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arXiv:quant-ph/0604132

Beating the spatial standard quantum limits via adiabatic soliton expansion and negative refraction

Mankei Tsang

Published Apr 18, 2006• 1 citation
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Abstract

Spatial quantum enhancement effects are studied under a unified framework. It is shown that the multiphoton absorption rate of photons with a quantum-enhanced lithographic resolution is reduced, not enhanced, contrary to popular belief. Finally, the use of adiabatic soliton expansion followed by negative refraction is proposed to beat both the standard quantum limit on the optical beam displacement accuracy, as well as that on the minimum spot size of quantum lithography.

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Spatial quantum enhancement effects are studied under a unified framework. It is shown that the multiphoton absorption rate of photons with a quantum-enhanced lithographic resolution is reduced, not enhanced, contrary to popular belief. Finally, the use of adiabatic soliton expansion followed by negative refraction is proposed to beat both the standard quantum limit on the optical beam displacement accuracy, as well as that on the minimum spot size of quantum lithography.
The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)$ quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.
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.
Quantum lithography (QL) has been suggested as a means of achieving enhanced spatial resolution for optical imaging, but its realization has been held back by the low multiphoton detection rates of recording materials. Recently, an optical centroid measurement (OCM) procedure was proposed as a way to obtain spatial resolution enhancement identical to that of QL but with higher detection efficiency (M. Tsang, Phys. Rev. Lett. 102, 253601 (2009)). Here we describe a variation of the OCM method with still higher detection efficiency based on the use of photon-number-resolving detection. We also report laboratory results for two-photon interference. We compare these results with those of the standard QL method based on multiphoton detection and show that the new method leads to superresolution but with higher detection efficiency.
I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber or coincidence detection. Using the same nonclassical states of light as those for quantum lithography, the proposed method requires only optical intensity measurements, followed by image postprocessing, to produce the same complex quantum interference patterns as those in quantum lithography. The method is expected to be experimentally realizable using current technology.
The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some NNN-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1∕N1∕\sqrt{N}1∕N​ enhancement (standard quantum limit) or a 1∕N1∕N1∕N enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.