When a Rydberg p-state is situated exactly in the middle of two s-states, important physical applications of Rydberg atoms in quantum logic become possible due to realization of the "dipole blockade" [1]. Quantitatively, the double-photon resonance occurs when the difference between quantum defects of the states involved in the coupling is equal to ½. We show here that the blockade effect is accomplished with the suppression of radiative spontaneous processes.
The reasons for suppressed photoionization were discussed in details by Seaton [2] (the Cooper minimum in atomic photoionization cross sections). His arguments about small overlap of wave functions associated with transitions are well established: the difference must be close to a half-integer value for the optical transition to be unefficient. The decrease in the efficiency of radiative processes can be interpreted using classical orbits of Rydberg electrons (RE) [2]. When a given l-state is very close to the continuum, the semi-classical treatment yields that the value is equal to the scattering angle of the slow RE by the ionic core. Hence, classical scattering does not occur when μΔ = 0.5, and, consequently, the probability of photon absorption is small, and there is no emission. The absence of classically emitted radiation obviously results in anomalously small natural linewidths.
Fig. 1 Natural emission spectra in Sommerfeld atom. Blockade effect is realized for β = 0.5
Such Rydberg l-states can be considered as metastable, and one could expect that these states possess some specific (quantum) futures that are caused solely by vacuum fluctuations. These features can be explored, for instance, in evaluating the entropy quanta ΔS_{sp}=4/3k, which are carried away by a spontaneously emitted photon. The interaction of RE with vacuum fluctuations can be described using the thermodynamics notation proposed by de Broglie [3]. Variation of the quantum spontaneous emission probability with the parameter , which is directly related to the RE scattering angle , is shown in Fig. 1 for the case of a Sommerfeld type model potential [2]. Photons are emitted by the (nr = 8, l = 1) level to a range of lower levels with radial quantum number . The area under curves is normalized to unity. In the vicinity of , where p-states are expected to become metastable (), the probability distribution of the emission acquires a form characteristic for black-body radiation, which agrees with the conceptions of de Broglie [3]