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Physical Review A

Periodic structures generated in a cloud of cold atoms

Dmitry Strekalov, Andrey V. Turlapov, Anantharaman Kumarakrishnan, Tycho Sleator

Published Aug 5, 2002• 46 citations
Publisher

Abstract

We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength $\ensuremath{\lambda}.$ We have detected structures of period $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Calculations indicate that these density gratings have period $\ensuremath{\lambda}/2N$ for integer N. While the structures with the period $\ensuremath{\lambda}/2$ are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorter-period gratings get converted into the structures with period $\ensuremath{\lambda}/2,$ readily detected in real time. Applications related to lithography are discussed.

DOI
10.1103/physreva.66.023601

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We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength \ensuremathλ.\ensuremath{\lambda}.\ensuremathλ. We have detected structures of period \ensuremathλ/2\ensuremath{\lambda}/2\ensuremathλ/2 and \ensuremathλ/4.\ensuremath{\lambda}/4.\ensuremathλ/4. Calculations indicate that these density gratings have period \ensuremathλ/2N\ensuremath{\lambda}/2N\ensuremathλ/2N for integer N. While the structures with the period \ensuremathλ/2\ensuremath{\lambda}/2\ensuremathλ/2 are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorter-period gratings get converted into the structures with period \ensuremathλ/2,\ensuremath{\lambda}/2,\ensuremathλ/2, readily detected in real time. Applications related to lithography are discussed.
We have studied sub-optical wavelength atomic gratings generated by the interference of atomic de Broglie waves in a time-domain interferometer. Three short optical standing- wave pulses, detuned from resonance with a cloud of approximately 100 (mu) K 85Rb atoms, act as phase gratings for atomic matter waves. Shortly after the first pulse, a modulation in the atomic density containing spatial harmonics of period (lambda) /2N appears ((lambda) is the optical wavelength, and N is any integer) and then rapidly vanishes due to the atomic thermal motion. The cloud maintains phase memory of this modulation, however, and the second pulse (applied at time T after the first one) results in a temporal sequence of atomic density gratings of periods (lambda) /2N. The appearance of a grating is referred to as an echo. The third pulse (and a subsequent traveling wave pulse) is used to detect these gratings. By this technique, we have created and detected in real time a grating with period (lambda) /4 at time 1.5T after the first pulse and observed new types of `echoes' caused by interaction of the de Broglie waves with all three phase gratings. This ability to produce sub-wavelength structures makes our techniques applicable to atomic beam lithography.
We have studied suboptical wavelength atomic gratings, generated by the interference of atomic de Broglie waves in a time-domain interferometer. Three short optical standing- wave pulses, detuned from resonance with a cloud of approximately 100 (mu) K85 Rb atoms, act as phase gratings for atomic matter waves. The first two standing- wave pulses, separated by time T, produce a sequence of atomic density gratings of periods $lamda/4 at time 1.5T after the first pulse. The dependence of our signals on the time separation of the pulses is in good agreement with our theoretical predictions. As far as we know, this is the first time when the formation of a high order matter-wave diffraction grating was observed in real time. This demonstrated ability to produce sub-wavelength structures makes our techniques applicable to atomic beam lithography.
We develop a versatile theoretical approach to the study of ultracold atom diffractive scattering from light-field gratings by combining calculations of the optical near field generated by evanescent waves close to the surface of periodic nanostructured arrays with atom wavepacket propagation techniques. Nanometric one dimensional (1D) and 2D arrays with subwavelength periodicity deposited on a transparent surface and optically coupled to an evanescent wave source exhibit intensity and polarization gradients on the length scale of the object and can produce strong near-field periodic modulation in the optical potential above the structure. As a specific and experimentally practical example we calculate the diffraction of cold Cs atoms dropped onto a periodic optical potential crafted from a 2D nanostructure array. For an ``out-of-plane'' configuration we calculate a wide diffraction angle $(\ensuremath{\simeq}2\ifmmode^\circ\else\textdegree\fi{})$ and about 6060%60 of the initial atom flux in diffraction orders $\ifmmode\pm\else\textpm\fi{}1,$ an encouraging result for future experiments.
In this article we illustrate important characteristics of the diffraction of cold atoms from periodic light potentials generated from coupling a light wave to dielectric nanostructures. We apply a recently developed theoretical approach to investigate the behavior of Cs atoms dropped onto a periodically modulated optical dipole potential where the period of the modulation is controlled by the periodicity of the dielectric array. These nanostructures take the form of one-dimensional line gratings or two-dimensional point gratings. We discuss several important parameters critical to the successful realisation of laboratory experiments and future atom-optical instrumentation using this new kind of atomic diffraction medium.
The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.
We first calculated the diffraction intensity distributions of the Dammann gratings illuminated by Gaussian light wave. The empirical equations were deduced by numerical calculations to calculate the parameters, such as the spatial period, the maximum intensity, and the maximum intensity gradient, of the optical trap array composed by a set of Dammann gratings and a focus lens. Thus, a novel type of optical trap array for trapping cold atoms (or molecules) was proposed and its features were discussed. The results showed the optical trap array with very short period could be generated. High optical dipole potential could be presented so as to have strong attractive force to the atoms to form atomic optical lattices of high lattice density. Compared with the optical lattices formed by standing wave interferences of CO2 laser, there are many unique advantages of which are formed by Dammann gratings.