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Study of quantum spin correlations of relativistic electron pairs Project status Nov. 2015 Jacek Ciborowski Marta Włodarczyk, Michał Drągowski, Artem Poliszczuk (UW) Joachim Enders, Yuliya Fritsche (TU Darmstadt) Warszawa 20.XI.2015 Quantum spin correlations In this exp: e1,e2 – electrons under study a, b - directions of spin projections (+- ½) 4 combinations for e1 and e2: ++, --, +-, -+ Probabilities: P++ , P+- , P-+ , P- - (ΣP=1) Correlation function : C = P++ + P-- - P-+ - P-+ Historical perspective • Einstein Podolsky Rosen (EPR) paradox (1935): QM is not a complete local realistic theory • Bohm & Aharonov formulation involving spin correlations (1957) • Bell inequalities (1964) a local realistic theory must obey a class of inequalities • practical approach to Bell’s inequalities: counting aacoincidences to measure correlations The EPR paradox Boris Podolsky Nathan Rosen Albert Einstein (1896-1966) (1909-1995) (1979-1955) A. Afriat and F. Selleri, The Einstein, Podolsky and Rosen Paradox (Plenum Press, New York and London, 1999) Bohm’s version with the spin Two spin-1/2 fermions in a singlet state: E.g. if spin projection of 1 on Z axis is measured 1/2 spin projection of 2 must be -1/2 All projections should be elements of reality (QM predicts that only S2 and David Bohm (1917-1992) Sz can be determined) Hidden variables? ”Quantum Theory” (1951) Phys. Rev. 85(1952)166,180 The Bell inequalities J.S.Bell: Impossible to reconcile the concept of hidden variables with statistical predictions of QM If local realism quantum correlations measured on remote systems must fulfill a class of inequalities John S. Bell (1928-1990) J.S. Bell, Physics, 1 (1964) 195 Experiments with photons After 1982 (Aspect, Zeilinger, Gisin, others): • Singlet state pairs of entangled photons • Violation of the Bell’s inequalities established • No energy dependence of the correlation function • QM is nonlocal • ”Spooky action at a distance” Spukhafte Fernwirkung - letter from A.Einstein to M.Born, 3 March 1947) Experiments with low energy protons • Lamehi, Rachti, Mittig 1976 Saclay (France) • Hamieh et al. 2004 KVI (Holland) • Sakai et al. 2006 RIKEN (Japan) p(d,2He) n (270 MeV) Violation of the Bell’s inequalities in the sector of non-relativistic massive fermions confirmed What next? Theoretical grounds: spin correlations of massive relativistic particles considered M. Czachor (UG) Phys.Rev. A 55 (1997) 72 J. Rembieliński (UŁ) Phys. Rev. A 66 (2002) 052114 + co-workers Phys. Rev. A 68 (2003) 042107 For various Phys. Rev. A 72 (2005) 012103 two-particle Phys. Rev. A 74 (2006) 042103 pure states Phys. Rev. A 77 (2008) 012103 (singlet, triplet) Phys. Rev. A 79 (2009) 014102 Example: results for a singlet Rembieliński et al. Relativistic correction depends on outgoing momenta How to verify? 1. Find a suitable two body relativistic process and measure spin correlations EXPERIMENT 2. Calculate spin correlations for this process THEORY 3. Compare theoretical predictions and the results of measurements Concept of the measurement: a fruitful compromise • Practical choice: e-e- e-e- -- polarised Møller scattering (3 MeV beam) • Density matrix ρ - according to beam polarisation • Unpolarised target • Spin projection measurement using Mott polarimetry ( a k 1 b k 2 ) • Compromise: mixture of singlet and triplet states • Fruitful : new effects in the correlation function Not a Bell test experiment Calculation of correlations Once the spin operator assumed, the correlation function for a and b can be calculated: ˆ ˆ C ( a , b ) Tr [ a S b S ] - spin - momentum density matrix ˆ S - spin operator Formulae more complicated for probabilities (not shown);calculations completed, full understanding in progress P. Caban, J. Rembieliński, M. Włodarczyk, Phys. Rev. A 88 (2013) 032116 S - Newton Wigner spin operator J. Rembielinski et al. Phys. Rev.A 88 (2013) 022119 Ann. Phys. 330 (2013) 263 Identical results of calculations obtained in the QFT approach P. Caban, J. Rembieliński, Einstein-Podolsky-Rosen correlations of Dirac particles: Quantum field theory approach, Phys. Rev. A, 74 (2006) 042103 Also: P. Caban, J. Rembieliński, Lorentz-covariant reduced spin density matrix and Einstein-Podolsky-Rosen-Bohm correlations, Phys. Rev. A, 72 (2005) 012103 Møller-Mott: description of variables The Mott condition: a k1 b k2 The observable: spin projection Prediction for the correlation function Incident polarised beam, energy T, unpolarised target, sharp momentum states, directions a and b in the scatt. plane, equal final state momenta C independent of beam polarisation Two extrema No radiative corrections included (≈1%) Prediction for probabilities Beam 3 MeV α – angle between vec.a and scatt. plane, equal final state momenta, vec. b in