Measuring a coherent superposition

Atoms and molecules prepared in well-defined coherent superpositions of energy states exhibit many interesting properties, such as dark resonances [1], subrecoil laser cooling [2–5], electromagnetically induced transparency [6–8], radiation amplification without population inversion [9–12], refractive index enhancement without absorption [13], and enhanced harmonic generation [14,15]. Coherent superpositions are essential to the implementation of quantum computation and quantum cryptography or, more generally, quantum information [16,17]. Various techniques are available for preparing coherent superpositions. Some of them are sensitive to pulse fluence (the time integrated pulse area), e.g., radio frequency or microwave excitation [18–20], resonant optical pulses [12], and trains of identical pulses [11]. Techniques based on stimulated Raman adiabatic passage (STIRAP) [21–23] are relatively insensitive to pulse area, e.g., fractional STIRAP [24–28] and tripod-linkage adiabatic passage [29]. To verify the reliability of these techniques it is essential to have a method for measuring the parameters of the created coherent superposition – the populations, the relative phase between the two states, and the degree of coherence. In this paper, we propose such a method. It is based on coupling the two states comprising the superposition to a third state (excited and subject to radiative decay), by means of two laser pulses, thus mapping the superposition parameters onto the population of the excited state. This population could then be observed