We describe how to reconstruct individual classical trajectories from spectroscopic data. The ac dipole moment of a trajectory can be found from the effect of an oscillating field on the spectrum. The inverse Fourier transform of such data yields the component of the electron trajectory along the direction of the oscillating field. We demonstrate the method by experimentally extracting z͑t͒ for two electron trajectories that influence the Stark spectrum of Rydberg lithium. Within the experimental resolution, the reconstructed orbits agree well with classical predictions. [S0031-9007 (98)06988-9] PACS numbers: 32.60. + i, 03.65.Sq, 05.45. + bThe classical behavior of a dynamical system is expected to be derivable from its underlying quantum structure, and new methods of connecting classical and quantum approaches continue to be developed. Periodic orbit theory [1] and its variants allow one to learn about the actions and stabilities of classical orbits from a system's quantum density of states (though it is typically used the other way around). There are only a few methods that can be used to find the trajectories themselvestheir position as a function of time-and the methods are either indirect [2] or require knowledge of the quantum wave functions in addition to the spectrum [3,4]. We present here the results of a new study in which semiclassical methods are used to reconstruct a trajectory from experimental spectroscopic data.When we speak of the "classical trajectory of an electron," we mean, of course, the path the electron would follow if it obeyed the laws of classical mechanics. In quantum mechanics an electron is not a localized object moving along a path. Nevertheless, a classical path is significant even in the quantum world-in semiclassical theories we use classical paths to construct wave functions and spectra. We demonstrate here that the process is invertible: under appropriate conditions such classical paths can be reconstructed from observed quantum spectra.Rydberg atoms in external fields are an excellent laboratory for studying semiclassical methods experimentally. Their spectra can be interpreted with a variation of the periodic orbit theory known as closed orbit theory [5,6]. Closed orbit theory relates fluctuations in the atomic photoabsorption spectrum to the system's classical closed orbits (orbits that begin and end at the nucleus). A spectrum taken under conditions obeying classical scaling laws can be Fourier transformed to yield a "recurrence spectrum," in which each closed orbit appears as a peak in a plot of intensity vs action [7]. This procedure establishes the existence and action of the closed orbits, and provides some information about their stabilities and initial directions. From the change in peak positions when experimental parameters are changed, it is also possible to learn about the periods and average electric dipole moments of the orbits [8]. However, the orbits themselves (the electron position as a function of time) have hitherto been experimentally inaccessible.The id...