Damping of local Rabi oscillations in the presence of thermal motion

Physical Review A (Impact Factor: 2.81). 08/2012; 87(6). DOI: 10.1103/PhysRevA.87.063402
Source: arXiv


We investigate both theoretically and experimentally the effect of thermal
motion of laser cooled atoms on the coherence of Rabi oscillations induced by
an inhomogeneous driving field. The experimental results are in excellent
agreement with the derived analytical expressions. For freely falling atoms
with negligible collisions, as those used in our experiment, we find that the
amplitude of the Rabi oscillations decays with time $t$ as $\exp[-(t/\tau)^4]$,
where the coherence time $\tau$ drops with increasing temperature and field
gradient. We discuss the consequences of these results regarding the fidelity
of Rabi rotations of atomic qubits. We also show that the process is equivalent
to the loss of coherence of atoms undergoing a Ramsey sequence in the presence
of static magnetic field gradients - a common situation in many applications.
In addition, our results are relevant for determining the resolution when
utilizing atoms as field probes. Using numerical calculations, our model can be
easily extended to situations in which the atoms are confined by a potential or
to situations where collisions are important.

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    ABSTRACT: We have studied the coherent evolution of ultracold atomic rubidium clouds subjected to a microwave field driving Rabi oscillations between the stretched states of the F=1 and F=2 hyperfine levels. A phase winding of the two-level system pseudo-spin vector is encountered for elongated samples of atoms exposed to an axial magnetic field gradient and can be observed directly in state-selective absorption imaging. When dispersively recording the sample-integrated spin population during the Rabi drive, we observe a damped oscillation directly related to the magnetic field gradient, which we quantify using a simple dephasing model. By analyzing such dispersively acquired data from millimeter sized atomic samples, we demonstrate that field gradients can be determined with an accuracy of $\sim25$ nT/mm. The dispersive probing of inhomogeneously broadened Rabi oscillations in prolate samples opens up a path to gradiometry with bandwidths in the kilohertz domain.
    Preview · Article · Aug 2013 · Physical Review A