Figure 1

Partial level scheme of ${\mathrm{Yb}}^{+}$ (drawn to scale). The ${}^{2}S_{1∕2}\leftrightarrow {}^{2}P_{1∕2}$ transition at $369.53\mathrm{nm}$ is used for Doppler-cooling and to observe ion fluorescence. The branching ratio from ${}^{2}P_{1∕2}$ to the low-lying metastable ${}^{2}D_{3∕2}$ state is measured to be $0.00501\left(15\right)$ (see Appendix ). This metastable state is depopulated by light at $935.2\mathrm{nm}$ resonant with the ${}^{2}D_{3∕2}\leftrightarrow {}^{3}D[3∕2]_{1∕2}$ transition, which quickly returns the ion to the cooling transition [34, 35]. The ion also reaches the ${}^{2}F_{7∕2}$ state on the order of a few times per hour, at which point it is returned to the cooling cycle using light near $638.6\mathrm{nm}$. Inset: schematic of the linear rf-Paul trap used in this experiment.Reuse & Permissions

Figure 2

Experimental apparatus for locking the $739.05\mathrm{nm}$ laser to an iodine-stabilized cavity. The current of the diode laser is weakly modulated at $120\mathrm{MHz}$ via a bias $T$. Approximately $25\mathrm{mW}$ of $739.05\mathrm{nm}$ light is diverted from the main $400\mathrm{mW}$ beam to the iodine setup (Fig. 3). The error signal generated by the iodine setup is sent to a proportional-integral-derivative (PID) servo controller, the output of which is sent to the piezo of the reference cavity. An additional $120\mathrm{\mu }\mathrm{W}$ of the main $739.05\mathrm{nm}$ beam is sent to this reference cavity. The cavity reflection is measured with a radio-frequency photodiode (rf-PD), and the resulting electronic signal is sent through an amplifier and mixed with a $120\mathrm{MHz}$ signal to produce an error signal. The lock is achieved by feeding back to both the laser grating and diode current with appropriate filter electronics. In the figure: PBS is a polarizing beamsplitter, $\lambda ∕2$ is a half waveplate, and $\lambda ∕4$ is a quarter waveplate.Reuse & Permissions

Figure 3

Setup for locking to molecular iodine via saturated absorption spectroscopy. About $25\mathrm{mW}$ of $739.05\mathrm{nm}$ light is incident on the fiber-coupled electro-optic modulator (EOM) with $6\mathrm{mW}$ of this light transmitted. Approximately 1/3 of the power is transferred into each of the two first-order sidebands. The beam is then split into reference, probe, and pump beams by a glass plate. The pump beam passes through an acousto-optic modulator (AOM) [driven by a voltage-controlled oscillator (VCO)] which is frequency modulated at $22\mathrm{kHz}$, imprinting this modulation on the pump beam. The pump and probe beams are counter-propagating and focused through the iodine vapor cell. Ultimately, the probe and reference beams are incident on a photoreceiver. A lock-in amplifier mixes the $22\mathrm{kHz}$ signal with the signal from the photoreceiver, and the resulting error signal is sent to the proportional-integral-derivative (PID) controller that controls the cavity length.Reuse & Permissions

Figure 4

Hyperfine structure of the iodine absorption line approximately $10\mathrm{GHz}$ [48] detuned from half the frequency of the ${}^{2}S_{1∕2}\leftrightarrow {}^{2}P_{1∕2}$ transition of ${}^{171}\mathrm{Yb}^{+}$ $\left(739.05\mathrm{nm}\right)$. Each point is separated in frequency by $0.5\mathrm{MHz}$, and was integrated for about $1.5\mathrm{s}$. The absolute positions of the features are accurate to within $20\mathrm{MHz}$, while the frequency splittings between iodine resonances are accurate to within $5\mathrm{MHz}$.Reuse & Permissions

Figure 5

The ${}^{171}\mathrm{Yb}^{+}$ qubit (not to scale). The ${}^{2}S_{1∕2}\mid F=1,m_F=0⟩$ state is defined to be $\mid 1⟩$, and the ${}^{2}S_{1∕2}\mid F=0,m_F=0⟩$ state is defined to be $\mid 0⟩$. (a) State initialization to $\mid 0⟩$ by application of light resonant with the ${}^{2}S_{1∕2}\mid F=1⟩\leftrightarrow {}^{2}P_{1∕2}\mid F=1⟩$ transition. (b) Detection of the qubit state. If the qubit state is $\mid 1⟩$, the $369.53\mathrm{nm}$ light applied for detection is nearly on resonance, and the ion scatters many photons. If the state is $\mid 0⟩$, very few photons are scattered. Measurements of the hyperfine splitting of the ${}^{2}S_{1∕2}$ and ${}^{2}P_{1∕2}$ levels are found in Refs. 24, 23, respectively. Details regarding our measurement of the hyperfine splitting of ${}^{2}D_{3∕2}$ and ${}^{3}D[3∕2]_{1∕2}$ are found in Appendix .Reuse & Permissions

