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arXiv:0903.4268 · New Journal of Physics

An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography

Hugo V. Cable, Reeta Vyas, Surendra Singh, Jonathan P. Dowling

Published Nov 30, 2009• 5 citations

Abstract

We investigate the use of an optical parametric oscillator (OPO), which can generate relatively high-flux light with strong non-classical features, as a source for quantum lithography. This builds on the proposal of Boto et al (2000 Phys. Rev. Lett. 85 2733), for etching simple patterns on multi-photon absorbing materials with sub-Rayleigh resolution, using two-mode entangled states of light. We consider an OPO with two down-converted modes that share the same frequency but differ in field polarization or direction of propagation, and derive analytical expressions for the multi-photon absorption rates when the OPO is operated below, near and above its threshold. Because of strong non-classical correlations between the two modes of the OPO, the interference patterns resulting from the superposition of the two modes are characterized by an effective wavelength that is half of their actual wavelength. The interference patterns resulting when the two modes of the OPO are used for etching are also characterized by an effective wavelength half that for the illuminating modes. We compare our results with those for the case of a high-gain optical amplifier source and discuss the relative merit of the OPO.

DOI: 10.1088/1367-2630/11/11/113055

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We investigate the use of an optical parametric oscillator (OPO), which can generate relatively high-flux light with strong non-classical features, as a source for quantum lithography. This builds on the proposal of Boto et al (2000 Phys. Rev. Lett. 85 2733), for etching simple patterns on multi-photon absorbing materials with sub-Rayleigh resolution, using two-mode entangled states of light. We consider an OPO with two down-converted modes that share the same frequency but differ in field polarization or direction of propagation, and derive analytical expressions for the multi-photon absorption rates when the OPO is operated below, near and above its threshold. Because of strong non-classical correlations between the two modes of the OPO, the interference patterns resulting from the superposition of the two modes are characterized by an effective wavelength that is half of their actual wavelength. The interference patterns resulting when the two modes of the OPO are used for etching are also characterized by an effective wavelength half that for the illuminating modes. We compare our results with those for the case of a high-gain optical amplifier source and discuss the relative merit of the OPO.

Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by [Agarwal et al., Phys. Rev. Lett. 86, 1389 (2001)]. We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. The present paper opens interesting perspectives for the implementation of such an advanced interferometrical setup.

We present a theoretical analysis of the properties of an unseeded optical parametic amplifier (OPA) used as the source of entangled photons for applications in quantum lithography. We first study the dependence of the excitation rate of a two-photon absorber on the intensity of the light leaving the OPA. We find that the rate depends linearly on intensity only for output beams so weak that they contain fewer than one photon per mode. We also study the use of an N-photon absorber for arbitrary N as the recording medium to be used with such a light source. We find that the contrast of the interference pattern and the sharpness of the fringe maxima tend to increase with increasing values of N, but that the density of fringes and thus the limiting resolution does not increase with N. We conclude that the output of an unseeded OPA exciting an N-photon absorber provides an attractive system in which to perform quantum lithography.

We investigate a quantum interferometric lithography system using pair-coherent states as resources to excite an

N

-photon recording medium. The interference pattern is found to have half the period of the classical light interference pattern limited by the Rayleigh criterion. The fringe visibility is nearly unity in the low-flux region and decreases with increasing values of the average photon number. We show that as

N

increases, the high-flux limit visibility increases and the bright-fringe width decreases; however, the fringe period and spacing remain the same. Compared with the results using two-mode squeezed vacuum states, although our results have the same high-flux limit visibility, we can get higher contrast and narrower bright-fringe patterns under the same conditions of light flux and lithography material. Our approach sheds light on quantum lithography with nonclassical light and reveals how pair-coherent states can be superior to two-mode squeezed vacuum states.

Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.

The visibility and quality of optical images is ultimately limited not by diffraction but by the quantum noise affecting each pixel of a detector. Multimode non-classical states of light, characterized by spatial quantum correlation or local reduced quantum noise, permit in principle to go beyond the standard quantum limit and therefore to improve transverse optical resolution. It has been predicted that Optical Parametric Oscillators (OPO) operating simultaneously on many transverse modes are good candidates for generating multimode non-classical states of light. We perform an experiment showing that a c.w. confocal OPO above threshold emits such states. Below threshold, the OPO is turned to a multimode optical parametric amplifier.

We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two χ^2 level oscillation thresholds that are therefore remarkably lower than for a χ^3 OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a χ^2 cascaded device also has potential applications in frequency conversion to far infra-red regimes. But, most importantly, it can generate novel multi-partite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian, and therefore not describable by any semi-classical model.