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Quantum Electronics and Laser Science Conference

Is entanglement dispensable in quantum lithography?

Milena D’Angelo, Giuliano Scarcelli, Yanhua H. Shih

Published May 1, 2007• 1 citation
Publisher

Abstract

Can classical light simulate the effect of quantum lithography? The analysis of the two-photon image generated both by entangled two-photon and by chaotic radiation indicates that only entanglement can double the resolution of an image.
DOI
10.1109/qels.2007.4431244

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The working principle of quantum lithography has been demonstrated a few years ago: entangled N-photon systems can improve the spatial resolution of an imaging system by a factor of N, despite the classical Rayleigh limit. Recently, a number of experiments successfully simulated certain features of quantum imaging and two-photon interference-diffraction by using chaotic light in coincidence detection experiments. Can classical light simulate the effect of imaging type quantum lithography? This article attempts to provide an answer to this currently debated question.
Since the early days of quantum mechanics, physicists have been puzzled by the counterintuitive consequences of entanglement. Quantum imaging is one of the most intriguing effects exhibiting the typical nonlocal behavior of entangled states and has in fact stimulated an intense debate regarding fundamental issues of quantum theory. Recently, particular attention has been given to the possibility of simulating quantum imaging classically, that is, without entanglement. The study of quantum imaging has also lead to useful practical applications such as high precision nonlocal timing-positioning and quantum lithography, in which measurements may achieve resolution even beyond the classical limits. In this paper, we first introduce the concept of quantum imaging and emphasize its peculiar quantum nature through a set of inequalities derived from the historical argument of Einstein, Podolsky and Rosen (EPR). The EPR inequalities are the quantitative formulation of the very different physics governing entangled and separable systems. We show that two-photon imaging may achieve its fundamental limit only through nonlocal measurements realized on entangled photon pairs. Furthermore, we show that quantum imaging may be exploited to overcome the Rayleigh diffraction limit; this is the basic idea behind quantum lithography. Finally, we discuss the possibility of extending the coherent two-photon imaging typical of entangled photon pairs to incoherent coincidence imaging, by employing chaotic light. From an applicative viewpoint, chaotic radiation may represent the ideal candidate for mimicking quantum ghost imaging, provided adequate detection schemes are developed.
The advantages of using nonclassical states of light for optical imaging are discussed, with special emphasis on the new field of quantum optical lithography. The classical resolution limit given by the Rayleigh criterion is approximately half of the optical wavelength. However, it has been argued that, by using special quantum states of light and a multiphoton-sensitive material or detector, this limit can be broken. Here, a brief and rigorous overview of this problem is provided, some particularly widespread misconceptions are addressed, and turning quantum lithography into a practical technology is discussed.
We formulate an image-forming optical theory of quantum lithography in which Entangled-photon pairs generated by spontaneous parametric down-conversion play an important role. Our optical system consists of an image-forming system, an illumination system with a second-order nonlinear medium, and two-photon absorbing materials. We evaluate the resolution of the quantum lithography system by using the optical transfer function and show a super-resolving condition which is, however, difficult to achieve.
The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.