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Fortschritte der Physik

Increasing the Visibility of Multiphoton Entanglement

Matteo G. A. Paris

Published May 1, 2000• 6 citations
Publisher

Abstract

The entanglement between the two beams exiting a Mach-Zehnder interferometer fed two squeezed states involves many photons. We evaluate the degree of this multiphoton entanglement in terms of the excess entropy of the pure state at the output. A novel kind of fourth-order correlation function based on homodyne detection is suggested to reveal entanglement. Apart from the very low signals regime homodyne-like detection shows a higher fringes visibility than the measurement of the coincidence counting rate.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<511::aid-prop511>3.0.co;2-7

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The entanglement between the two beams exiting a Mach-Zehnder interferometer fed two squeezed states involves many photons. We evaluate the degree of this multiphoton entanglement in terms of the excess entropy of the pure state at the output. A novel kind of fourth-order correlation function based on homodyne detection is suggested to reveal entanglement. Apart from the very low signals regime homodyne-like detection shows a higher fringes visibility than the measurement of the coincidence counting rate.
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are functions of the internal phase shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuums at the input lead to maximum entangled state at the output. The fringe visibilities resulting from measuring the coincidence counting rate or the squared difference photocurrent are evaluated and compared to each other. Homodynelike detection turns out to be preferable in almost all situations, with the exception of the very-low-signal regime.
A new method for detecting a squeezed state by coincidence counting or cross correlation of the signals from two photodetectors is proposed. The two light beams falling on the two detectors are obtained from the two outputs of a homodyne beam splitter, whose inputs are the squeezed light and the local oscillator beam. With fast detectors the squeezing gives rise to excess photon coincidence counts. When a spectral analysis of the photoelectric currents is made, squeezing shows up as a positive cross correlation between the two signals, whereas unsqueezed light always produces negative correlations. Although the technique does not always cause the effects of local oscillator fluctuations to cancel out, as does the method of Yuen and Chan [Opt. Lett. B8R, 177 (1983)], they cancel in special cases, and the method has the advantage of being largely unaffected by detector after-pulsing. A simple combination of autocorrelation and cross-correlation measurements yields the degree of squeezing.
A two-photon interference experiment is presented in which an entangled pair of photons generated from a parametric down-conversion was incident on two input ports of a Mach-Zehnder interferometer. The experiment was carried out using two photon coincidence detection with two detectors at the two output ports of the interferometer. The measured coincidence counts exhibit an interference effect with visibility of 0.75 at simultaneous inputs and 0.38 at inputs with different arrival times according to the degree of photon number entanglement.
We present a method of directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique, and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light, and parity detection may be practically implemented for an arbitrary photon flux. Specifically we investigate a two-mode, squeezed-light, Mach-Zehnder interferometer and show how the parity of the output state may be obtained. We also show that the detection may be described independent of the parity operator, and that this "parity-by-proxy" measurement has the same signal as traditional parity.
Pairs of 826.8-nm correlated photons, generated by parametrically down-converting 413.4-nm krypton-ion laser light, are directed into a single Mach-Zehnder interferometer such that each photon of the pair enters a different input port. The rate of coincidence at the two output ports displays oscillations (as the path-length difference is swept) with a spatial period equal to the 413-nm wavelength of the pump photons, and with a visibility of 62% when the path-length difference exceeds the coherence length of the individual photon beams. This unequivocally demonstrates the nonclassical and entangled nature of the two-photon state.