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

4. Continuously monitored Bose condensates: quasiprobability distributionsFigure 4.8: Conditional dynamics of 〈 〉Ĵ x c (continuous line) and 〈 Ĵ z (dashed line) when Γ=16〉cfor different atom-atom interaction strengths. In (a), Θ=0.01, in(b),Θ=0.50, and in (c),Θ=2.00. The time axis is scaled by t 0 =1/Ω.50 c(a)3020(b) c0 50 100 150 2001000−10−20−30 x c z c−40−500 50 100 150 200−50t/t 0t/t 02010(c)0−10−20−30 c c−40−500 50 100 150 200t/t 0classical trajectory (Fig. 2.2(a)).The atomic Q functions corresponding to these simulations appear in Figs. 4.9 to 4.11.In the collisionless case (Θ = 0) for a measurement of strength of Γ = 16 (Fig. 4.9), anasymmetric bulge in the distribution develops over time which precesses around the Ĵzaxis. The distribution eventually moves away from the south pole of the sphere, whileremaining compact, and this corresponds to the growth of tunnelling oscillations seen inFig. 4.7(a). When the measurement strength is strong (Fig. 4.10), the distribution movesaway from the south pole quickly, and then advances and retreats towards the equator,with frequent phase jumps. At about t =35t 0 ,theQ function reaches the equator, atwhich point full tunnelling oscillations appear in Fig. 4.7(b).From this time on, the92