Abstract
We present a detailed theory of the Rydberg blockade, including contributions from multiple intermediate-state excitations. Two fields drive transitions between ground and Rydberg levels via an off-resonance intermediate state. Assuming a perfect blockade, we calculate the probability to excite fully symmetric collective states having either zero or one Rydberg excitation, but an arbitrary number of intermediate-state excitations. Both ``bare'' state and ``dressed'' state approaches are used for (1) constant amplitude driving fields and (2) adiabatic pulse driving fields. It is shown that a dressed state approach offers distinct advantages when multiple intermediate-state excitations occur. In the case of fixed amplitude fields, the multiple intermediate excitations can result in comblike modulated populations of individual states having one Rydberg excitation and $n\ensuremath{\ll}N$ intermediate-state excitations. However, when summed over all such state populations, most of the modulation disappears and the system is described to a good approximation by an effective two-level model. In the case of adiabatic, pulsed fields, there is no such modulation and an effective two-level model (in the dressed basis), corrected for light shifts, can be used to model the system. In addition to solving this problem using conventional methods, we show that similar results could be obtained using a form of the Holstein-Primakoff transformation.
Published Version
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