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

5. Weak force detection using a double Bose-Einstein condensateFigure 5.2: The probability distribution resulting from the homodyne measurement. The fringescorresponding to adjacent m values can be distinguished if the coherent amplitude of the light fieldα 0 is large enough.p(x)4σy(0)sin χ tI(m-1) y(0)sin χt Imy(0)sin χt I(m+1)xwhere η = η ∞(1 − e−γT ) and γ is the damping rate of the cavity. The lower bound onthe atom-light coupling becomesχt I >4√ η|y(0)|=2√ η|α0 | . (5.27)Thus the effects of detector inefficiencies and a low damping rate can be overcome bystarting with a large coherent state amplitude in the cavity. For example, with a detectorefficiency of η ∞ = .5 and cavity parameters as given in table 3.1, then for γT ≫ 1, thelower limit on the interaction time ist I > 4.3 × 10 −4 s, (5.28)which is quite small. For a typical damping rate of γ =1.5×10 9 s −1 , the required dampingtime T is also small.5.5 Phase errors and phase diffusionInteratomic collisions are necessary to produce the initial superposition of condensates inthe first stage of the scheme, but their effect on subsequent stages of the measurementscheme is unwanted. A Feshbach resonance[89] could be used to tune the collisional termto zero. However, this technique may be unfeasible[164], so we will now discuss briefly the113