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arXiv:physics/9905043 · Physical Review Letters

Large Contributions of Negative-Energy States to Forbidden Magnetic-Dipole Transition Amplitudes in Alkali-Metal Atoms

Igor Savukov, Andrei Derevianko, H. G. Berry, W. R. Johnson

Published Oct 11, 1999• 29 citations
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Abstract

The influence of negative-energy states (NES) on forbidden magnetic-dipole ${\mathrm{ns}}_{1/2}\ensuremath{-}(n+1){s}_{1/2}$ transitions in alkali-metal atoms is investigated. We find that the NES contributions are significant in almost all cases and, for rubidium, reduce the transition rate by a factor of 8. We tabulate magnetic-dipole $({M}_{1})$ transition amplitudes for the alkalis. Our ${M}_{1}$ value for cesium, where accurate measurements are available, differs from experiment by $16%$. We briefly discuss the feasibility of an experimental test of NES effects.

DOI
10.1103/physrevlett.83.2914

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The influence of negative-energy states (NES) on forbidden magnetic-dipole ns1/2\ensuremath−(n+1)s1/2{\mathrm{ns}}_{1/2}\ensuremath{-}(n+1){s}_{1/2}ns1/2​\ensuremath−(n+1)s1/2​ transitions in alkali-metal atoms is investigated. We find that the NES contributions are significant in almost all cases and, for rubidium, reduce the transition rate by a factor of 8. We tabulate magnetic-dipole (M1)({M}_{1})(M1​) transition amplitudes for the alkalis. Our M1{M}_{1}M1​ value for cesium, where accurate measurements are available, differs from experiment by 1616%16. We briefly discuss the feasibility of an experimental test of NES effects.
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
Abstract The “mixing” of magnetic sublevels of the ground and excited levels of an atomic transition with magnetic sublevels of a nearby transition (in the hyperfine structure of atoms of alkali metals) is responsible for a strong modification of its probability. A dramatic manifestation of this mixing effect is a huge increase in the probability of the atomic transition in magnetic fields that is forbidden by selection rules in zero magnetic field B = 0; the latter is called a magnetically induced (MI) transition. Two MI transitions with different dependences on B have been studied. Another dramatic manifestation of the mixing effect is that there are atomic transitions whose frequency is practically fixed in a wide range of magnetic fields, i.e., the slope S [MHz/G] of the frequency shifts as a function of B is practically zero, with the transition probability being significant. We call these transitions “unmoved” transitions (UTs). We have studied the UTs of 87Rb atoms, the D2 line, |1, +1〉 → |1', +1'〉 and Cs atoms, the D2 line, |3, –3〉 → |5', –4'〉, where the quantum numbers F and mF of the excited and ground levels are marked with and without primes, respectively. We show that in the range B = 180–705 G for 87Rb, the D2 line, |S| ≤ 0.03 MHz/G; for comparison, S ≈ 3.6 MHz/G for 87Rb in the same B range for the MI transition |1, +1〉 → |3', +2'〉 is greater by a factor of 120. A second laser was used to control the UT amplitude. Our theoretical model describes well the experiment.
Atomic transitions in alkali metals that have zero probability in the absence of a magnetic field but have large probabilities in the presence of a magnetic field are called magnetically induced (MI). They are of interest because of their large probabilities, which exceed the probabilities of usual transitions in a wide magnetic field range. Magnetically induced transitions are classified as type-1 (MI1) and type-2 (MI2) and their total number is about 100. In this work, MI2 transitions are examined between ground Fg and excited levels Fe of the hyperfine structure satisfying the condition Fe−Fg=ΔF=±2{{F}_{{\text{e}}}} - {{F}_{{\text{g}}}} = \Delta F = \pm 2Fe​−Fg​=ΔF=±2 , which are forbidden in zero magnetic field but have large probabilities in the presence of a magnetic field. The probabilities of the MI2 transitions with ΔF=+2\Delta F = + 2ΔF=+2 and the MI transitions with ΔF=−2\Delta F = - 2ΔF=−2 are maximal in the case of optical radiation with the σ+ and σ– polarizations, respectively. This difference is called type-1 magnetically induced circular dichroism (MICD1). It has been shown for the first time that the probability of the strongest MI2 transition in the 85Rb atom corresponding to the D2 line in magnetic fields >100 G in the case of σ+{{\sigma }^{ + }}σ+ radiation is larger than the probability of the strongest MI2 transition in the case of σ– radiation by a factor of 2.5. This difference is called type-2 magnetically induced circular dichroism (MICD2). It has been shown how to determine the strongest MI transition for any alkali metal atom, which is important for its application in magneto-optical processes. Theoretical curves reproduce well experimental results.
In collisions of Rydberg atoms with charged projectiles at velocities approximately matching the speed of the Rydberg electron vn{v}_{n}vn​ (matching velocity), nnn being the principal quantum number of the Rydberg level, the dipole-forbidden transitions with large angular-momentum transfer $\ensuremath{\Delta}l\ensuremath{\gg}1$ substantially dominate over dipole-allowed transitions $\ensuremath{\Delta}l=1$, although both are induced by the dipole interaction. Here it is shown that as the projectile velocity decreases the adiabatic character of the depopulation depends on the energy distribution of states in the vicinity of the initial level. If the spectrum is close to degeneracy (as for high-lll levels) the dipole-forbidden depopulation prevails practically over the entire low-velocity region, down to velocities $\ensuremath{\sim}{n}^{3}[\frac{\ensuremath{\Delta}E}{\mathrm{Ry}}]{v}_{n}$, where $\ensuremath{\Delta}E$ is the energy spacing adjoining to the level due to either a quantum defect or the relevant level width or splitting, whichever is greater. If the energy gaps are substantial (as for strongly nonhydrogenic sss and ppp levels in alkali-metal atoms), then the fraction of dipole transitions in the total depopulation reaches a flat minimum just below the matching velocity and then grows again, making the progressively increasing contribution to the low-velocity depopulation. The analytic models based on the first-order Born amplitudes (rather than the two-level adiabatic approximation) furnish reasonable estimates of the fractional dipole-allowed and dipole-forbidden depopulations.
The sss-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the sss-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable sss-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (52{}^{52}52Cr, 164{}^{164}164Dy, 168{}^{168}168Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\ensuremath{\epsilon}}_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of 7{}^{7}7Li, 39{}^{39}39K, and 133{}^{133}133Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.
When atoms are placed in a static magnetic field, they undergo shifts of their energy levels and changes in their transition probabilities. These two effects must be taken into account when considering absorption profiles of alkali-metal D lines, which result from the contribution of many transitions influenced by the laser spectrum and Doppler broadening. The model presented here gives the D-line absorption coefficients of alkali-metal vapors in the presence of an arbitrary static magneitc field. They are evaluated considering various laser polarizations. Experimental measurements of D-line absorption profiles for 85Rb^{85}\mathrm{Rb}85Rb, 87Rb^{87}\mathrm{Rb}87Rb, and 133Cs^{133}\mathrm{Cs}133Cs isotopes show excellent agreement with theoretical predictions.