Proposal for a scalable universal bosonic simulator using individually trapped ions

We describe a possible architecture to implement a universal bosonic simulator using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.

Figure 1

The configuration of our ion-trap UBS is an array of storage traps. Only one ion is trapped in each trap, which is a harmonic well. The traps are separated by a distance $L$, which is large enough to prevent disruption from the others. The position displacement of the $i$th ion $x_i$ is accounted for with respect to the trap center.

Figure 2

(a) A displacement operator is implemented by changing the trapping center of the harmonic well. (b) A phase-shift operator or a squeezing operator is implemented by varying the harmonic potential strength. (c) An extra quartic potential is applied to implement the nonlinear phase gate.

Figure 3

Displacement of ions and variations of potentials during a beam-splitter operation. The origin is defined as the midpoint between two storage traps. Step I, ions are transported by the harmonic well from storage traps to the pick-up position. Step II, the double well is switched on to pick up ions. Step III, separation of the double well shrinks. Step IV, separation of the double well extends and brings the ions back to the pick-up position. Step V, the double well is switched off, and the harmonic wells pick up ions and bring them to the storage traps.

Figure 4

Fidelity of the phonon state after a 50:50 beam-splitter operation with ${\omega }_0^2{\sigma }^2=2,3,4,5,7,9$. Total time for the double well to bring ions from and back to the pick-up position (steps II$-$IV in Fig. 3) are about $11,13,15,17,20,22\times 1/{\omega }_0$, respectively. The minimum separation between ions is about 1 $l_0$ in all six runs. The dotted line shows a benchmark of 0.99 fidelity.

Figure 5

Variations of potentials during heatless ion separation. Step I, a quartic potential is added to the common trap to form a double well. Step II, the double well extends and separates the ions to pick-up position. Step III, the harmonic wells pick up the ions and bring them to storage traps.