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Physica Scripta

Time domain spectroscopy of Rydberg atoms

Thomas F. Gallagher

Published Sep 5, 2007• 1 citation
Publisher

Abstract

One of the most powerful forms of time domain spectroscopy is Fourier transform spectroscopy, pioneered by Pierre Jacquinot. Fourier transform spectroscopy has been widely applied, and it provides the basis of methods used to study Rydberg atoms in the time domain. While results obtained in the time and frequency domains are equivalent, it is often useful to think about a problem in both domains, and the application of time domain spectroscopy to Rydberg atoms has led to many new insights.

DOI
10.1088/0031-8949/76/4/n07

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One of the most powerful forms of time domain spectroscopy is Fourier transform spectroscopy, pioneered by Pierre Jacquinot. Fourier transform spectroscopy has been widely applied, and it provides the basis of methods used to study Rydberg atoms in the time domain. While results obtained in the time and frequency domains are equivalent, it is often useful to think about a problem in both domains, and the application of time domain spectroscopy to Rydberg atoms has led to many new insights.
There is a mathematical method for finding frequency components and their amplitudes, or spectra from periodic patterns. It is called Fourier transform (FT) spectral analysis. In this chapter, how we apply Fourier transform to the following subjects will be explored, emphasizing theoretical discussions: electronics circuits and telecommunication; spectroscopy—magnetic resonance, and IR-spectroscopy; optics—one- and two-dimensional diffractions, lens, hologram, and x-ray diffraction; stochastic process—central limit theorem, Brownian motion, fluctuation–dissipation theorem, and motional narrowing; spectral method for solving diffusion equation and Green’s function for wave equation; and quantum mechanics—wave packet, group velocity, imaginary time Schrödinger equation, Heisenberg’s uncertainty principle, and the Born approximation of scattering of a particle of potential.
We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin-orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin-orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials.
This topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground-states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.