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Adiabatic elimination of a nearly resonant quantum state

Quantum systems with multiple states are often reduced to simpler systems by adiabatic elimination of far-off-resonant states. This method provides accurate coupling and Stark shifts in the reduced system for very large values of the detunings only, far greater than that of the relevant couplings. We introduce two alternative techniques for exclusion of an off-resonant state based on the adiabatic and superadiabatic approximations, which provide far more accurate expressions for the coupling and the Stark shifts in the reduced system, and which are valid in much broader ranges of interaction parameters than the traditional adiabatic elimination method. The reason is that the conditions for the adiabatic and superadiabatic approximations only demand, for smooth pulse shapes, the detuning to be greater than the Fourier width of the pulse; hence, these approximations can be used even when the couplings exceed the detunings, i.e. when the excluded states can be described as ‘nearly resonant’. The error of the adiabatic and superadiabatic approximations can be easily suppressed below the quantum computing benchmark of 10−4, an objective that is hard to achieve with the traditional adiabatic elimination method.