Color Centers in Diamond as Practical Single-Photon Source to Illustrate Quantum Complementarity
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0956-J02-01
Color Centers in Diamond as Practical Single-Photon Source to Illustrate Quantum Complementarity Vincent Jacques, Steven Regnnie, Dominique Chauvat, and Jean-François Roch LPQM, ENS Cachan, 61 avenue du Président Wilson, Cachan, 94235, France
ABSTRACT A recent experiment performed by S. S. Afshar [reviewed in M. Chown, New Scientist 183, 30 (2004)] has been interpreted as a possible violation of the complementarity principle of quantum mechanics. Starting from a single-photon wavefront-splitting interference experiment, we propose a new scheme for Afshar’s experiment, and we show that Afshar’s interpretation is incorrect. Furthermore, this design is well suited to illustrate the complementarity inequality in the interesting intermediate regimes with partial fringe visibility and partial which-path information. INTRODUCTION Complementarity is at the heart of the foundations of quantum mechanics. It means that every quantum mechanical system has at least two properties which cannot be observed simultaneously. When Bohr first reviewed this concept in 1927 [1], he used the example of the wave and particle-like behaviors of a quantum object, which are “mutually exclusive” in a single experiment. Since then, complementarity has often been superficially identified to the waveparticle duality of matter, but this concept is actually more general. This dual behavior is usually illustrated by means of interferometers. The wave-like property is evidenced by the interference visibility V whereas the particle-like behavior can be documented by recording the path followed by each particle inside the interferometer. Bohr's complementarity states that the visibility V and the which-path information (WPI) are two complementary observables. Then, with full knowledge of the WPI no interference can be observed, and conversely, in absence of WPI, an interference with perfect visibility is measured. This has been clearly confirmed by experiments performed with a wide range of quantum objects like electrons [2], neutrons [3], atoms [4], molecules [5], and photons [6,7]. The usual explanation refers to Heisenberg's position-momentum uncertainty. However, it has been shown that under certain circumstances, this uncertainty relation cannot explain the loss of interference [8,9] and one should refer to the entranglement between the internal state of the quantum object and the path followed by the particle in the interferometer. Interesting situations are the intermediate regimes with partial fringe visibility and partial WPI. An expression which quantifies wave-particle duality in these situations is given by the inequality [10-12] : V 2 + P2 ≤ 1 (1) where P is the predictability, which is a quantitative measurement of the WPI defined as the difference between the particle probability to follow path 1 of the interferometer and the one to follow path 2 [12]. The complementarity inequality has already been tested with success using
atoms [13,14], nuclear spins [15] and light emitted by an attenuated laser [16,17]. Note that in th
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