Wave-particle dualism and complementarity unraveled by a different mode

The precise knowledge of one of two complementary experimental outcomes prevents us from obtaining complete information about the other one. This formulation of Niels Bohr’s principle of complementarity when applied to the paradigm of wave-particle dualism—that is, to Young’s double-slit experiment—implies that the information about the slit through which a quantum particle has passed erases interference. In the present paper we report a double-slit experiment using two photons created by spontaneous parametric down-conversion where we observe interference in the signal photon despite the fact that we have located it in one of the slits due to its entanglement with the idler photon. This surprising aspect of complementarity comes to light by our special choice of the TEM01 pump mode. According to quantum field theory the signal photon is then in a coherent superposition of two distinct wave vectors giving rise to interference fringes analogous to two mechanical slits.

[1]  John C Howell,et al.  Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. , 2004, Physical review letters.

[2]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[3]  Mandel,et al.  Observation of nonclassical effects in the interference of two photons. , 1987, Physical review letters.

[4]  R. Dong,et al.  Triplet-like correlation symmetry of continuous variable entangled states , 2009, 0906.1163.

[5]  Yakir Aharonov,et al.  Time and the Quantum: Erasing the Past and Impacting the Future , 2005, Science.

[6]  M. Scully,et al.  Directed spontaneous emission from an extended ensemble of N atoms: timing is everything. , 2006, Physical review letters.

[7]  J. Wheeler,et al.  Quantum theory and measurement , 1983 .

[8]  M. Scully,et al.  Quantum eraser: A proposed photon correlation experiment concerning observation and , 1982 .

[9]  Shih,et al.  Delayed "Choice" quantum eraser , 1999, Physical review letters.

[10]  B. Englert,et al.  Fringe Visibility and Which-Way Information: An Inequality. , 1996, Physical review letters.

[11]  B. Englert,et al.  Quantum optical tests of complementarity , 1991, Nature.

[12]  A. Einstein.  On the Quantum Theory of Radiation , 1983 .

[13]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[14]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[15]  Aephraim M. Steinberg,et al.  Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer , 2011, Science.

[16]  Walther,et al.  Delayed-choice experiments in quantum interference. , 1987, Physical review. A, General physics.

[17]  Thomas Young,et al.  On the theory of light and colours , 1967 .

[18]  R. Glauber.  Quantum Theory of Optical Coherence , 2006 .

[19]  William K. Wootters,et al.  Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle , 1979 .

[20]  D. Walls,et al.  Path detection and the uncertainty principle , 1994, Nature.

[21]  J. Eisert,et al.  Two-dimensional characterization of spatially entangled photon pairs , 2009, 0905.4830.

[22]  Wineland,et al.  Young's interference experiment with light scattered from two atoms. , 1993, Physical review letters.

[23]  G. Rempe,et al.  Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer , 1998, Nature.

[24]  M. S. Zubairy,et al.  Relation between wave-particle duality and quantum uncertainty , 2012 .

[25]  Thomas Young,et al.  II. The Bakerian Lecture. On the theory of light and colours , 1802, Philosophical Transactions of the Royal Society of London.

[26]  N. Bohr.  The Quantum Postulate and the Recent Development of Atomic Theory , 1928, Nature.