Quantum mechanics and reality

Transcription

1 Quantum mechanics and reality Margaret Reid Centre for Atom Optics and Ultrafast Spectroscopy Swinburne University of Technology Melbourne, Australia Thank you!

2 Outline Non-locality, reality and quantum mechanics: Einstein-Podolsky-Rosen (EPR) paradox Schrodinger cat Bell s theorem: Bell inequalities Entanglement and Steering Experiments Macro-scopic reality EPR and Schrodinger cat Genuine multipartite nonlocality: GHZ states CV EPR Entangled atoms Macroscopic realism: Leggett- Garg inequalities

3 EPR paradox 1935 Einstein, Podolsky and Rosen argument Einstein was unhappy about quantum mechanics Believed it was correct but incomplete:

4 Quantum mechanics and reality ( ) Ψ = 1 2 x + x ʹ Principle of superposition Not one or the other until measured: Dirac Cannot view things as existing until they are measured? But why would this be a problem?

5 Quantum mechanics and reality ( ) Ψ = 1 2 x + x ʹ You might argue. Fundamental indeterminacy in nature? Heisenberg microscope Interaction of a microscopic system with any measurement apparatus? But this is not a resolution 2 problems put forward

6 Problem 1: Schrodinger s cat 1935 Ψ = 1 2 ( dead + alive ) Quantum mechanics predicts macroscopic superpositions How does not one or the other until measured work for macroscopic superpositions? Dead and alive?

7 Diosi/ Penrose theories propose collapse mechanism for massive objects Diosi Penrose decoherence time for massive object m

8 Problem 2: Einstein-Podolsky-Rosen (EPR) paradox 1935 X

9 Nonlocal measurements B A

10 Entanglement and correlation Spatial separation Ψ = 1 2 ( dead + alive ) Entangled superposition state Alice s spin measurement is correlated with Bob s cat being dead or alive EPR assume: ( no action-at-a-distance ) Local realism So, EPR argue, Bob s cat was dead or alive (all along) so it seems we need predetermined hidden variables to complete QM?

11 The quantum mixture Bell But,..this case arises all the time We understand correlation well- caused by past events

12 The quantum mixture Ψ = 1 2 ( dead + alive ) ρ mix = 1 2 ( dead dead + alive alive ) We would say, the cat is in the probabilistic mixture.dead or alive Or the superposition is equivalent to such a mixtureso realism holds BUT - for some quantum states, EPR showed differently..

13 EPR Entangled states Entangled states are non-separable: 2 classic EPR entanglement states Ψ = 1 2 ( ) Bell state, Bohm s EPR paradox δ(x A x B )δ( p A + p B ) Alice can predict both Bob s x (and p) with no fuzziness - despite uncertainty relation! Both conditional variances are zero: Δ 2 (x B x A ) 0 Δ 2 ( p B p A ) 0

14 EPR paradox: 2 elements of reality δ(x A x B )δ( p A + p B ) Hidden variables

15 Simple experimental criterion for EPR paradox EPR criterion

16 Bohm s qubit version EPR paradox Ψ = 1 2 ( )

17 EPR s hopes of a local hidden variable (LHV) theory

18 Bell s theorem- no Local Hidden Variable theories consistent with QM Consider experiment to measure spin correlation: spin ½ system E(θ,φ) = J θ A J φ B IF we assign local hidden variables to each spin: CHSH-Bell inequality S = E(θ,φ) E( θ ʹ,φ) + E(θ, φ ʹ ) + E( θ ʹ, φ ʹ ) 2 Quantum Mechanics predicts a violation of Bell s inequality! Ψ = 1 2 ( ) S = 2 2 (Tsirelson) maximum QM value

19 Experiments confirm Bell s nonlocality Clauser, Aspect, Zeilinger E(θ,φ) = J θ A J φ B cos2(b a) = cos2(φ θ)

20 Schrodinger s cat and macroscopic reality

21 Harmonic Oscillator- coherent states Define quadratures- position momentum X =a + + a P = (a a + ) /i Define the coherent (Gaussian) state α = exp α 2 2 α n n! n Measure quadrature X position - P(x) n =0

