Are Dynamical Quantum Jumps Detector Dependent?

Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by a measurement device, and that different detection schemes result in different types of jumps (or diffusion). Here we propose experimental tests to rigorously prove the detector dependence of the stochastic evolution of an individual atom. The tests involve no special preparation of the atom or field, and the required efficiency can be as low as $\eta \approx 58\%$.

Figure 1

(a) As a function of efficiency $\eta$, we plot: (red dashed) $E[(⟨{\widehat{\sigma }}_x{⟩}^{\mathrm{S}}{)}^2]$ for the SAID unraveling, large $\Omega$ limit; (solid blue) $E[(⟨{\widehat{\sigma }}_y{⟩}^{\mathrm{Y}}{)}^2+(⟨{\widehat{\sigma }}_z{⟩}^{\mathrm{Y}}{)}^2]$ for the Y-homodyne unraveling, in the large $\Omega$ limit; (green dot-dashed) $E[(⟨{\widehat{\sigma }}_x{⟩}^{\mathrm{S}}{)}^2]$ for the X-homodyne unraveling from simulations with $\Omega =5\gamma$. (b) $S^{\mathrm{S},\mathrm{Y}}({\eta }_{\mathrm{Y}},{\eta }_{\mathrm{S}})$ is plotted with the blue shaded regime ($S>1$) representing when the experiment would rule out all theories of objective atomic state reduction. (c) is the same as (b) with SAID replaced by X-homodyne detection and $\Omega =5\gamma$ for both unravelings. (d) The efficiency required for X and Y homodyne to have $S>1$, as a function of $\Omega /\gamma$. For more details see text.