Quantum decoherence: From the self-induced approach to Schrödinger-cat experiments

Transcription

1 Quantum decoherence: From the self-induced approach to Schrödinger-cat experiments Maximilian Schlosshauer Department of Physics University of Washington Seattle, Washington

2 Very short biography Born in Munich, Germany Ancient Greek Interest in QM Undergraduate studies (Physics) at Freiburg University, Germany Visiting Graduate Studies at the University of Washington, Seattle MSc (Physics) from Lund University, (theoretical biophysics) Sweden Ph.D. (Physics) studies at the University of Washington, Seattle with Arthur Fine (main field of research: decoherence)

3 Self-induced decoherence Alternative viewpoint on decoherence M. Castagnino and O. Lombardi, Phys. Rev. A 72, (2005) M. Castagnino and O. Lombardi, Int. J. Theor. Phys. 42, 1281 (2003) M. Castagnino and R. Laura, Int. J. Theor. Phys. 39, 1737 (2000) M. Castagnino and R. Laura, Phys. Rev. A 62, (2000) M. Castagnino, Int. J. Theor. Phys. 38, 1333 (1999) R. Laura and M. Castagnino, Phys. Rev. A 57, 4140 (1998) R. Laura and M. Castagnino, Phys. Rev. E 57, 3948 (1998) M. Castagnino and R. Laura, Phys. Rev. A 56, 108 (1997) Basic claim: decoherence does not require split into system + environment (and ignorance of the latter) instead, decoherence can also occur in closed systems if the total Hamiltonian has a continuous spectrum

4 Basic formalism: 1. Expand observables and states in continuous eigenbasis { E } of Hamiltonian: Ô = de O E E E + de de O EE E E Ψ(t) = de e iet E Ψ 0 E 2. Compute expectation value of Ô: Ô Ψ(t) = de O E E Ψ 0 Ψ 0 E + de de e i(e E )t O EE E Ψ 0 Ψ 0 E 3. Destructive interference for large t: Ô Ψ(t) de O E E Ψ 0 Ψ 0 E off-diagonal terms E E vanish

5 Is this decoherence? No! off-diagonal terms do not vanish individually presupposes existence of ensemble of values of measurements assumption of closed systems is unrealistic energy as preferred basis useless described destructive interference mechanism does not describe physically meaningful/relevant decoherence process!

6 Application to simple spin model (single qubit interacts with qubit bath) : Decoherence factor for EV of local observables: r(t) = k Ψ 0 φ k 2 e ie kt Decoherence factor for EV of global observables: r(t) = k r k e iϕ k e ie kt Analytical prediction: Fluctuation of ϕ λ will counteract destructive-interference effect of E λ t.

7 Numerical simulation: Confirms prediction no suppression of off-diagonal terms occurs: decoherence factor log r(t) t random global observable random local observable -25 various serious challenges to the self-induced decoherence approach! [M. Schlosshauer, Phys. Rev. A 72, (2005)]

8 Mesoscopic Schrödinger cats and decoherence Rapidly growing number of experiments that demonstrate existence of superpositions on increasingly large scales Quantum domain extended into macroscopic realm Where is the boundary (if any)? What role does decoherence play here? I will discuss three experiments: 1. SQUIDs 2. Diffraction of C 70 molecules 3. Bose-Einstein condensation

9 Quantifying the macroscopicity of superpositions Ψ = 1 2 ( A + B ) When does this represents a Schrödinger-cat state? Two conditions: (1) Macrosopic difference between A and B in some extensive quantity (relative to microsopic reference value) large extensive difference S ext. (2) Large degree of entanglement S ent in (multiparticle) state Ψ large number of microsopic constituents.

