent states. Consider a function F (x) having a Taylor expansion aroundIn this note we will collect the formulas concerning our solution of the normal ordering problem for F (a † ) r a s , where a, a † are the boson annihilation and creation operators, a, a † = 1, and r and s are positive integers. The normally ordered form of the operator, where in N (F ) all the a's are to the right. It satisfies the operator identity:Furthermore, an auxiliary symbol : O(a, a † ) : will be used, which means expand O in powers of a and a † and order normally assuming they commute [1], [2].The combinatorial numbers S(n, k), known as Stirling numbers of the second kind, and their sums B(n), the Bell numbers, arise naturally in the normal ordering procedure for r = s = 1, as follows [3]:which may be taken as definitions of S(n, k) and B(n). In the present work we shall treat the case of general (r, s), consequently generalizing these combinatorial numbers.For the moment we restrict ourselves to the case r ≥ s, the other alternative being treated later. We do not give the proofs of the formulas here; they will be given elsewhere [4]. The case r = s = 1 is known [1], [2] and some features of the r > 1, s = 1 case have been published [5]. When needed we shall refer to [1], [2] and [5] where particular cases of our more general formulas are discussed.We define the set of positive integers S r,s (n, k) entering the expansion:(a † ) r a s n = N (a † ) r a s n = (a † )n(r−s) ns k=s S r,s (n, k)(a † ) k a

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Optical spectroscopy of trapped neutral atoms

Cited by 2 publications

References 235 publications

Resonance-enhanced ionization spectroscopy of laser-cooled rubidium atoms

Resonance-enhanced ionization spectroscopy of laser-cooled rubidium atoms

The general boson normal ordering problem

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