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Physical Review A

Generation of three-photon entangled state by quantum interference between a coherent state and parametric down-conversion

Farbod Shafiei, P. Srinivasan, Z. Y. Ou

Published Oct 4, 2004• 34 citations
Publisher

Abstract

Three-photon entangled states such as a Greenberger-Horne-Zeilinger state can be produced by mixing a weak coherent state with parametric down-conversion. Quantum interference between the two states is responsible for the cancellation of unwanted photon states. Two schemes of interference are considered and both are shown to produce the entangled state.

DOI
10.1103/physreva.70.043803

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Three-photon entangled states such as a Greenberger-Horne-Zeilinger state can be produced by mixing a weak coherent state with parametric down-conversion. Quantum interference between the two states is responsible for the cancellation of unwanted photon states. Two schemes of interference are considered and both are shown to produce the entangled state.
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.
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We propose two interesting methods of generating the four-photon WWW state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon WWW state, the three-photon Greenberger-Horne-Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general nnn-photon WWW state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.
We experimentally demonstrated a three-photon interference on a beam splitter between a weak coherent state and a two-photon state produced by a spontaneous parametric down conversion. It indicates that a combined three-photon probability amplitude, which is formed by the two-photon state and one-photon from the coherent state, can be used to interfere with another three-photon probability amplitude from the coherent state. The observed three-photon coincidence rate showed that the interference depended on not only the relative phase between the two interference field but also the amplitude of the weak coherent state. This may introduce another free parameter for preparing quantum state, such as high N00N state, with quantum interference.
A number of multiphoton interference schemes involving independent fields from parametric down-conversion are analyzed. They include fourth-order (two-photon) interference between two fields from two independent parametric down-conversion processes, interference with two independent single photon Fock states (produced by gated parametric down-conversion), and quantum state teleportation and entanglement swapping. It is shown that the visibility in these interference experiments is related to a quantity that is responsible for the photon bunching effect in one of the fields (signal or idler) from the parametric down-conversion process. Besides the two-photon interference schemes, a four-photon interference scheme is discussed where we consider four-photon partition at a beamsplitter. It is found that probability distribution of the partition is dramatically changed by four-photon interference of six paths and the four-photon effect also depends on the same quantity responsible for photon bunching. We will discuss the difference between two-photon interference and four-photon interference.
We report a new method for generation of polarization-entangled photon pairs in maximally entangled polarization states. Our approach is based on quantum interference between two polarization states which are non-orthogonal. We present necessary and sufficient conditions for generation the photon pair in a maximally entangled state. The effect of dependence of entanglement on the phase between the interfering states of photons is investigated theoretically and demonstrated experimentally with quantum states produced via spontaneous parametric down-conversion in the double-crystal scheme.