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An Easy Road to High NOON

Yaron R. Silberberg

Published Jan 1, 2011• 0 citations
Publisher

Abstract

‘High-NOON’ states were generated by multiphoton interference of ‘quantum’ down-converted light with a ‘classical’ coherent state. Super-resolving phase measurements with up to five entangled photons were demonstrated with a visibility higher than obtainable without entanglement.
DOI
10.1364/qels.2011.qthn1

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By combining a coherent state with fields from a number of parametric down-conversion processes, we are able to generate arbitrary NNN-photon entangled states, including the maximally entangled photon-number state or the so-called NOON state $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)$. This is achieved through destructive quantum interference for the cancellation of the unwanted states.
"Schrodinger's cat" is a gedankenexperiment intended to highlight conceptual difficulties in the interpretation of quantum mechanics. The generation of 'cat-like' states is central to numerous quantum information protocols. In particular, much attention has been drawn by states containing N photons in a superposition of all being in one of two designated modes. These maximally path entangled states, known as 'NOON' states, exhibit enhanced phase sensitivity and allow reaching the fundamental quantum limit of precision measurement. Such states could also be used for obtaining 'super-resolution' in quantum lithography. Creation of NOON states in the lab, has been limited to N=3. Surpassing this has proven a formidable experimental challenge. Here, we realize a scheme for generation of high fidelity NOON states with arbitrarily large N. We demonstrate the versatility of the scheme by measuring up to N=5 in a single setup, this is in contrast to previous experiments which were custom-designed for a specific N. The scheme is based on high order interference between 'quantum' down-converted light and 'classical' coherent light in the photon number basis. Our results verify the high degree of path entanglement which emerges naturally from the interference of two ubiquitous, easy to generate, states of light.
We show how to reach high fidelity NOON states with a high count rate inside optical interferometers. Previously, it has been shown that by mixing squeezed and coherent light at a beam splitter, it is possible to generate NOON states of arbitrary N with a fidelity as high as 94%. The scheme is based on higher-order interference between “quantum” down-converted light and “classical” coherent light. However, this requires optimizing the amplitude ratio of classical to quantum light, thereby limiting the overall count rate for the interferometric super-resolution signal. We propose using coherent beam stimulated noncollinear two-mode down-converted light as input to the interferometer. Our scheme is based on the stimulation of noncollinear parametric down conversion by coherent light sources. We get a better flexibility of choosing the amplitude ratio in generating NOON states. This enables super-resolution intensity exceeding the previous scheme by many orders of magnitude. Therefore, we hope to improve the magnitude of N-fold super-resolution in quantum interferometry for arbitrary N using bright light sources. We give improved results for N = 4 and 5.
Difference-phase (or Hanbury Brown--Twiss type) intensity interference of classical light is considered in higher orders in the intensity. It is shown that, while the visibility of sum-phase (NOON-type) interference for classical sources drops with the order of interference, the visibility of difference-phase interference has opposite behavior. For three-photon and four-photon interference of two coherent sources, the visibility can be as high as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon interference of space-time and polarization types has been observed in experiment, for both coherent and pseudothermal light.