Fig. 3. Measuring ground state energies at spontaneous SUSY breaking point.

a, b Phonon number distribution of the ground states |ψ₊〉 and |ψ₋〉, respectively, by fitting the time evolution under a blue-sideband driving as shown in the inset. The estimated average phonon numbers are ${\overline{n}}_{+}=0.47\pm 0.19$ and ${\overline{n}}_{-}=0.42\pm 0.21$, respectively. c Measuring $\left.⟨\right){\sigma }_x\left(a+a^{†}\right)\left.⟩\right)$ by fitting the spin-up state population under a spin-dependent force. The dynamics can be fitted by an analytic formula (solid curves, see Methods) and then the slope at t = 0 can be extracted as (−25.5 ± 1.9) kHz and (−32.3 ± 1.8) kHz for |ψ₊〉 and |ψ₋〉, respectively. Each data point is averaged over N = 200 experimental shots. Error bars represent one standard deviation. Combining the two results, we measure the average energy of the two ground states as E₊ = 2π × (7.3 ± 1.9) kHz and E− = 2π × (5.2 ± 2.1) kHz with the ideal value E₀ = ω/2 = 2π × 5 kHz. The two levels are degenerate within about one standard deviation.