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Journal of Optics B Quantum and Semiclassical Optics

Improving quantum microscopy and lithography via Raman photon pairs: II. Analysis

Marlan O. Scully, C. H. Raymond Ooi

Published Jul 28, 2004• 31 citations
Publisher

Abstract

We show that by using the strongly correlated photon pairs generated in a Raman quantum erasure scheme (Scully M and Drühl K 1982 Phys. Rev. A 25 2208), it is possible to exceed the Rayleigh resolution limit of classical microscopy. The complete analysis of the underlying physics is given here. Further discussion of the physics and potential applications are presented in a companion paper (Scully M O 2004 Improving quantum microscopy and lithography via Raman photon pairs: I. Biological applications, submitted).

DOI
10.1088/1464-4266/6/8/030

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We show that by using the strongly correlated photon pairs generated in a Raman quantum erasure scheme (Scully M and Drühl K 1982 Phys. Rev. A 25 2208), it is possible to exceed the Rayleigh resolution limit of classical microscopy. The complete analysis of the underlying physics is given here. Further discussion of the physics and potential applications are presented in a companion paper (Scully M O 2004 Improving quantum microscopy and lithography via Raman photon pairs: I. Biological applications, submitted).
In ordinary (classical) microscopy and lithography, the limit of resolution is governed by the wavelength of light used to il-luminate the sample. However, by using the correlated photon pairs produced in Raman quantum erasure, the resolution of two-photon quantummicroscopy is substantially improved. To that end, we here derive the two-photon quantum state gener-ated by sequential Raman emissions and investigate potential applications. The photon-photon correlation function for Ra-man pairs is of interest in itself and has features in common with photon antibunching. 1Asim Barut enjoyed and brought joy to all of Physics. He was interested in Concepts of Physics, Vol. II (2005) 261
Summary form only given. Recently, Boto et al. (see Phys. Rev. Lett., vol. 85, p. 2773, 2000) showed that using N entangled photons and an N-photon responsive lithographic recording medium, one could potentially write lithographic gratings with a resolution that is N times better than the classical Rayleigh criterion. An anticipated experimental difficulty is that such beams are weak, yet strong fields are needed to excite the N-photon absorption process. For the case of N=2, which was described in detail by Boto et al., we propose a method to overcome this problem. We also propose to use this idea "in reverse" to perform microscopy with better resolution than aloowed by the Rayleigh limit.
Higher-order correlations of the radiation field improve resolution in stellar interferometers, as in the Hanbury-Brown–Twiss effect. It is also possible to improve microscopic resolution beyond the Rayleigh limit by using quantum light fields composed of entangled photons. Focusing on two photons, we distinguish two types of entanglement: frequency entanglement, where the photons in different paths are correlated in frequency, and path entanglement, where the correlation between paths is in photon number. Two paradigms of quantum microscopy are discussed: spectral microscopy, where path- and frequency-entangled photons produced in cascade decay of two atoms make possible sub-natural linewidth resolution of atomic levels, and spatial microscopy, where path-entangled photons emitted by an atomic array produce sub-wavelength diffraction resolution as compared to an equivalent classical grating. These scenarios require two-photon correlation or coincidence measurements. The connection between the two paradigms, and the two types of entanglement, highlights the link between the temporal and spatial aspects of quantum interferometry.
State-of-the-art microscopes use intense lasers that can severely disturb biological processes, function and viability. This introduces hard limits on performance that only quantum photon correlations can overcome. In this talk I will report recent work from my laboratory which demonstrates this absolute quantum advantage [1]. We show, specifically, that quantum correlations enable signal-to-noise beyond the photodamage-free capacity of conventional microscopy. Broadly, this represents the first demonstration that quantum correlations can allow sensing beyond the limits introduced by optical intrusion upon the measurement process. We achieve this in a coherent Raman microscope, which we use to image molecular bonds within a cell with both quantum-enhanced contrast and sub-wavelength resolution. This allows the observation of nanoscale biological structures that would otherwise not be resolved. Coherent Raman microscopes allow highly selective biomolecular finger-printing in unlabelled specimens, but photodamage is a major roadblock for many applications. By showing that this roadblock can be overcome, our work provides a path towards order-of-magnitude improvements in both sensitivity and imaging speed.
High Resolution Image Download MS PowerPoint Slide The resolution of a classical imaging system is limited by diffraction. This limit can be overcome, for example, by implementing various forms of localization microscopy in which the center of a fluorescence distribution is estimated to an accuracy scaling with the square root of the number of detected photons, N . In quantum imaging the object can be illuminated using correlated photon-pairs, leading early work to suggest that a 2 improvement could be obtained as a result of averaging the position of N = 2 events. However, similar to quantum lithography, which relies upon quantum illumination using entangled photon-pairs and two-photon absorption, the minimum resolvable feature size is reduced by a factor of 2, not just 2 . Quantum imaging schemes can also lead to a factor of 2 improvement. By using a similar source of correlated photon-pairs to illuminate an object, a single-photon sensitive camera to detect the photon-pairs, and an image processing algorithm to record and sum the bisector positions of the transmitted photon-pairs, we realize a similar factor of ×2 improvement in image resolution, surpassing that of most earlier quantum imaging work.