Macrorealism, the freedom-of-choice loophole, and an EPR-type BEC experiment Faculty of Physics, University of Vienna, Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences Max Planck Institute for Quantum Optics Garching, July 12 th 2011 Johannes Kofler

With photons, electrons, neutrons, molecules etc. With cats? |cat left  + |cat right  ? Double slit experiment When and how do physical systems stop to behave quantum mechanically and begin to behave classically?

Two schools: -Decoherence uncontrollable interaction with environment; within quantum physics -Objective collapse models (GRW, Penrose, etc.) forcing superpositions to decay; altering quantum physics Alternative answer: -Coarse-grained measurements measurement resolution is limited; within quantum physics Macroscopic superpositions A. Peres, Quantum Theory: Concepts and Methods, Kluver (2002)

Leggett and Garg (1985): Macrorealism per se “A macroscopic object, which has available to it two or more macroscopically distinct states, is at any given time in a definite one of those states.” Non-invasive measurability “It is possible in principle to determine which of these states the system is in without any effect on the state itself or on the subsequent system dynamics.” t = 0 t t1t1 t2t2 Q(t1)Q(t1)Q(t2)Q(t2) Macrorealism

Dichotomic quantity: Temporal correlations t = 0 t t1t1 t2t2 t3t3 t4t4 tt Violation  macrorealism per se or/and non-invasive measurability failes All macrorealistic theories fulfill the Leggett-Garg inequality The Leggett-Garg inequality

½ Rotating spin ½ particle (eg. electron) Rotating classical spin vector (e.g. torque) K > 2: Violation of the Leggett-Garg inequality K  2: Classical time evolution, no violation classical limit Precession around axis with frequency  (through manetic field or external force) Measurement along orthogonal axis Violation of the inequality

Initial state State at later time t Measurement Survival probability Leggett-Garg inequality t t 1 = 0t2t2 t3t3 tt tt Choose  can be violated for any  E ??! classical limit Violation for arbitrary Hamiltonians J. Kofler and Č. Brukner, PRL 101, (2008)

Coarse-grained measurements Model system:Spin j macroscopic: j ~ Arbitrary state: -Assume measurement resolution is much weaker than the intrinsic uncertainty such that neighbouring outcomes are bunched together into “slots” m. m = –jm = +j m = -Measure J z, outcomes: m = – j, –j+1,..., +j (2j+1 levels) Why no violation in everyday life?

Fuzzy measurement classical limit Sharp measurement of spin z-component Violation of Leggett-Garg inequality for arbitrarily large spins j Classical physics of a rotating classical spin vector Q = +1 Q = –1 –j–j +j –j–j Coarse-grained measurement J. Kofler and Č. Brukner, PRL 99, (2007) Example: Rotation of spin j

Neighbouring coarse-graining (many slots) Sharp parity measurement (two slots) Violation of Leggett-Garg inequality Classical physics Slot 1 (odd)Slot 2 (even) Note: Coarse-graining  Coarse-graining

To see the quantumness of a spin j, you need to resolve j 1/2 levels Superposition vs. mixture

Hamiltonian: But the time evolution of this mixture cannot be understood classically: Produces oscillating Schrödinger cat state: Under fuzzy measurements it appears as a statistical mixture at every instance of time: time Non-classical Hamiltonians J. Kofler and Č. Brukner, PRL 101, (2008)

Oscillating Schrödinger cat “non-classical” rotation in Hilbert space Rotation in real space “classical” Complexity is estimated by number of sequential local operations and two-qubit manipulations Simulate a small time interval  t O(N) sequential steps 1 single computation step all N rotations can be done simultaneously Non-classical Hamiltonians are complex

Exponential decay of survival probability -Leggett-Garg inequality is fulfilled (despite the non-classical Hamiltonian) -However: Decoherence cannot account for a continuous spatiotemporal description of the spin system in terms of classical laws of motion. -Classical physics: differential equations for observable quantitites (real space) -Quantum mechanics: differential equation for state vector (Hilbert space) Monitoring by an environment

Relation quantum-classical

Quantum mechanics and realism Bohr and Einstein, Kopenhagen interpretation (Bohr, Heisenberg) 1932von Neumann’s (wrong) proof of non-possibility of hidden variables 1935Einstein-Podolsky-Rosen paradox 1952De Broglie-Bohm (nonlocal) hidden variable theory 1964Bell’s theorem on local hidden variables 1972First successful Bell test (Freedman & Clauser) A brief history of hidden variables

