Demonstration of a Dressed-State Phase Gate for Trapped Ions

We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.

Figure 1

Experimental setup for the entangling gate. Beams with wave vectors ${\mathbf{k}}_{\mathbf{C}\mathbf{o}\mathbf{1}}$ and ${\mathbf{k}}_{\mathbf{90}}$, with a frequency difference of ${\omega }_0+{\omega }_{\nu }+\delta$, are used to nonresonantly drive a sideband transition. Their alignment provides a wave vector difference $\mathbf{\Delta }{\mathbf{k}}_{\mathbf{z}}$ such that only vibrational modes along the trap axis are excited. Carrier transitions can be driven either with copropagating laser beams having wave vectors ${\mathbf{k}}_{\mathbf{C}\mathbf{o}\mathbf{1}}$ and ${\mathbf{k}}_{\mathbf{C}\mathbf{o}\mathbf{2}}$ or with a microwave field introduced with a helical antenna.

Figure 2

Gate timing sequence. (a) For the microwave-induced-carrier gate we perform a $\pi$ rotation with a $\pi /2$-phase shift that refocuses the fast spin oscillations induced by the carrier and suppresses errors in the gate timing [33]. (b) For the laser-induced-carrier gate we switch the phase of the carrier by $\pi$ during the second half of the sideband drive.

Figure 3

Evolution of the populations of $|\downarrow \downarrow ⟩$ (blue points), $|\uparrow \uparrow ⟩$ (red), and antialigned spin states (green) as a function of the duration of simultaneous application of laser-induced carrier and detuned sideband excitation. The phase of the carrier is shifted by $\pi$ at half of the interrogation time for each point. The gate time for this case is approximately $105\mu \mathrm{s}$, at which point the Bell state ${\Psi }_{\mathrm{Bell}}=(1/\sqrt{2})(|\downarrow \downarrow ⟩+|\uparrow \uparrow ⟩)$ (in the ideal case) is created. The solid lines show the results of simulation that include the errors listed in Table . Error bars are standard errors determined from the measured standard deviation of the points.

Figure 4

The parity oscillation of the microwave-induced-carrier gate is obtained by adding an analysis $\pi /2$ pulse with a variable phase $\varphi$ at the end of the gate and measuring the parity, $P_2+P_0-P_1$, of the qubit populations. The contrast of the parity oscillation is extracted to be 0.960(8) by fitting $A\cos (2\varphi +{\varphi }_0)+B$ to the data points. Together with a population measurement of $P_2+P_0=0.988(4)$ after the gate, a fidelity of 0.974(4) is deduced. Error bars are standard errors determined from the error in the fits to the fluorescence count histograms.