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QUANTUM MECHANICS IN THE MACROSCOPIC LIMIT: WHAT DO RECENT EXPERIMENTS TELL US? A. J. Leggett University of Illinois at Urbana-Champaign JP 1 MESO/MACROSCOPIC TESTS OF QM: MOTIVATION At microlevel: (a) | + | (b) | OR | how do we know? At macrolevel: (a) OR (b) : quantum superposition classical mixture Interference + OR quantum superposition macrorealism Decoherence DOES NOT reduce (a) to (b)! Can we tell whether (a) or (b) is correct? Yes, if and only if they give different experimental predictions. But if decoherence no interference, then predictions of (a) and (b) identical. must look for QIMDS quantum interference of macroscopically distinct states What is “macroscopically distinct”? (a) “extensive difference” (b) “disconnectivity” D ~large number of particles behave differently in two branches Initial aim of program: interpret raw data in terms of QM, test (a) vs (b). JP 2 WHY HAS (MUCH OF) THE QUANTUM MEASUREMENT LITERATURE SEVERELY OVERESTIMATED DECOHERENCE? (“electron-on-Sirius” argument: ~ a–N ~ exp – N ← ~ 1023 Just about any perturbation decoherence) 1. Matrix elements of S-E interaction couple only a very restricted set of levels of S. 2. “Adiabatic” (“false”) decoherence: Ex.: spin-boson model Hˆ Hˆ Hˆ Hˆ s S E E Hˆ s x Hˆ E set of SHO's with lower frequency cutoff min Hˆ ˆ C xˆ oscillator coords. S E z un (t 0) | | displaced state of oscillation 1 0 ˆ s (t 0) (trivially) 0 0 un (t ~ / un ) | 1 (| | | | ), 2 exp F 0 FC factor 1 0 2 ˆ s (t ~ / nn ) 1 0 2 decohered?? (cf. neutron interferometer) JP 3 The Search for QIMDS 1.Molecular diffraction* ~100 nm } C60 z I(z) ↑ z Note: (a.) Beam does not have to be monochromated 2 f () A3exp( o)2 /m (o ~1 8m) (b.) “Which-way” effects? Oven is at 900–1000 K many vibrational modes excited 4 modes infrared active absorb/emit several radiation quanta on passage through apparatus! Why doesn’t this destroy interference? __________________________________ *Arndt et al., Nature 401, 680 (1999); Nairz et al., Am. J. Phys. 71, 319 (2003). JP 4 The Search for QIMDS (cont.) 4. Superconducting devices ( : not all devices which are of interest for quantum computing are of interest for QIMDS) Advantages: — classical dynamics of macrovariable v. well understood — intrinsic dissipation (can be made) v. low — well developed technology — (non-) scaling of S (action) with D. bulk superconductor RF SQUID Josephson junction London penetration depth trapped flux “Macroscopic variable” is trapped flux [or circulating current I] JP 5 JP 6 JP 7 WHAT IS THE DISCONNECTIVITY “D” (“SCHRÖDINGER’S-CATTINESS”) OF THE STATES OBSERVED IN QIMDS EXPERIMENTS? i.e., how many “microscopic” entities are “behaving differently” in the two branches of the superposition? Fullerene (etc.) diffraction experiments: straightforward, number of “elementary” particles in C60 (etc.) (~1200) Magnetic biomolecules: number of spins which reverse between the two branches (~5000) Quantum-optical experiments matter of definition SQUIDS e.g. SQUIDS (SUNY experiment): (a) naïve approach: no. of C. pairs Ð ~ ÐN/2 , N / 2 mutually orthogonal C. pair w.f. : Fermi statistics! D ~ N ~ 109 1010 (b) how many single electrons do we need to displace in momentum space to get from to ? (Korsbakken et al., preprint, Nov. 08) D ~ N (s / F ) ~ 103 104 : intuitively, severe underestimate in “BEC” limit (e.g. Fermi alkali gas) (c) macroscopic eigenvalue of 2-particle density matrix (corresponding to (fairly) orthogonal states in 2 branches): D ~ N ( / F ) ~ 106 107 FP 8 JP 9 WHAT HAVE WE SEEN SO FAR? 1. If we interpret raw data in QM terms, then can conclude we have a quantum superposition rather than a mixture of meso/macroscopically distinct states. However, “only 1 degree of freedom involved.” 2. Do data exclude general hypothesis of macrorealism? NO 3. Do data exclude specific macrorealistic theories? e.g. GRWP Ghirardi, Rimini, Weber, Pearle NO (fullerene diffraction: N not large enough, SQUIDS: no displacement of COM between branches) Would MEMS experiments (if in agreement with QM) exclude GRWP? alas: coll x, collapse rate in GRWP theory dec ( x)2 decoherence rate acc. to QM do not gain by going to larger x (and small x may not be enough to test GRWP) JP 10 * *S. Aaronson, STOC 2004, p. 118. JP 11 Df: K K (tt t t ) Q t Q t 1 2 3 4 1 Q t Q t 3 4 exp 2 exp Q t Q t 2 Q t Q t 1 4 3 exp exp Take t t t t t t / 4 tunnelling frequency 2 2 3 2 4 3 Then, (a) Any macrorealistic theory: K2 (b) Quantum mechanics, ideal: K=2.8 (c) Quantum mechanics, with all the real-life complications: K>2 (but <2.8) Thus: to extent analysis of (c) within quantum mechanics is reliable, can force nature to choose between macrorealism and quantum mechanics! Possible outcomes: (1) Too much noise KQM <2 (2) K>2 macrorealism refuted (3) K<2: ? ! JP 12 JP 13