Realism: [J. F. Clauser & A. Shimony, Rep. Prog. Phys. 41, 1881 (1978)] Hidden variables λ determine outcome probabilities: p(A,B|a,b,λ) Realism: [J. F. Clauser & A. Shimony, Rep. Prog. Phys. 41, 1881 (1978)] Hidden variables λ determine outcome probabilities: p(A,B|a,b,λ) Locality: (OI)Outcome Independence:p(A|a,b,B,λ) = p(A|a,b,λ)& vice versa (SI)Setting Independence:p(A|a,b,λ) = p(A|a,λ) & vice versa Freedom of Choice:(FC) p(a,b|λ) = p(a,b)  p(λ|a,b) = p(λ) [J. S. Bell, Physics 1, 195 (1964)] [J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)] λ Bell’s assumptions

Realism + Locality + Freedom of Choice  Bell‘s Inequality CHSH form: |E(a 1,b 2 ) + E(a 2,b 1 ) + E(a 2,b 1 ) - E(a 2,b 2 )|  2 The original Bell paper (1964) implicitly assumes freedom of choice: A(a,b,B,λ)A(a,b,B,λ) locality (outcome and setting independence)  (λ|a,b) A(a,λ) B(b,λ) –  (λ|a,c) A(a,λ) B(c,λ) freedom of choice explicitly: implicitly: Bell’s theorem

Locality loophole: There may be a communication from the setting or outcome on one side to the outcome on the other side Closed by Aspect et al., PRL 49, 1804 (1982) & Weihs et al., PRL 81, 5039 (1998) Fair-sampling loophole: The measured events stem from an unrepresentative subensemble Closed by Rowe et al., Nature 409, 791 (2001) Freedom-of-choice loophole: The setting choices may be correlated with the hidden variables Closed by Scheidl et al., PNAS 107, (2010) [this talk] Loopholes

144 km Geography

144 km B TenerifeLa Palma A x t E a b Locality: A is space-like separated from B (OI) and b (SI) B is space-like separated from A (OI) and a (SI) Freedom of choice: a and b are random and space-like separated from E Space-time diagram

144 km Source 6 km fiber channel Alice 144 km free-space link Tenerife NOT QRNG 1.2 km RF link OGS La Palma 144 km free-space link Bob QRNG Geographic details

Polarizer settings a, b0°, 22.5°0, 67.5°45°, 22.5°45°, 67.5° Correlation E(a,b)0.62 ± ± ± 0.01–0.57 ± 0.01 Obtained Bell value S exp 2.37 ± 0.02 Coincidence rate detected: 8 Hz Measurement time: 2400 s Number of total detected coincidences: Experimental results T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N. Langford, T. Jennewein, and A. Zeilinger, PNAS 107, (2010)

Important remarks In a fully deterministic world, neither the locality nor the freedom-of- choice loophole can be closed: Setting choices would be predetermined and could not be space-like separated from the outcome at the other side (locality) or the particle pair emission (freedom-of-choice). Thus, we need to assume stochastic local realism: There, setting choices can be created randomly at specific points in space-time. We have to consistently argue within local realism: The QRNG is the best candidate for producing stochastic settings. Practical importance: freedom of choice can be seen as a resource for device-independent cryptography and randomness generation/amplification

Rupert UrsinSven RamelowXiao-Song Ma Thomas Herbst Lothar RatschbacherAlessandro FedrizziNathan Langford Thomas JenneweinAnton Zeilinger Thomas Scheidl Acknowledgments

Colliding BECs A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, PRL 99, (2007) Cigar-shaped BEC of metastable He 4 (high internal energy) Three laser beams kick the atoms: Recoil velocity: Two freely falling species are produced and undergo s-wave scattering Momentum-entangled particle pairs are produced, lying on a shell in velocity space:

Proposal: The double double slit If the condensate is too small, there is a product of one-particle interference patterns: If the condensate is sufficiently large, one obtains two-particle interference (conditional interference fringes):

Experimental conditions (I)Sufficiently large source size S x to achieve well defined momentum correlation (  p x  S x –1 ) and wash out the single-particle interference pattern: (II)Sufficiently small source to not wash out the two-particle interference pattern: (III)Resolution of interference fringes: (IV)Ability to identify pairs, i.e. coincidences: In preparation (2011)

Two-particle interference In preparation (2011)

Michael KellerMaximilian EbnerMateusz Kotyrba Mandip SinghAnton Zeilinger Acknowledgments

Coarse-grained measurements are a way to understand the quantum-to-classical transition (complementary to decoherence) We simultaneously closed the locality and the freedom-of-choice loophole; a loophole-free Bell test is still missing Summary Proposal: A BEC double double slit experiment can show EPR-type entanglement of massive particles

Thank you for your attention!

Appendix

Coarse-grained measurements: any quantum state allows a classical description This is macrorealism per se. Probability for outcome m can be computed from an ensemble of classical spins with positive probability distribution: Macrorealism per se

Experimental setup