Timeline: Bohm (1951) EPR (1935) CHSH (1969) Bell (1964) Theory. Freedman Clauser (1972) Aspect (1982) Weihs (1998) Weinland (2001) Zeilinger (2010)

Transcription

1 1.EPR paradox 2.Bohm s version of EPR with spin ½ particles 3.Entangled states and production 4.Derivation of CHSH inequality - S parameter for mixed and entangled state 5. Loopholes 6.Experiments confirming Quantum Mechanics Timeline: Theory EPR (1935) Bohm (1951) Bell (1964) CHSH (1969) Experiment Freedman Clauser (1972) Aspect (1982) Weihs (1998) Weinland (2001) Zeilinger (2010)

2 EPR The quest for completeness In an article (1935), Einstein- Podolsky-Rosen questioned the completeness of quantum mechanics. Bohm s EPR: System of 2 spatially separated entangled spin ½ particles

3 P a,, X a P b,, X b If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. Not so in Quantum Mechanics. Cannot always measure two observables simultaneously. Conlusion of EPR: Quantum Mechanics is incomplete.

4

5 Entanglement The characteristic trait of QM, the one that enforces its entire departure from the classical line of thought The best possible knowledge of the whole does not include the best possible knowledge of its part Schrödinger Naturwissenschaften 23, 807 (1935)

6 Hidden variables? Postulating hidden variables would restore realism and locality

7 Realism The measurement results are determined by properties the particles carry prior to and independent of observation. World passive observer

8 Locality The results obtained at one location are independent of any actions performed at space-like separation. J.S. Bell, On the Einstein-Podolsky- Rosen Paradox, Physics1, pp , 1964

9 EPR-Bohm Singlet state Ψ = 1 2 ( a b a b ) Combined system: spin 0 Decay into 2 particles of spin ½ Particles cease to interact after decay, total spin of system remains 0. predicts opposite results for the measurement of the same components of the spin of two particles

10 Since particles no longer interact, the properties of one particle appear to be affected by operations on the other, influence that propagates faster than c.

11 Bertlmann s socks! EPR discussion does not impress if one considers classical systems correlated in some ways Many examples of classical correlations in everyday life

12 Bertlmann always wears socks of different colours One cannot predict with certainty which colours will show up on a particular day. Bertlmann s socks! Observation of one sock gives information on the other J.S. Bell (1981)

13 Such correlations are easy to accept: There are REAL ATTRIBUTES (e.g. colour) in advance, which predetermine the outcome of a particular observation.. No communication between the socks!

14 Entanglement of pure states Composite quantum system ψ system = ψ i, j Separable state α system Entangled state ij i = A j B ψ A i j 2 a 1, i, j = ψ B ψ ψ 2 A H A 2 B H B ψ system ψ A ψ B

15 Experimental Bell Tests Clauser PRL 36, 1223 (1976) Fry & Thompson PRL 37, 465 (1976) Aspect et al., PRL 47, 460(1981) Perrie et al., PRL 54, 1790 (1985) PRL 28, 938 (1972) Approx. 0.1 events per second (1 nm bandwidth)

16 Possible Loopholes Detection-efficiency loophole (η > 85 %) Einstein-Locality loophole Random-settings loophole (free-variables/free-will criterion)

17 Closing loopholes I Locality loophole [Aspect et al., PRL 49, 1804 (1982)]

18 Closing loopholes II Locality and randomness loophole [Weihs et al., PRL 81, 5039 (1998)] Separation 400m, so that individual measurements are faster than 1.3 µs (space-like seperated) Actually done in 100ns Fast modulators switching Fed by physical random number generator (500 MHz) Violation Bell S=2.73±0.02

19 Closing loopholes III Detection loophole [Rowe et al., Nature 409, 791 (2001)] 9 Be + -Ions Nature 409, 774 (2001)

20 Closing loopholes IV Free will loophole [Scheidl et al., PNAS, (2010)]

21 Closing loopholes IV Space like separation of settings and creation of entanglement

22 Space Quest Objectives of an accommodation of a QCT: One clear vision of the science community is to establish a worldwide network for quantum communication - a task that can only be realized by tackling the additional challenge of bringing concepts and technologies of quantum physics to space. First steps: Accommodation of a quantum communication optical transmitter module on a satellite. Distribution of - faint laser pulses - single photons - entangled photon pairs Space-QUEST Vision: Quantum satellite network 22

23 Spontaneous Parametric Down Conversion (SPDC) with nonlinear crystals P i (1) (2) (3) = χij E j + χijk E jek + χijkl E jek El +K Non-linearity Non-linear optical χ (2) process (BBO, LNB, KTP) Spontaneous decay of a pump photon via momentum- and energy-conservation Strong time-correlation of emerging pair (depends on pump bandwidth and coherence length of downconverted photons)

24 Phase matching condition Simply conservation of energy and momentum! r r r ω + pump = ωsignal ωidler kpump = ksignal + kidler Not so simple in practice: crystals are birefringent media (BBO, LNB, KTP, ) Refractive index depends on: frequency, polarisation and propagation direction k r r ω = n( ω, p, s) c Phase matching is only fullfilled for a certain direction and polarisation at given frequency

25 Entanglement Sources Type II Type II: signal and idler are orthogonal polarised UVpump Signal (vertical) BBO crystal Idler (horizontal) Kwiat et al, PRL 75, 4337 (1995)

26 Typical setup Focusing optics nonlinear crystal UV Laser diode ~20 mw 405 nm Compensation Filter and fiber optics couplers

27 Entanglement Type I: signal, idler have same polarisation Need two crystals, rotated by 90 Pairs polarised in H and V Entanglement: photon pairs need to be indistinguishable H V H 810 H e iθ V 810 V 1550 No information in which crystal it was produced Simple, but longitudinal walk-off (chromatic dispersion)

28 Setups