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Physical Review A

Scheme for generating a superposition of two- and four-photon maximally entangled states: Application to four-photon quantum photolithography

Christopher C. Gerry, Adil Benmoussa

Published Sep 11, 2002• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.033804

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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.
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.
Maximally entangled photonic states of a two-mode field have applications in Heisenberg-limit interferometry and in photolithography where they may be used to transfer images with resolutions exceeding the Rayleigh diffraction limit. In a recent paper by one of us [C. C. Gerry, Phys. Rev. A 61, 043811 (2000)] it was shown that a nonlinear four-wave mixer could produce the requisite states for input states containing only even photon numbers. For superpositions of even number states the output is just a superposition of maximally entangled even states. In the present paper we extend the earlier work to consider both even coherent states and squeezed vacuum states as inputs and study their applications to interferometry and lithography.
Abstract Multipartite entanglement plays a central role in optical quantum technologies. One way to entangle two photons is to prepare them in orthogonal internal states, for example, in two polarisations, and then send them through a balanced beam splitter. Post-selecting on the cases where there is one photon in each output port results in a maximally entangled state. This idea can be extended to schemes for the post-selected generation of larger entangled states. Typically, switching between different types of entangled states requires different arrangements of beam splitters and so a new experimental setup. Here, we demonstrate a simple and versatile scheme to generate different types of genuine tripartite entangled states with only one experimental setup. We send three photons through a three-port splitter and vary their internal states before post-selecting on certain output distributions. This results in the generation of tripartite W, G and GHZ states. We obtain fidelities of up to ( 87.3 ± 1.1 ) % with regard to the respective ideal states, confirming a successful generation of genuine tripartite entanglement.
We present a scheme to produce an entangled four-photon W state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters, and four mirrors. A photon Einstein-Podolsky-Rosen pair and two single photons are required as the input modes. The projection on the W state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector, the W state of three photons can be generated.
We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.