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Abstract
We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quite tractable and it is possible to produce entangled states involving a large number of photons.
Highlights
A spontaneous parametric down-conversion (PDC) source[29,30] is capable of emitting pairs of strongly time-correlated photons in two spatial modes
N are input ports and each port is supplied with an arbitrary single-photon state, while bi, i = 1, 2, n are the corresponding outputs, respectively. θ and 2θ represent phase shifts in the coherent probe beam α induced by Kerr interaction between photons
Creation of multiphoton entangled states with linear optics and weak nonlinearities Let ai, i = 1, 2, n represent input ports with respective spatial modes, namely signal modes, and α is a coherent beam in probe mode
Summary
Before describing the proposed scheme, let us first give a brief introduction of the Kerr nonlinearities. Θ and 2θ represent phase shifts in the coherent probe beam α induced by Kerr interaction between photons. Creation of multiphoton entangled states with linear optics and weak nonlinearities Let ai, i = 1, 2, , n represent input ports with respective spatial modes, namely signal modes, and α is a coherent beam in probe mode. When the signal photons travel to the PBSs, they will be individually split into two spatial modes and interact with the nonlinear media so that pairs of phase shifts θ and 2θ are induced on the coherent probe beam, respectively. A straightforward calculation shows that φm(x) = α sin(mθ)[x − 2α cos(mθ)]/m mod 2π After these feed-forward phase shifts have been implemented and the signal photons pass through the PBSs, one can obtain the desired states as follows. More generally, we may project out a group of multiphoton entangled states involving generalized Dicke states
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