Simple Manipulation of a Microwave Dressed-State Ion Qubit

Many schemes for implementing quantum information processing require that the atomic states used have a nonzero magnetic moment; however, such magnetically sensitive states of an atom are vulnerable to decoherence due to fluctuating magnetic fields. Dressing an atom with external fields is a powerful method of reducing such decoherence [N. Timoney et al., Nature (London) 476, 185 (2011)]. We introduce an experimentally simpler method of manipulating such a dressed-state qubit, which allows the implementation of general rotations of the qubit, and demonstrate this method using a trapped ytterbium ion.

Figure 1

(a) The $S_{1/2}$ ground state of the ${}^{171}\mathrm{Yb}^{+}$ ion consisting of the $F=0$ state $|0⟩$ and three $F=1$ states $|-1⟩$, $|0^{\prime }⟩$, and $|+1⟩$ whose degeneracy is lifted by an applied magnetic field. The hyperfine splitting ${\omega }_0/2\pi$ is 12.6 GHz and ${\omega }_{\mathrm{B}}^{+}/2\pi$ is 13.7 MHz for a field of 9.8 G. Due to the second order Zeeman shift $({\omega }_{\mathrm{B}}^{+}-{\omega }_{\mathrm{B}}^{-})/2\pi =-30\mathrm{kHz}$. Resonant microwave fields can be applied to manipulate or dress the ion, and a radio-frequency field can drive transitions between the $F=1$ levels. (b) Rabi oscillations between the first-order magnetic field insensitive $|0⟩$ and $|0^{\prime }⟩$ states, with a Rabi frequency of $2\pi \times 342\mathrm{kHz}$. (c) Schematic of the dressed-state pulse sequence. The STIRAP process is “paused” when ${\Omega }_{\mu \mathrm{w}}^{+}={\Omega }_{\mu \mathrm{w}}^{-}$, dressing the ion. Once dressed-state manipulation is complete the STIRAP process is completed, returning the ion to the bare states. The STIRAP pulses are Gaussian, of width $t_{\mathrm{w}}$ and offset $t_{\mathrm{off}}$.

Figure 2

Decay of the $|D⟩$ state. The ion is held in the $|D⟩$ state for a variable length of time. After the STIRAP is completed, a $\pi$ pulse swaps the population in $|-1⟩$ and $|0⟩$ before readout. The lifetime of the dressed-state $|D⟩$ is 550 ms, for microwave Rabi frequencies during $t_{\mathrm{DS}}$ of $2\pi \times 16\mathrm{kHz}$. The peak microwave Rabi frequency during the STIRAP was $2\pi \times 25\mathrm{kHz}$, and the pulses were characterized by $t_{\mathrm{w}}=450\mu \mathrm{s}$ and $t_{\mathrm{off}}=356\mu \mathrm{s}$.

Figure 3

Rabi oscillations between the $|D⟩$ and $|0^{\prime }⟩$ states. Based on the short time behavior, the Rabi frequency ${\Omega }_{\mathrm{rf}}^{\prime }=2\pi \times 1.9\mathrm{kHz}$. The frequency of oscillation appears changed for pulse lengths over 100 ms due to slow fluctuations of experimental parameters; a steady increase in the rf Rabi frequency of only 0.5% over the 4.5 minutes required to take the data is sufficient to create the observed apparent frequency of oscillation.

Figure 4

Ramsey fringe within the dressed-state qubit. Two $\pi /2$ pulses (between the $|D⟩$ and $|0^{\prime }⟩$ states), detuned from resonance, are separated by a variable time. During the separation time the ion and rf develop a phase difference, causing the second $\pi /2$ rotation to be performed about a different axis in the $x-y$ plane of the Bloch sphere. From the fringe period, a detuning ${\delta }_{\mathrm{rf}}=2\pi \times 160\mathrm{Hz}$ is inferred.