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Decoherence is a major obstacle to any practical implementation of quantuminformation processing. One of the leading strategies to reduce decoherence isdynamical decoupling --- the use of an external field to average out the effectof the environment. The decoherence rate under any control field can becalculated if the spectrum of the coupling to the environment is known. Wepresent a direct measurement of the bath coupling spectrum in an ensemble ofoptically trapped ultracold atoms, by applying a spectrally narrow-band controlfield. The measured spectrum follows a Lorentzian shape at low frequencies, butexhibits non-monotonic features at higher frequencies due to the oscillatorymotion of the atoms in the trap. These features agree with our analyticalmodels and numerical Monte-Carlo simulations of the collisional bath. From theinferred bath-coupling spectrum, we predict the performance of well-knowndynamical decoupling sequences: CPMG, UDD and CDD. We then apply thesesequences in experiment and compare the results to predictions, finding goodagreement in the weak-coupling limit. Thus, our work establishes experimentallythe validity of the overlap integral formalism, and is an important steptowards the implementation of an optimal dynamical decoupling sequence for agiven measured bath spectrum.

Direct Measurement of the System-Environment Coupling as a Tool For Understanding Decoherence and Dynamical Decoupling