In this paper, photonic entanglement and interference are described and analyzed with the language of quantum information process. Correspondingly, a photon state involving several degrees of freedom is represented in a new expression based on the pe
rmutation symmetry of bosons. In this expression, each degree of freedom of a single photon is regarded as a qubit and operations on photons as qubit gates. The two-photon Hong-Ou-Mandel interference is well interpreted with it. Moreover, the analysis reveals the entanglement between different degrees of freedom in a four-photon state from parametric down conversion, even if there is no entanglement between them in the two-photon state. The entanglement will decrease the state purity and photon interference visibility in the experiments on a four-photon polarization state.
We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys. Rev. Lett. {bf
71}, 1355 (1993)] but the phase information is extracted by a quantum state projection measurement. The phase precision is about $1.4/N$ for large photon number $N$, which approaches the Heisenberg limit of 1/N. Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of $0.291pm 0.001$ beating the standard quantum limit of $1/sqrt{N} = 1/2$ for four photons.
By using an asymmetric beam splitter, we observe the generalized Hong-Ou-Mandel effects for three and four photons, respectively. Furthermore, we can use this generalized Hong-Ou-Mandel interferometer to characterize temporal distinguishability.
Stimulated emission of two photons is observed experimentally in the parametric amplification process and is compared to a three-photon interference scheme. We find that the underlying physics of stimulated emission is simply the constructive interfe
rence due to photon indistinguishability. So the observed signal enhancement upon the input of photons is a result of multi-photon interference of the input photons and the otherwise spontaneously emitted photon from the amplifier.
Two experiments of four-photon interference are performed with two pairs of photons from parametric down-conversion with the help of asymmetric beam splitters. The first experiment is a generalization of the Hong-Ou-Mandel interference effect to two
pairs of photons while the second one utilizes this effect to demonstrate a four-photon de Broglie wavelength of $lambda/4$ by projection measurement.
Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by W
ang and Kobayashi (Phys. Rev. A {bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.
Multi-photon interference is at the heart of the recently proposed linear optical quantum computing scheme and plays an essential role in many protocols in quantum information. Indistinguishability is what leads to the effect of quantum interference.
Optical interferometers such as Michaelson interferometer provide a measure for second-order coherence at one-photon level and Hong-Ou-Mandel interferometer was widely employed to describe two-photon entanglement and indistinguishability. However, there is not an effective way for a system of more than two photons. Recently, a new interferometric scheme was proposed to quantify the degree of multi-photon distinguishability. Here we report an experiment to implement the scheme for three-photon case. We are able to generate three photons with different degrees of temporal distinguishability and demonstrate how to characterize them by the visibility of three-photon interference. This method of quantitative description of multi-photon indistinguishability will have practical implications in the implementation of quantum information protocols.
A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state (the {it NOON}-state). The result of this projection measurement shows a typical interference fringe with an $N$-photon d
e Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to arbitrary $N$-photon states projection measurement can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.
