Neutron Optical Studies of Fundamental Phonemana in Quantum Mechnics

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1 EmQM Oct Neutron Optical Studies of Fundamental Phonemana in Quantum Mechnics Yuji HASEGAWA Atominsitut, TU-Wien, Vienna, AUSTRIA I. Introduction: neutron interferometer & polarimeter II. Uncertainty relation for error-disturbance V. Summary 1

2 The neutron Particle Feels four-forces Wave m = (1) x kg s = 1 2 = (18) x J/T = 887(2) s R = 0.7 fm = 12.0 (2.5) x10-4 fm3 u - d - d - quark structure CONNECTION de Broglie B H( h m. v Schrödinger r,t) i ( r,t) t & boundary conditions c h = (20) x m m.c For thermal neutrons = 2 Å, 2000 m/s, 20meV h B = 1.8 x m m.v 1 c 10-8 m 2k p v. t 10-2 m v (5) x 106 m d 0 2 (4) m... mass, s... spin,... magnetic moment, c... Compton wavelength, B decay lifetime, R... (magnetic) confine- debroglie wavelength, c... ment radius,... electric polarizability; all other -B coherence length, p... packet measured quantities like electric charge, magnetic two level system length, d... decay length, k. monopole and electric dipole moment are com- momentum width, t... chopper patible with zero B opening time, v... group velocity, phase. 2

3 Neutrons s in quantum mechanics Particle and wave properties p = mv = h/λ (L. De Broglie) Schroedinger equation ( r, t) i H( r, t) t (E. Schrödinger) Uncertainity Δx Δp h/4π M.C.Escher, 1938 (W. Heisenberg) 3

4 Neutron interferometry Neutrons m = kg s = 1 2 h = J/T Sample o II Phase Shifter H-Detector = 887 s R = 0.7 fm I O-Detector u d d quark structure I= I +e i o II 2 4

5 Neutron interferometer family 5

Two-particle vs. two-space entanglement 2-Particle Bell-State = 1 2 I II + I II I, II represent 2-Particles Quantum contextuality 2-Space Bell-State = 1 2 s I p + s II p s, p represent 2-Spaces, e.g., spin & path Violation of Bell-like inequality S' E' 1, 1 +E' 1, 2 E' 2, 1 +E' 2, 2 = 2.

6 Two-particle vs. two-space entanglement 2-Particle Bell-State = 1 2 I II + I II I, II represent 2-Particles Quantum contextuality 2-Space Bell-State = 1 2 s I p + s II p s, p represent 2-Spaces, e.g., spin & path Violation of Bell-like inequality S' E' 1, 1 +E' 1, 2 E' 2, 1 +E' 2, 2 = > 2 Hasegawa et al., Nature2003, NJP2011 Kochen-Specker-like contradiction 1 63% E ˆ ˆ ˆ ˆ xey E' X1Y2Y 1X Hasegawa et al., PRL2006/2009 Tri-partite entanglement (GHZ-state) Neutron I ( E0) i i i e II e e ( E0 r ) M Measured Hasegawa et al., PRA2010 6

7 W- and GHZ- states in a single neutron system W state: GHZ state: 7 D. Erdösi et al. New J. Phys. 15 (2013)

8 Cheshire Cat 1: paradoxical behavior of neutrons 1 2 -x I + +x II 1 -x I + II 2 T. Denkmayr et al., to be published 8

9 Cheshire Cat 2: neutron(cat neutron(cat) ) in upper path T=1 T=0.8 T=0.6 9

10 Cheshire Cat: spin(smile spin(smile) ) in lower path IH IO IH IO IH IO IO: with spin-analysis 10

11 Neutron polarimetry - Non-commutability of j, PRA (1999) - Bell-Test, PLA (2010) - Leggett-Test, NJP (2012) - GHZ-entanglement, NJP (1012) - Spin-rotation coupling 11

12 Neutron polarimetry: tri-partite entanglement 12 M=4: for perfect circumstances

13 Uncertainty relation: historical 1 In 1927 Heisenberg postulated an uncertainty principle: γ-ray thought experiment p1q1 h with q 1 (mean error) & p 1 (discontinuous change) in modern treatment for commuting observables: 13 ( Q) ( P) 2 :error of the first measurmen ( Q) : disturbanceon the second measurement (P)

14 Uncertainty relation: historical 2 Kennard considered the spread of a wave function ψ : standard deviations Robertson generalized the relation to arbitrary pairs of observables in any states ψ 1 ( A) ( B) A, B 2 dependent on the state but independent of the appartus 14 1 Is ( A) ( B) A, B generally valid? 2

15 Universally valid uncertainty relation by Ozawa First term: error of the first measuremt, disturbance on the second measurement 15 :error of the first measurmen ( A) : disturbanceon the second measurement ( B) :standarddeviations second and third terms: crosstalks between spreads of wavefunctions and error/disturbance M. Ozawa, Phys. Rev. A 67, (2003).

16 Error and disturbance for projective measurement 16

17 Experimental scheme Successively measurement of 2 noncommuting observables A and B Apparatus 1 measures O A, Apparatus 2 measures B 17

18 Theoretical predictions 1 For error and disturbance: For the standard deviations: 18

19 Theoretical predictions 2 -Heisenberg s relation - new uncertainty relation 19

20 Experimental setup 20

21 Experimental setup 21

22 Experimental data 22

23 Results: error-disturbance trade-off ( A) A O O A A O A ( A I) O ( A I) A A A 23

24 Results: new/old uncertainty relation New uncertainty principle :errorof the first measurmen ( A) : disturbanceon the second measurement ( B) :standard deviations Heisenberg product 24 J. Erhart et al., Nature Phys. 8, (2012)

25 Results 1: incident spin-state state ( s>= >) s 0, 0 25 G. Sulyok et al., PRA. 88, (2013)

26 Results 2: polar angle of O A [O A ] θ(o A ) = /12 θ(o A ) = /3 New sum is always above border! G. Sulyok et al., PRA. 88, (2013) 26

27 Results 3: polar angle of B [[ B] (B) = /6 (B) = /4 Asymmetry appears! G. Sulyok et al., PRA. 88, (2013) 27

28 Results 4: azimuthal angle of B [[ B] (B) = 2/3 (B) = 5/6 Sum touches the border! G. Sulyok et al., PRA. 88, (2013) 28

29 Publications by other groups ArXiv;

30 Concluding remarks Neutron interferometer and polarimeter are effective tools for investigations of quantum mechanics. Universally valid uncertainty-relation by Ozawa is experimentally tested. - Neutron s spin measurement confirmed the new error-disturbance uncertainty relation. - New sum is always above the limit! Heisenberg product is often below the limit! 30

31 Neutron Quantum Optics generation Yuji Hasegawa Sam Werner Helmut Racuh Gerald Badurek Jürgen Klepp Stephan Sponar Masanao Ozawa Michael Zawisky Katharina Durstberger Hartmut Lemmel Georg Sulyok Daniel Erdösi Claus 31 Schmitzer Hannes Bartosik Jacqueline Erhart Bülent Demirel Tobias Denkmayr Hermann Geppert

Beyond Heisenberg s uncertainty principle:

Theory Seminar@MPP, München 21. May 2013 Beyond Heisenberg s uncertainty principle: Error-disturbance uncertainty relation studied in neutron s successive spin measurements Yuji HASEGAWA Atominsitut, TU-Wien,