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Quantum lithography by coherent control of classical light pulses

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Abstract

The smallest spot in optical lithography and microscopy is generally limited by diffraction. Quantum lithography, which utilizes interference between groups of N entangled photons, was recently proposed to beat the diffraction limit by a factor N. Here we propose a simple method to obtain N photons interference with classical pulses that excite a narrow multiphoton transition, thus shifting the “quantum weight” from the electromagnetic field to the lithographic material. We show how a practical complete lithographic scheme can be developed and demonstrate the underlying principles experimentally by two-photon interference in atomic Rubidium, to obtain focal spots that beat the diffraction limit by a factor of 2.

©2004 Optical Society of America

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Figures (4)

Fig. 1.
Fig. 1. Schematic setup for generation of sub diffraction limited spots by quantum interference. A glass plate delays half of a planar ultrashort pulse with respect to the other half. As a result, the non-linear lithographic medium at the focus is excited by two consecutive pulses with a space-variant relative delay; thus generating a space-dependent two-photon interference. Fine tuning the delay can be performed by a small tilt of the glass.
Fig. 2.
Fig. 2. Calculated sub diffraction-limit spots (line), as compared to the diffraction-limited single-photon spot (dashed). (a), (b) are the two-photon and four-photon spots respectively of the two segment configuration of Fig. 1. (c), (d) show the same spots assuming four equal non-overlapping segments instead of two. (e), (f) show these spots when a third pulse with two offset foci is used to suppress the side lobes. All segments are assumed to be illuminated by a uniform plane wave pulse.
Fig. 3.
Fig. 3. Experimental configuration and relevant level diagram for atomic Rb. The cylindrical telescope weakly focuses the beam into the Rb Cell, the delay line controls the interference and the CCD records the image of the fluorescence spot. The cylindrical lens in front of the cell tightly focuses the beam in the perpendicular dimension.
Fig. 4.
Fig. 4. Experimental results. (a) images and transverse cross sections of “dark spots” (destructive at the center) for a short relative delay (crosses - data, gray line - theoretical fit) and a long relative delay (circles - data, line - theoretical fit), demonstrating the double resolution of two-photon interference compared to one-photon interference. (b) is the corresponding two-photon “bright spot” as compared to the diffraction limited one-photon spot (dashed). All experimental cross sections were averaged over the center portion of the image (18 pixel lines) to reduce noise. The theoretical fits assume a Gaussian beam profile with a narrow gap in the middle.

Equations (2)

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I ( x ) E 1 N ( x ; ω A ) + E 2 N ( x ; ω A ) 2 ,
k = 1 M E k N ( x f ) 2 = I ( x f ) ,
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