scatt.plane, pol.vec. perpendicular to scatt.plane (z) 0.35 Beam polarisation 3 extreme configurations: (T1) Transverse perpendicular to the scattering plane (T2) Transverse in the scattering plane ( L) Longitudinal Probabilities P++ , P+- , P-+ , P–- depend on beam polarisation while C does not Focus on probablilities Probability functions P++ , P-- , P-+ , P-+ = functions of ( Tbeam, θscatt, spin projection directions a and b , beam polarisation vector ) Max effect for symmetric scattering (equal final state momenta) a,b,c – as in header, pol= 0.35 Experimental Method: Mott scattering d d A=S(θ) Pn [1 S( )Pnˆ] d d A is L-R asymmetry S(θ) – Sherman function (a.k.a. analysing power) (need large values of S; 0<S<1 ) - Sherman function e (Au) Backward e- scattering to access significant sensitivity to electron polarisation (significant values of S) Low energies - more multiple Coulomb scattering in detectors and target (btw:a typical electron polarimeter) • High beam intensity • Narrow beam • 2 arms • Small apertures • High counting rates • High precision • No tracking The principle of measurement Møller scattering on atomic electrons, Mott polarimetry (makes use of L-R asymmetry)a and b For two electrons: count coincidences L1L2 R1R2 L1R2 R1L2 ( PLL, PRR, PLR, PRL) Define directions by selecting regions of counting Determining probabilities C(a,b) = P++ + P-- - P+- - P-+ Beam, targets • S-DALINAC TU Darmstadt • 3 MeV extraction (1.5 MeV symmetric Møller) • T & L beam polarization (35--85%) • Møller target – unpolarized 20 µm Be, scatt. on atomic electrons, low A • µA currents • Au 10 µm Mott target • O(10) days beam time (must) **The double polarimeter** Backward Mott scattering Be - Møller tgt Au - Mott tgt Forward beam absorber H: Σ energy = Tbeam No tracking Technical data • Length approx. 60 cm main pipe ϕ80 mm • 25 µm ϕ30 mm Be target (Møller scattering) • 2 legs at 26.75 degrees (symmetric Møller) • ±2 degrees aperture for Møller • 2 arms at each leg at 120 degrees (Mott) • 10 µm Au Mott target • ±8 degrees aperture for Mott • Beam dump, Møller dump graphite • 4 scintillation counters at each arm Basic difficulties • Divergent flux of secondary Møller electrons • Low flux intensity in each polarimeter • Large leg and arm aperture needed • Averaging over Møller and Mott angles (energy) i.e. over Sherman function • Low rate of coincidences, need stat. 105 • Short available beam time (10 days) • Beam 1014 electrons/s (µA) Prob. per beam e: Møller x (Mott) 2 10-7 x (10-5 ) 2 approx 10-16 Rate <0.01 events /s, 102 events/day Simulations • Double polarimeter – Geant4 Marta – Mathematica – cross checks J.C. • Depolarisation – PEBSI – Michał, Guenter Weber GSI/Jena (+our contribution); cross check Mathematica: Marta • Beam monitoring – Geant4 Marta, Artem • Derivation of results – Mathematica J.C. • Scintillation counters – Fluka + Photrack (light collection) (N. Ghal-Eh,Iran) Geant4 Depolarisation,MCS • Beam is prepared at A • Møller scattering at IP • Møller electrons leaving target at B1, B2 • Distance A-IP - beam depolarisation • Distances IP-B – outgoing elctron depolarisation • Effects at IP: • Smeared kinematics (known) • Smaller polarisation value of the beam (under study) • Smeared orientation of the polarisation vector (idem) • Effects on the Møller electrons: • Change in state between IP to B (idem) Angles between initial and final vector: θ* - polarisation; θ – momentum; in 25 µm Be target Beam monitoring • Monitor beam condition in time • Determine beam position at Be target • Beam direction • Shape of the beam spot Use data from 4 counters viewing the beam spot – backward Mott scattering of the beam Under study Status: experiment • Geant4 simulations - advanced • Technical design of the double polarimeter – in progress • Construction – spring 2016 • Scintillation counters – tested • Financial support from Poland and Germany (DAAD, NCN, UW, TUD) • Electronics – recuperated at TUD • First physics run – late 2016 Status: theory Ongoing work (Łódź, Warsaw): • Determination of magnitude of entanglement • Analysis of singlet and triplet contribution • Results for unconstrained directions a and b (if other polarimetry methods, e.g. Møller) • Results for a polarised beam on a polarised arget (up to 8% for Fe) • Colliding polarised beams Expected first results • Data analysis in 2017 • First measurement at one beam polarisation and one detector setting (directions a,b) • Total uncertainty for probabilities of order 20% e.g. P=0.3 ±0.06 at 3 MeV beam • Understanding the detector • Comparison with theoretical predictions • Interpretation in terms of singlet/triplet contribution, magnitude of entanglement, regarding the spin observables in rQM Experimental prospects 1. Energy scan, including low
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