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arXiv:1302.2475 · Physical Review A

Synthesis of arbitrary, two-mode, high-visibility N -photon interference patterns

Saroosh Shabbir, Marcin Świłło, Gunnar G. Bjork

Published May 15, 2013• 7 citations
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Abstract

Using coherent states, linear optics, and $N$-photon detection we demonstrate the synthesis of arbitrary interference patterns and establish that neither the shape nor the visibility of $N$-photon interference patterns can be used as a quantum signature in general. Specific examples include saw-curve and rectangle-curve interference patterns and phase super-resolution with period shortening of up to 60 times compared to ordinary interference. The former two have visibility close to 100$%$ and the latter has visibility in excess of 57$%$.

DOI
10.1103/physreva.87.053821

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Using coherent states, linear optics, and NNN-photon detection we demonstrate the synthesis of arbitrary interference patterns and establish that neither the shape nor the visibility of NNN-photon interference patterns can be used as a quantum signature in general. Specific examples include saw-curve and rectangle-curve interference patterns and phase super-resolution with period shortening of up to 60 times compared to ordinary interference. The former two have visibility close to 100% and the latter has visibility in excess of 57%.
In recent years there have been many demonstrations of phase super-resolution - previously thought to be a manifestly quantum phenomenon - using classical light, but at the expense of reduced interference visibility. It is therefore of interest to delineate what interference effects belong to the realm of classical world, and which require quantum states. Generalizing Hofmann's method of post-selection projection, we show that essentially any interference curve can be synthesized with high visibility with coherent state input. The method is based on the mathematical observation that any polynomial can be completely factored over the field of complex numbers. Hence, any two-mode, N-photon state can be written as a product of N single-photon, two-mode states, and the corresponding measurement projector can be experimentally implemented using beam splitters, phase-shifters, and N-photon coincidence measurements.
We discuss how to use coincidence detection to generate unusual, nonsinusoidal interference curves by using not a single detector, but several in coincidence. The method works for both strong (classical) and weak (on the few-photon level) light, although in the latter case the detection becomes probabilistic with low efficiency. Using the method, one can tailor the coincidence measurement setup to obtain essentially any interference pattern. We then use the method to experimentally demonstrate phase-difference state interference patterns in the few-photon regime that are highly nonsinusoidal. We also discuss optimal implementation of the method with regard to fluctuations and success probability, and we analyze the origin and magnitude of errors.
We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.
Classically, the spatial resolution of the image of an object is usually determined by the Rayleigh criterion. However, quantum properties of light have been exploited to form images with resolutions exceeding this criterion and beating the standard quantum limit, which allow high measurement sensitivity. We found that it is possible to super-resolve a distributed object made of two parts that are spatially separated but when superposed over each other form an object. A coincidence interference pattern of a nonlocal two-photon system with periodicity proportional to $\ensuremath{\lambda}/2$ was measured even when each photon, with wavelength of $\ensuremath{\lambda}$, has been scattered by different parts of an object, none of them being the object itself.
Spatial interference of quantum mechanical particles exhibits a fundamental feature of quantum mechanics. A two-mode entangled state of N particles known as N00N state can give rise to non-classical interference. We report the first experimental observation of a three-photon N00N state exhibiting Young's double-slit type spatial quantum interference. Compared to a single-photon state, the three-photon entangled state generates interference fringes that are three times denser. Moreover, its interference visibility of 0.49 ± 0.09 is well above the limit of 0.1 for spatial super-resolution of classical origin. The demonstration of spatial quantum interference by a N00N state composed of more than two photons represents an important step towards applying quantum entanglement to technologies such as lithography and imaging.