Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

2. Properties of an atomic Bose condensate in a double-well potentialFigure 2.21: Conditional (thin line) and unconditional (thick line) evolution of a 100-atom condensatein a noisy double-well potential, for Θ=0.9 (below critical). In (a), γ/Ω=10and in (b),γ/Ω = 100. The unconditional evolution is calculated from 100 trajectories. The time axis hasbeen scaled by t 0 =1/Ω.0.5(a)0.30.2(b)0.100−0.1−0.2conditionalunconditional−0.50 100 200t/t 0300 400−0.3−0.4conditionalunconditional−0.50 100 200 300 400t/t 0end of the simulation. Of course this conditional evolution has no meaning in the originalphysical situation of a condensate in a noisy potential - only the mean evolution has anycorrespondence. However the individual trajectories do have a physical interpretation asthe system evolution conditioned on the results of a certain measurement process. Thetype of measurement model (and hence conditional evolution) is not unique for a givenunconditional master equation (Eq. (2.85)). For example, the stochastic unravelling maybe accomplished by a diffusive process, rather than this jump process, and it is to such asituation that we turn in Ch. 3.58