10 SQUIDs Setup: Superconducting loop interrupted by a Josephson junction, immersed into an external magnetic field. supercurrent flows around the loop Effective potential: QM two-state system Superpositions as energy eigenstates: Ψ ± = 1 2 ( L ± R )

11 Measurement of E proof of existence of superposition of µa currents running in opposite directions. [J. R. Friedman et al., Nature 406, 43 (2000)] Coherent quantum tunneling: p L (t) = cos 2 ( Et/2) M. J. Everitt et al., Phys. Rev. A 69, (2004)

12 Role of decoherence: Localization in flux space (not position space) preferred basis = flux eigenstates. Nicely explained by the stability criterion: [Ĥ int, P n ] = 0 n. SQUID coupled to dissipative environment (harmonic heat bath of bosons): Ĥ int ( L L R R )( ) c α x α α M. J. Everitt et al., Phys. Rev. A 69, (2004)

13 Molecular diffraction Two slit type experiments with massive molecules (Zeilinger et al.): C 70 (diameter about 1 nm) fluorinated fullerene C 60 F 48 (m = 1632 amu) biomolecule tetraphenylporphyrin C 44 H 30 N 4 (m = 614 amu, width over 2 nm) C 70 C 60 F 48 C 44 H 30 N 4 strong particle aspect : large number of highly excited internal degrees of freedom ( finite temperature); emission of photons and electrons; etc.

14 Interference pattern: B. Brezger et al., Phys. Rev. Lett. 88, (2002) single-particle interference! QM superpositions in configuration space describe individual states that can exhibit interference effects without any statistical aspect!

15 Role of decoherence: Can directly resolve and observe the gradual action of decoherence on macrosopic scales: L. Hackermüller et al., Appl. Phys. B 77, 781 (2003) each collision with a gas particle encodes whichpath information about C 70 trajectory decoherence in the spatial wave function of the C 70 molecules (environmental states approx. orthogonal) Note: Bohr s complementarity principle consequence of entanglement: Observability of interference pattern ( wave aspect ) amount of which-path information ( particle aspect )

16 Looking ahead: Data from L. Hackermüller et al., Appl. Phys. B 77, 781 (2003) decoherence allows for precise quantification of conditions for observation of quantum effects!

17 Bose-Einstein condensation Cool down rubidium gas to µk (up to 10 7 atoms) formation of condensate described by single N- particle wave function: N Ψ N (r 1,r 1,,r N ) = e iφ ψ(r i ) i=1 BEC = single macrosopic quantum system Two slit type experiment with BECs: Y. Shin et al., Phys. Rev. Lett. 92, (2004)

18 Macrosopic number-difference superpositions using BECs: Two different internal states A and B for each atom create number-difference superposition: Ψ = 1 2 ( na,n n A + N n A, n A ) Not yet experimentally realized! Problem: Decoherence (mainly scattering between condensate and noncondensate atoms) E.g., atom loss: â 1 ( N, 0 + 0, N ) = N N 1, 0 But: Decoherence (again) allows to understand and quantify the required conditions for BEC cat states.

19 How macrosopic are the observed superpositions? Experiment S ext S ent S ext S ent SQUID C Bose-Einstein not yet experimentally achieved SQUID currently leading ( special scaling property) C 70 (maybe) most counterintuitive (spatial superpositions, paths about 1 mm apart) BEC (if realized) close to SQUIDs...

20 Status of physical collapse theories Physical collapse theories are (in principle) testable! Current experiments cannot disprove these theories: C 70 experiments: 11 orders of magnitude away; Proposed mirror-superposition experiment (10 14 atoms in a superposition; Marshall et al., PRL 91, ): 6 orders of magnitude away; SQUID: spatial localization mechanism only yields small reduction of the supercurrent below detectable level; no reduction onto current states.

21 Where do we go from here? Summary: Experiments indicate exactness of Schrödinger equation also in the mesoscopic/macroscopic realm Restrictions observed in experiments can be explained through decoherence Possible next steps: (1) Devise EPR/Bell-type experiments that could exclude a large class of macrorealistic theories (or disprove the exactness of unitary QM) Leggett s inequality [Suppl. Prog. Theor. Phys. 69, 80 (1980); J. Phys.: Condens. Matter 14 (2002)]

22 (2) Demonstrate interference between biologically distinct states of the same biomolecule. Presumably difficult (but interesting!): distinctness extremely complex everyday-world parameters (RT, etc.) May ease discomfort with the many worlds/minds view... perception of single stochastic outcomes? neuronal decoherence, dynamically autonomous branching of observer states, etc. (feasible, but needs to be made more precise... ) [M. Schlosshauer, eprint quant-ph/ , submitted to Annals of Physics]