22 The cat is a superposition of 2 coherent states Ψ = 1 2 ( α + α ) Δ inf x =1

23 Distinguishing Schrodinger s cat from any quantum mixture P( p) Δ inf p <1

24 EPR paradox with a S cat

25 EPR paradox with a S cat

26 Decoherence- interaction with environment α η out Yurke, Stoler,PRL ρ mix = 1 2 The S cat decoheres to a quantum mixture ( α α + α α ) Interference originates from off-diagonal terms in density matrix ρ sup = 1 2 Δp =1 ( α α + α α + α α + α α ) Greater α implies greater sensitivity to decoherence

27 Photon Cats Haroche Grangier experiments

28 Measuring cat decoherence

29 3 famous types of entanglement Not all entanglement is the same Classification of entanglement Entanglement failure of quantum separability ρ = R P R ρ A R ρ B R P(x θ A,x φ B ) = R ρ(λ) P Q (x A θ,λ) P Q (x B φ,λ) Bell s nonlocality: failure of local hidden variables (LHV) ie hidden variable separability P(x θ A, x φ B ) = R ρ(λ) P(x A θ,λ) P(x B φ,λ) dλ dλ

30 Where does EPR paradox fit in? P(x θ A,x φ B ) = R ρ(λ) P (x A θ,λ) P Q (x B φ,λ) dλ EPR steering iff this model fails Wiseman, Jones, Doherty, PRL 2007; Steering Concept introduced in Schrodinger s famous reply to EPR paradox, 1935 Generalised EPR paradox for different measurements Alice appears to steer Bob s state from distant site EPR argument Alice can infer Bob s outcomes: x and p Local realism implies elements of reality for Bob If these elements of reality inconsistent with a quantum state then Quantum Mechanics is incomplete Cavalcanti Jones Wiseman and R,PRA 2009; R et al, RMP, 2009

31 Hierarchy of quantum nonlocality Corresponds to a failure of different separability LHS models: Entanglement nonlocality: Failure of Local Quantum State (LQS) model Alice Bob Werner PRA; Wiseman, Jones, Doherty, PRL 2007; distinct classes of nonlocality EPR steering nonlocality: Failure of Hybrid LHV-LQS model Bell s nonlocality: Failure of Local Hidden Variable (LHV) State model Cavalcanti, Jones, Wiseman, R, PRA 2009

32 Qubit spin nonlocality inequalities

33 Experimental loophole-free demonstration of EPR paradox steering nonlocality Zeilinger experiment Wittman et al, 2012

34 Bigger systems predicted to show Bell nonlocality Higher dimension qudits : d outcomes Ψ = 1 d d 1 j =0 jj Multi-site qubits genuine nonlocality Chen et al, PRA, 2006 Ψ GHZ = 1 2 ( N N ) Mermin, PRL; HDR, PRA 2011

35 Genuine multipartite entanglement A B Ψ GHZ = 1 2 ( N N ) C Verifying genuine tripartite entanglement: need to exclude all 2-body entanglement Leads to criteria: The Greenberger-Horne-Zeilinger cat state is N-partite entangled

36 GHZ cat states using photons Pairs of polarization-entangled photons (one photon H polarized and the other V) are generated by a short pulse of light. Observation of the GHZ correlations requires two pairs. The photon registered at T is always H and its partner in b is V. The photon reflected at the polarizing beam-splitter (PBS) in arm a is always V, being turned into equal superposition of V and H by the /2 plate, and its partner in arm b must be H. If all four detectors register at the same time, the two photons in D 1 and D 2 must either both have been VV and reflected by the last PBS or HH and transmitted. The photon at D 3 was therefore H or V, respectively. Zeilinger experiments N=4 (now ~ 6-8)

37 GHZ cat states using ion traps (N=14) Wineland, Blatt experiments

38 BUT how many qubits share a Bell nonlocality? Ψ GHZ = 1 2 ( N N ) Verifying genuine tripartite Bell nonlocality need to exclude all 2-body Bell nonlocality Leads to criteria: Svetlichny s Bell inequality The Greenberger-Horne-Zeilinger state is N-partite Bell nonlocal BUT not yet shown for N>3?