Figure 6

The experimental setup for initialization, manipulation, and detection of the ${}^{171}\mathrm{Yb}^{+}$ qubit. The $7.37\mathrm{GHz}$ EOM in the cooling beam is tuned so that the positive second-order sideband is on resonance with the ${}^{2}S_{1∕2}\mid F=0⟩\leftrightarrow {}^{2}P_{1∕2}\mid F=1⟩$ transition, preventing population trapping in $\mid 0⟩$ during cooling. The EOM in the pump/detect beam at $2.1\mathrm{GHz}$ is used to optically pump the ion into $\mid 0⟩$ during state initialization. The $935.2\mathrm{nm}$ beam passes through a widely tunable fiber EOM, which is used to generate a frequency component to depopulate the ${}^{2}D_{3∕2}\mid F=2⟩$ manifold during cooling and optical pumping. The AOMs are used to quickly turn the beams on and off. The AOM in the cooling beam is tuned such that the diffracted beam is about half a linewidth $(\approx 10\mathrm{MHz})$ away from resonance to achieve efficient cooling. The pump/detect beam is tuned only $\approx 3\mathrm{MHz}$ from resonance to generate more scattering events, reducing the time needed to distinguish between qubit states with high fidelity. Microwaves ($\mu$waves) at about $12.643\mathrm{GHz}$ are sent to the trap for single-qubit manipulation.Reuse & Permissions

Figure 7

(a) Histograms of detected photons after the ion is prepared in each of the two qubit states. The detection interval is $1000\mathrm{\mu }\mathrm{s}$, with $0.8\mathrm{\mu }\mathrm{W}$ of $369.53\mathrm{nm}$ light focused to $\approx 30\mathrm{\mu }\mathrm{m}$. Black histogram: The ion is initialized to the $\mid 0⟩$ state. Transitions to ${}^{2}P_{1∕2}\mid F=0⟩$ are forbidden by selection rules, the incident light is detuned from ${}^{2}P_{1∕2}\mid F=1⟩$ by the combined hyperfine splitting of $14.7\mathrm{GHz}$, and therefore the atom scatters very few photons. The histogram is the result of $15290$ measurements. Grey histogram: The ion is initialized to $\mid 0⟩$, and then rotated to $\mid 1⟩$ by application of microwaves. During the detection interval, the incident light is on resonance with the ${}^{2}S_{1∕2}\mid F=1⟩\to {}^{2}P_{1∕2}\mid F=0⟩$ transition and the atom scatters many photons. The histogram is the result of $16497$ measurements. (b) Rabi oscillations between the $\mid 0⟩$ and $\mid 1⟩$ states by application of microwaves at $12.642821\mathrm{GHz}$. The time required to drive a $\pi$ pulse is $6.0\mathrm{\mu }\mathrm{s}$. Each point is the result of 1000 measurements.Reuse & Permissions

Figure 8

Measurement of the coherence time of the ${}^{171}\mathrm{Yb}^{+}$ qubit. (a) The series of microwave pulses used for this measurement. The two $\pi ∕2$ pulses are separated by a variable time $T(+\Delta t)$, to measure the decay in the amplitude of the Ramsey fringe as a function of time. (b) Observed Ramsey fringes in the parity of the states of the two ions for delay times $T=0\mathrm{ms}$ and $T=800\mathrm{ms}$. (c) Decay in the amplitude of the observed Ramsey fringe as function of delay time $T$. The line is a Gaussian fit to the data, with a $1∕e$ decay time of $2.5\left(3\right)\mathrm{s}$.Reuse & Permissions

Figure 9

Data used to determine the branching ratio of the ${}^{2}P_{1∕2}$ level. (a) Exponential decay in the fluorescence of a trapped ${}^{174}\mathrm{Yb}^{+}$ ion, indicating population trapping in ${}^{2}D_{3∕2}$. During this time, $\approx 29\mathrm{\mu }\mathrm{W}$ of $369.53\mathrm{nm}$ light was incident on the ion, with the $935.2\mathrm{nm}$ laser detuned approximately $3\mathrm{GHz}$ from the ${}^{2}D_{3∕2}\leftrightarrow {}^{3}D[3∕2]_{1∕2}$ transition. Data collection time was $5\min$, and is analyzed with $16\mathrm{ns}$ binning. The gray line is an exponential (plus background) fit to the data. (b) Exponential fit decay parameters $b={\mathcal{P}}_{P_{1∕2}}\gamma R$ for a range of $369.53\mathrm{nm}$ laser intensities. Error bars are taken to be $\pm 10\%$ the measured $369.53\mathrm{nm}$ power, to account for possible intensity drifts of the laser during the measurement. The line is a fit to the function $p=\left(2b{p}_{sat}\right)∕(\gamma R-2b)$ with two fit parameters: $p_{sat}$ and $\gamma R$.Reuse & Permissions