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arXiv:0801.3531 · Physical Review A

Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography

Fabio Sciarrino, Chiara Vitelli, F. De Martini, Ryan T. Glasser, Hugo V. Cable, Jonathan P. Dowling

Published Jan 22, 2008• 48 citations
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Abstract

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.

DOI
10.1103/physreva.77.012324

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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.
The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal et al., J. Opt. Soc. Am. B 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled $\ensuremath{\mid}N00N⟩$ state $(\ensuremath{\mid}2,0⟩+\ensuremath{\mid}0,2⟩)∕\sqrt{2}$. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. A large family of entangled output states are found. Specific output states allow for the heralded creation of N=4N=4N=4 N00NN00NN00N states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.
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.
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.
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 achieves phase superresolution using fragile, experimentally challenging entangled states of light. We propose a scalable scheme for creating features narrower than classically achievable with reduced use of quantum resources and, consequently, enhanced resistance to loss. The scheme is an implementation of interferometric lithography using a mixture of a spontaneous parametric down-converted entangled state with intense classical coherent light. We measure coincidences of up to four photons mimicking multiphoton absorption. The results show a narrowing of the interference fringes of up to 30% with respect to the best analogous classical scheme using only 10% of the nonclassical light required for creating NOON states.
Two-photon interferometric quantum photon lithography for light of wavelength \ensuremath{\lambda} is capable of beating the Rayleigh diffraction limit of resolution \ensuremath{\lambda}/4 to the level of \ensuremath{\lambda}/8. The required twin single-photon states ∣1〉a∣1〉b,|1{〉}_{a}|1{〉}_{b},∣1〉a​∣1〉b​, which are converted into maximally entangled states by a 50:50 beam splitter, can be generated from a nondegenerate parametric amplifier initially in vacuum states and with a weak pump field. Increasing the pump strength can slightly increase the production rate of the desired state and it will also increase the production of the twin two-photon states ∣2〉a∣2〉b,|2{〉}_{a}|2{〉}_{b},∣2〉a​∣2〉b​, which leads to an unwanted background term. In this paper we show that, assuming a weak pair coherent state as input to the amplifier, quantum interference can be used to quench the production of the ∣2〉a∣2〉b|2{〉}_{a}|2{〉}_{b}∣2〉a​∣2〉b​ state and to enhance the production of the ∣1〉a∣1〉b|1{〉}_{a}|1{〉}_{b}∣1〉a​∣1〉b​ state by almost sixfold.