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arXiv:0705.0047 · Physical Review A

High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light

Holger Friedrich Hofmann, Takafumi Ono

Published Sep 28, 2007• 105 citations
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Abstract

We show that the quantum interference between down-converted photon pairs and photons from coherent laser light can produce a maximally path entangled $N$-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the two-photon coherence of down-converted light into an almost optimal $N$-photon coherence.

DOI
10.1103/physreva.76.031806

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We show that the quantum interference between down-converted photon pairs and photons from coherent laser light can produce a maximally path entangled NNN-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the two-photon coherence of down-converted light into an almost optimal NNN-photon coherence.
It is shown that the addition of down-converted photon pairs to coherent laser light enhances the N -photon phase sensitivity due to the quantum interference between components of the same total photon number. Since most of the photons originate from the coherent laser light, this method of obtaining non-classical N -photon states is much more efficient than methods based entirely on parametrically down-converted photons. Specifically, it is possible to achieve an optimal phase sensitivity of about δϕ 2 = 1/ N 3/2 , equal to the geometric mean of the standard quantum limit and the Heisenberg limit, when the average number of down-converted photons contributing to the N -photon state approaches .
Normally, the signal and idler photons produced in the process of parametric down- conversion exhibit no second-order interference. However, in the presence of an external laser beam that follows the path of the signal photon and induces stimulated down-conversions, one would expect coherence to develop between the down-converted signal and idler beams. We have demonstrated the existence of this phenomenon in an experiment with two down-converters pumped by similar pump beams, in which two mutually coherent laser beams followed the paths of the two down-converted signal photons and induced coherence between the two down- converted idler beams. The induced coherence gives rise to observable interference effects, which are presented.
"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 discuss the situation in which idler beams from two parametric down-converter crystals are allowed to interfere. We show that, when two mutually coherent signal beams derived from a common laser are injected into the down-converters, the two idler beams can become mutually coherent also. Moreover, the resulting interference pattern can, in principle, have 100% visibility when the number of injected photons per unit down-converter bandwidth is large. This is just the condition for stimulated down-conversion to dominate over spontaneous down-conversion.
We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off detectors with low efficiencies and available resource states under current technology.
We study multiphoton quantum-interference effects at a beam splitter and its connection to the prospect of attaining interferometric phase-shift measurements with noise levels below the standard quantum limit. Specifically, we consider the mixing of the most classical states of light coherent states with the most nonclassical states of light number states at a 50 : 50 beam splitter. Multiphoton quantum-interference effects from mixing photon-number states of small photon numbers with coherent states of arbitrary amplitudes are dramatic even at the level of a single photon. For input vacuum and coherent states, the joint photon-number distribution after the beam splitter is unimodal, a product of Poisson distributions for each of the output modes but with the input of a single photon, the original distribution is symmetrically bifurcated into a bimodal distribution. With a two-photon-number state mixed with a coherent state, a trimodal distribution is obtained, etc. The obtained distributions are shown to be structured so as to be conducive for approaching Heisenberg-limited sensitivities in photon-number parity-based interferometry. We show that mixing a coherent state with even a single photon results in a significant reduction in noise over that of the shot-noise limit. Finally, based on the results of mixing coherent light with single photons, we consider the mixing coherent light with the squeezed vacuum and the squeezed one-photon states and find the latter yields higher sensitivity in phase-shift measurements for the same squeeze parameter owing to the absence of the vacuum state.