39 Continuous Variable (CV) Nonlocality Two coupled harmonic oscillators (fields a and b) Define X and P for each ΔX ΔP 1 Squeezed quadratures when EPR entanglement when D = Δ(X A X B ) 2 + Δ(P A + P B ) 2 < 4 EPR steering paradox when ε = Δ(X B X A )Δ(P B P A ) <1 δ(x A x B )δ( p A + p B ) ΔX θ <1

40 How is CV EPR entanglement generated? Two-mode squeezed state H = κe(a + b + + ab) Gross et al, Nature, 2010 Optical parametric down conversion (OPA) Δ(X A X B ) 2 = Δ(P A + P B ) 2 κ 't = e Δ(X A + X B ) 2 = Δ(P A P B ) 2 = e κ 't SQUEEZING!

41 EPR entanglement using squeezing 2 optical Parametric amplifiers (oscillators) EPR fields Kimble, Bachor, Lam, Leuchs experiments

42 Entanglement shows as noise reduction Optical Parametric Oscillator (OPO or OPA) Vacuum noise level (coherent state) Squeezed noise level D = Δ(X A X B ) 2 + Δ(P A + P B ) 2 < 4 ε = Δ(X B X A )Δ(P B P A ) <1

43 CV EPR steering paradox how much spooky action at a distance? EPR criterion Modified PREMISE: Assume Alice s measurement can affect Bob s state, but only up to δ, no more measure Premise violated when

44 CV EPR steering nonlocality experiments Nonlocal shift δ is normalised to vacuum level (graduation assumes Gaussian statistics)

45 EPR spooky action-at-a-distance made larger using spin measurements J X ~ N ~ photons Different sort of homodyne measurement- Uses polariser beam splittersamplification occurs before choice of spin angle Bowen et al, PRL a + a ~ N b + b J Z B = (a + a b + b) /2

46 CV Bell nonlocality- Falsifying Local Hidden Variable theories for CV measurements Superposition of correlated coherent states Ψ = 1 2 ( α α + α α ) A B A B X B alive dead Quadrature outcomes X A and X B are correlated Binned as +1 or -1 (alive/ dead) Reveal violation of CHSH Bell inequality when α ~1 X A Gilchrist, Deuar, R,PRL and PRA

47 CV Bell nonlocality Superposition of correlated coherent states X B Ψ = 1 2 ( α α + α α ) A B A B Violations reduce as α increases X A Gilchrist, Deuar, R,PRL

48 What about macroscopic reality? Leggett Garg inequalities with BEC ground state Ψ = 1 2 ( dead + alive ) Leggett Garg premises Ψ = 1 ( 2 N N ) NOON states 1. Macroscopic realism: System is in one state or the other (cat is dead OR alive) 2. Macroscopic noninvasive measurability Possible at least in principle to determine which of the states cat is in, with an arbitrarily small influence on subsequent dynamics

49 Macroscopic reality: Leggett Garg dead alive Measure at successive times t i I(t i ) = +1 or 1 K ij = I(t i )I(t j ) Leggett Garg premises Leggett Garg inequality- three successive times LG = K 12 + K 23 K 13 1 Leggett Garg, PRL

50 BEC NOON states- we solve H = κ(a + b + b + a) + g [ 2 a+ a + aa + b + b + bb] Ng/κ >>1 Leggett Garg inequality violated- LG=1.5 LG = K 12 + K 23 K 13 1 Two-state tunneling regime Long tunnelling times Fragile to decoherence

51 Generalised LG inequalities H = κ(a + b + b + a) + g [ 2 a+ a + aa + b + b + bb] Generalised Leggett Garg inequality violated: LG=1.42 LG = K l 12 + K l 23 K u 13 1 Violation for more realistic parameters T~0.3 s

52 SUMMARY Predictions of the unreality of Quantum Mechanics extremely well verified But these are still very tiny quantum systems- Penrose Diosi times EPR steering nonlocality for S cats Failure of mesoscopic quantum reality Testing Mesoscopic Local Reality directly for S cats remains a challenge