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Physical Review A

Enhanced generation of twin single-photon states via quantum interference in parametric down-conversion: Application to two-photon quantum photolithography

Christopher C. Gerry

Published Apr 2, 2003• 5 citations
Publisher

Abstract

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 $|1{〉}_{a}|1{〉}_{b},$ 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 $|2{〉}_{a}|2{〉}_{b},$ 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 $|2{〉}_{a}|2{〉}_{b}$ state and to enhance the production of the $|1{〉}_{a}|1{〉}_{b}$ state by almost sixfold.

DOI
10.1103/physreva.67.043801

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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.
We consider the action of a beam splitter with identical degenerate parametric down converters in each of the outputs and show that with single photons injected into each of the input ports, under certain conditions, a superposition of two- and four-photon maximally entangled states may be produced. Also we describe techniques for verifying the generation of the four-photon component of the state. We then discuss the application of such states to quantum photolithography assuming the existence of substrates capable of absorbing four photons. The two-photon component makes no contribution to the background.
Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.
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.
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.
An interferometric arrangement utilizing a pair of twin photons, generated by parametric down-conversion, is devised to show second-order interferences revealing de Broglie's wavelength of the photon pair as a whole and the Pancharatnam phase depending on the number of photons. This proposed experiment utilizes the phenomenon ``induced coherence without stimulated emission'' to generate a coherent superposition of states distinct from the usual superposition with beam splitters, where the photons are independently scattered. In this experiment interference occurs due to recombination of photon trajectories on a beam splitter and also through frustration or enhancement of the down-conversion processes.
Summary form only given. We demonstrate a proof-of-principle experiment of quantum lithography utilizing parametric down-converted photons and a transmission grating, and show that the diffraction of a multiphoton state can be also explained by the concept of the photonic de Broglie wave. Pairs of frequency-degenerate photons were collinearly generated by spontaneous parametric down-conversion (SPDC) in a 5 mm long KNbO/sub 3/ (KN) crystal pumped by the second harmonic light of a single longitudinal mode Ti:sapphire laser operating at 861.5 nm. The photon pairs were diffracted by a transmission grating (slit width: 125 /spl mu/m, period: 250 /spl mu/m), placed just after the KN crystal. In this geometry, each photon pair passes together through one of the grating slits. By rotating a mirror, we recorded spatial diffraction-interference patterns at a two-photon detector consisting of two avalanche photodiodes. For comparison, we also observed diffraction-interference patterns of chaotic light from a tungsten lamp using the same apparatus.