Fig. 4

Three-, four-, six- and eight-component states. a Creation of a multicomponent state begins by applying a set of SDKs to take the state \(\left| {{\psi _1}} \right\rangle\) (1) to the state \(\left| {{\psi _2}} \right\rangle\) (2). A microwave π/2 pulse rotates the qubit to produce the state \(\left| {{\psi _3}} \right\rangle = \left( {\left| \uparrow \right\rangle - \left| \downarrow \right\rangle } \right)\left| \alpha \right\rangle + \left( {\left| \uparrow \right\rangle + \left| \downarrow \right\rangle } \right) \left|- \alpha \right\rangle\) (3). Another set of SDKs generates the three- or four-component state. The diagram within the dashed box replaces the one in Fig. 1a for these experiments. b If θ = 0, two of the components rejoin and the state has the form \(\left| \alpha \right\rangle + \left| 0 \right\rangle + \left| { - \alpha } \right\rangle\). If θ = π/4, for instance, then a four-component state of the form \(\left| \alpha \right\rangle + \left| { - \alpha } \right\rangle + \left| {i\alpha } \right\rangle + \left| { - i\alpha } \right\rangle\) is generated. These configurations are depicted in the flags above the contrast curve. The final microwave pulse analyses the state contrast, and is plotted as a function of θ, which is compared with the predicted contrast curve with only the amplitude as a fitting parameter. Error bars are calculated with confidence interval of one sigma. c If the microwave π/2 pulse in a is replaced by a mπ pulse, then the second SDK set behaves as it would in the two-component experiment, with the exception that odd values of m are shifted by half of a trap period. We see this behaviour fits the predicted model well in the figure with m = 0 (purple), and m = 1 (gold). d The six- and eight-component state is created by extending the technique for the three- and four-component state with an additional microwave pulse and SDK set. e Contrast as a function of θ is used to verify the creation of the superposition state when compared to the model (solid line)