Decoherence or why the world behaves classically Daniel Braun, Walter Strunz, Fritz Haake PRL 86, 2913 (2001), PRA 67, & (2003)

why no interference from superposition ?

modern answer: dissipative influence of environment decoheres superpositions to mixtures Schrödinger 1935: why no interferences between macroscopically distinct states (“cat” states)? d q λ

systemreservoir

for quantities with meaningful limit like probabilities or mean values 1 But: damping brings about vastly different time scales: for coherences between macroscopically distinct states for

initial superposition with interference term

superposition collapsed to mixture

To study collapse, look at how interference term decays for decreases with Different scenarios by choice of distance :

1. Golden Rule: small perturb during dec; all expts thus far 3. ineffective during dec, strong for ineffective during dec 2. damping weak for

Scenario 1: Golden Rule, not to be (ab)used outside limit of validity! λ/d must not become too small! not applicable to macroscopic superpositions! long-time limit wavepackets have width λ and distance d in Q-space lowest-order perturbation theory w.r.t. to

current experiments all in GR regime: Wineland et al: superpositions of coherent states of translational motion of Be ions in Paul trap, damped through irradiation, fringes resolved; world record Zeilinger et al: multislit diffraction of: ; all dissipation carefully avoided; / 10 Haroche et al: superpositions of coherent or Fock states of microwave cavity mode s W ¸ 1 b sys u s b diss u 6 Wb dec b diss u u, decrease towould begin to invalidate GR

current experiments ctd Delft, Stony Brook, Orsay, all independent: superpositions of counterpropagating mA super- currents in small loops (SQUIDS); again, not very small λ d V d - 1

Scenario 3: lazy theorist’s favorite: only interaction effective; no free evolution during decoherence; applies to macroscopic superpositions H = H sys + H res + H int have widthand distancein -space

requires reservoir mean of exponentiated coupling agent B describes decoh

many-freedom bath:, world behaves classically! Universally so! BUT: central limit theorem: B Gaussian, corrections arise only for, vanish as

Thus far, superposed packets distinct in Q-space. What if packets far apart in other space (eigen- space of observable not commuting with Q) ? Same strategy, more technical hokuspokus, same conclusion: Scenario 2 with competition of bath correlation decay and decoherence?

Thus far,taken far apart in Q-space, i.e. eigenspace of system coupling agent in what iffar apart in P-space, ? naïve repetition of previous reasoning gives surprise:

with diffusion w.r.t. c.o.m. momentum, with diffusion constant independent of both and No accelerated decoherence? There is, just work harder!

a little bit of free motion with gives classical world

Scenario 2, at least as interesting: interaction picture:

again, Gaussian B by central limit theorem: classical world

CONCLUSION Collapse of superpositions to mixtures due to interaction with environment While all decoherence expts done thus far refer to Golden-Rule regime, Classical behavior of the macro-world, caused by extremely rapid decoherence of macroscopic superpositions, understood through simple short- time solution of Schrödinger’s equation