Fig. 2: Experimental results demonstrating “violation” of the Heisenberg uncertainty relation.
From: Retrodiction beyond the Heisenberg uncertainty relation
Value of \(\Delta {\hat{x}}_{\text{A}}\cdot \Delta {\hat{p}}_{\text{A}}\) as a function of (a) τ1 and (b) τ3 are shown respectively. The plotted values are inferred by (4) from the correlations between the optical Faraday rotation measurements. The Heisenberg uncertainty relation is represented by the value 1/2. In (a) τ3 = 2 ms, and in (b) τ1 = 1 ms, and τ4 = 1ms for both figures. The insets show the Wineland squeezing parameter \(10{\text{log}}_{10}({\xi }_{\,\text{R}\,}^{2})\) in dB units for \({\hat{x}}_{\,\text{A}\,}^{2}\) and \({\hat{p}}_{\,\text{A}\,}^{2}\) (See Supplementary Note 7). The error bars (one standard deviation) are derived from 5 identical experiments for \(\Delta {\hat{x}}_{\text{A}}\) and \(\Delta {\hat{p}}_{\text{A}}\) respectively, each consisting of 10,000 repetitions of the corresponding pulse sequences.
