Fig. 3
From: Ultrafast creation of large Schrödinger cat states of an atom
Cat state creation and verification. a The state \(\left| {{\psi _1}} \right\rangle = \left| \uparrow \right\rangle + \left| \downarrow \right\rangle\) (labelled “1”) is split using a set of SDKs to create the cat state \(\left| {{\psi _2}} \right\rangle = \left| \uparrow \right\rangle \left| \alpha \right\rangle + \left| \downarrow \right\rangle \left| { - \alpha } \right\rangle\) (“2”) that has a separation of Δα between its components. After evolution θ = ωT (ω/2π = 1.0 MHz), a second set of SDKs drives the state to \(\left| {{{\it{\Psi}} _{\rm{f}}}} \right\rangle = \left| \uparrow \right\rangle \left| {-\alpha {e^{ - i\theta }} + \alpha } \right\rangle + \left| \downarrow \right\rangle \left| {\alpha {e^{ - i\theta }} - \alpha } \right\rangle\). b Switching each successive laser pulse as an SDK, the cat state \(\left| {{\psi _2}} \right\rangle\) with Δα = 0.8 is generated in about 14 ns, Δα = 2.4 in 62 ns and Δα = 4.0 in 111 ns. The states are verified by observing contrast in the state \(\left| {{{\it{\Psi}} _{\rm{f}}}} \right\rangle\) (upper plot). We find the fidelity of each cat state \(\left| {{\psi _2}} \right\rangle\) to be 0.88(2), 0.76(2) and 0.59(3), respectively (lower plot). c Using the evolution of the atom in the trap to swap SDKs, the generation is slower but has higher fidelity because the laser beam paths are not alternating. The effective single SDK fidelities are 0.9912 and 0.98 for Doppler (black circles) and ground state (purple triangles) cooled atoms (lower plot; the dashed line in the lower plot signifies the limit of the Lamb-Dicke Regime (LDR)). These states are generated in times of \(\sim ({\rm{\Delta }}\alpha - 0.4) \times 1250\) ns. Again, the states are verified by observing contrast in the state \(\left| {{{\it{\Psi}} _{\rm{f}}}} \right\rangle\) (upper plot). The inset shows a cat state with separation Δα = 20 and revival peak contrast of C 0 = 0.19(3). In b, c, error bars are statistical with confidence interval of ± one standard deviation. The solid lines are fits to the underlying theory (Eq. 4, with the peak contrast as the only fit parameter)
