Figure 3: Unbalanced homodyne detection.
From: Interaction-free measurements by quantum Zeno stabilization of ultracold atoms
(a) The weak coupling of a large coherent state |α〉 with an arbitrary state |ψ〉 on an unbalanced beam splitter can be described by a displacement of the state, Dα|ψ〉. In our experiment, the displacement is realized by a microwave coupling between the condensate in the level (1, 0) and the state in the level (1, 1). (b) The displacement of Fock states |n〉 results in characteristic particle counting statistics of the displaced states. The corresponding probability distributions, as shown for Fock states with n=0 (solid line), 1 (dashed) and 2 (dash-dotted) particles, are Hermite polynomials with a linearly increasing variance. (c) Variance of the rescaled number of atoms N+1 in (1, 1) after unbalanced homodyne detection as a function of the evolution time. The variance in the absence of an absorbing object (blue circles) increases strongly with time according to Var(Dα |ξ〉)=cosh(2ξ)Vsn with ξ=tΩ and Ω=2π × 3.1 s−1 (blue line). In the presence of an absorbing object (orange squares), the variance is almost constant. A slight increase is compatible with the increased variance after a holding time without spin dynamics (grey triangles) and can be attributed to residual rf noise. The solid orange and the dashed grey line are guides to the eye. All error bars are on the order of the symbol size.
