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

3. Homodyne measurements on a Bose-Einstein condensateFigure 3.4: Fourier transform of some of the tunnelling data in Figs 3.3 & 3.8. In (a) Γ=0.16and Θ=0.0, in(b)Γ = 1600 and Θ=0.0, in(c)Γ=0.16 and Θ=0.5, andin(d)Γ=0.16 andΘ=2.0.2 x 104 ω/Ω1.5(a)800070006000(b) c1 c5000400030000.520001000 c00 1 2 3 4 5350030002500200015001000500(c)00 1 2 3 4 5ω/Ω c160014001200100000 1 2 3 4 5ω/Ω800600400200(d)00 1 2 3 4 5ω/Ω3.4(b)) picks out the tunnelling frequency Ω very strongly, so the fluctuations are mainlyin the amplitude of oscillations, not in the phase. When the measurement strength is verylarge (Γ =2.65 × 10 4 ), 〈 Ĵ x still indicates a tunnelling from one well to another, but〉cthe oscillations are no longer harmonic and appear quite random, both in frequency andamplitude.The equations for the unconditional dynamics (Eqs. (3.15a) to (3.16d)) show a decayin the oscillations of 〈 Ĵx〉 2 〈Ĵ 〉and2y for long times, which increases with the measurementstrength Γ. Figure 3.5 shows the unconditional dynamics for two different measurementstrengths. No such decay is seen in the individual trajectories, but rather there is adiffusion in the phase of the oscillation over long times which accounts for the decay in73