Many-particle interference beyond many-boson and many-fermion statistics

Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many- particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to much more diverse behavior than expected from the boson-fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle

[1]  Spatial quantum noise interferometry in expanding ultracold atom clouds , 2005, Nature.

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  Andreas Renz,et al.  Observation of Hanbury Brown–Twiss anticorrelations for free electrons , 2002, Nature.

[4]  F. Laloë,et al.  Quantum Properties of a Single Beam Splitter , 2010, 1004.1731.

[5]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[6]  Marek Żukowski,et al.  Realizable higher-dimensional two-particle entanglements via multiport beam splitters , 1997 .

[7]  Comparison of the Hanbury Brown–Twiss effect for bosons and fermions , 2006, Nature.

[8]  Yoon-Ho Kim,et al.  Four-photon indistinguishability transition , 2010, 1009.4998.

[9]  Creation of macroscopic superposition states from arrays of Bose–Einstein condensates , 2006, quant-ph/0608242.

[10]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[11]  Wojciech Tadej,et al.  A Concise Guide to Complex Hadamard Matrices , 2006, Open Syst. Inf. Dyn..

[12]  Dieter Meschede,et al.  Quantum Walk in Position Space with Single Optically Trapped Atoms , 2009, Science.

[13]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[14]  M. Nock.  Single photons for quantum information processing , 2006 .

[15]  R. Loudon.  FERMION AND BOSON BEAM-SPLITTER STATISTICS , 1998 .

[16]  Markus Tiersch,et al.  Zero-transmission law for multiport beam splitters. , 2010, Physical review letters.

[17]  Holland,et al.  The fermionic hanbury brown and twiss experiment , 1999, Science.

[18]  Yi Li,et al.  Unconventional states of bosons with the synthetic spin–orbit coupling , 2013, 1301.5403.

[19]  C. Ross.  Found , 1869, The Dental register.

[20]  Lipo Wang,et al.  Observation of Four-Photon Interference with a Beam Splitter by Pulsed Parametric Down-Conversion , 1999 .

[21]  B. M. Fulk.  MATH , 1992 .

[22]  M. Greiner,et al.  Probing the Superfluid–to–Mott Insulator Transition at the Single-Atom Level , 2010, Science.

[23]  M. Girardeau,et al.  Permutation Symmetry of Many-Particle Wave Functions , 1965 .

[24]  Yuan Liang Lim,et al.  Generalized Hong–Ou–Mandel experiments with bosons and fermions , 2005, quant-ph/0505034.

[25]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[26]  S. Hodgman,et al.  Direct Measurement of Long-Range Third-Order Coherence in Bose-Einstein Condensates , 2011, Science.

[27]  I. Bloch,et al.  Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice , 2006, Nature.

[28]  Hanbury Brown–Twiss interferometry for fractional and integer Mott phases , 2006, cond-mat/0604154.

[29]  Immanuel Bloch,et al.  Single-spin addressing in an atomic Mott insulator , 2011, Nature.

[30]  Immanuel Bloch,et al.  Single-atom-resolved fluorescence imaging of an atomic Mott insulator , 2010, Nature.

[31]  G. Guo,et al.  Observation of a generalized bunching effect of six photons. , 2009, Optics letters.

[32]  Lipo Wang,et al.  PHOTON BUNCHING AND MULTIPHOTON INTERFERENCE IN PARAMETRIC DOWN-CONVERSION , 1999 .

[33]  Andreas Buchleitner,et al.  Counting statistics of many-particle quantum walks , 2010, 1009.5241.

[34]  R. H. Brown,et al.  Correlation between Photons in two Coherent Beams of Light , 1956, Nature.

[35]  Teich,et al.  Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics. , 1989, Physical review. A, General physics.

[36]  Ronald L. Graham,et al.  On the permanent of Schur's matrix , 1976, Journal of the Australian Mathematical Society.