Single qubit manipulation in a microfabricated surface electrode ion trap

Scaling trapped ion systems to a large number of qubits necessitates the use of complex multi-segmented trap structures. Fabrication of trap structures with a large number of electrodes is feasible using established microfabrication techniques based on photolithography [11]. While surface electrode traps have been made in both single metal layer designs [29–31] and designs with multiple metal layers [32, 33], the multiple metal layers are essential to connect electrodes to input/output (I/O) bond-pads when designing complex traps with multiple trapping zones and junctions.

The radio frequency (RF) surface electrode Paul trap used in this work features two metal layers separated by an insulating layer [32, 34]. The geometry of the trap is a symmetric six-rail design (shown in figure 1(a)) with a 100 μm wide slot etched through the substrate to allow for backside ion loading and optical access. Adjacent to the slot are split central control electrodes, two electrodes with RF voltages applied and 40 outer segmented control electrodes. The control electrodes have quasi-static voltages applied to them and are often designated as DC electrodes. The top metal layer is separated from the bottom metal layer by 14 μm of oxide and each metal layer consists of 2.4 μm of aluminum. The two RF rails have a width of 60 μm and are separated by 140 μm. Together they have a capacitance of  ∼ 7 pF to RF ground. The equilibrium trapping position is  ∼ 80 μm above the trap surface. The oxide insulating layer is controllably etched back so that the oxide is cleared away from the RF ground directly under the gap between the electrodes and the electrode metal overhangs the oxide, thus reducing the amount of insulator visible from the trapping region (figure 1(b)). This overhang makes it possible to evaporate a different metal on the top electrodes without causing shorts. Two of the traps investigated had an additional 500 nm gold layer evaporated onto the top surface.

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The trap chip is mounted on top of a spacer in a 100-pin ceramic pin grid array (CPGA) package to facilitate lateral optical access. Wirebonds originate from the lower metal layer and feature low profile bonds protruding only a few tens of micrometers above the top metal plane. In addition, wirebonds are placed such that optical access is not obstructed. On the package for one of the gold-coated traps, a filter capacitor of  ∼ 1 nF was installed between each DC electrode and ground to filter the residual pick-up of RF voltages, which is crucial for eliminating ion micromotion. Each trap is electrically tested to ensure none of the electrodes are disconnected or shorted and thus fully functional.

The stability of ions trapped in surface traps is sensitive to collisions with background gas molecules as trap depths are much lower than macroscopic three-dimensional traps (typically less than a few hundred meV). The ion traps used in these experiments are housed in a spherical octagon vacuum chamber to allow for ample laser beam access. The vacuum chamber contains 96 electrical feedthroughs for DC electrodes. Separate electrical feedthroughs are used for the RF voltages to minimize pick-up of the RF signal on the DC electrodes, which can cause ion micromotion. A thin sheet of aluminum with a 2.5 mm wide viewing slit above the trapping zone is placed 3.8 mm from the trap surface to shield the trapped ions from residual electric fields due to charge build up on the vacuum viewport. For some experiments a non-evaporable getter (NEG) pump is placed 3.3 mm away from the trap, between the trap and the solid aluminum ground shield, to reduce the vacuum pressure close to the ion. The vacuum chamber is constantly pumped by an ion pump, a titanium sublimation pump and the NEG pump. The pressure of the vacuum system was below what is measurable by the ion gage used (< 1.9 × 10⁻¹¹ Torr) for all experiments.

The ion traps used in this experiment contain 42 DC electrodes. These electrodes are connected to a custom digital-to-analogue converter system outside of the vacuum chamber, used to provide the necessary DC voltages to the trap. The DC voltages are chosen to rotate the principal axes such that the cooling beam has a projection in each of the three principal axis directions, allowing for efficient Doppler cooling of all motional modes. Resistor–capacitor (RC) filters with a  ∼ 300 kHz cutoff frequency are placed just outside the vacuum chamber,  ∼ 330 mm away from the chip. Capacitive filters (900 pF) are located on the CPGA package, close to the ion trap chip. The RF trapping voltage is generated by a direct digital synthesizer, and supplied through an RF amplifier (gain of 40 dB) followed by a helical resonator (resonance at ω_RF = 27.8 MHz, Q_loaded = 280) [35].

The qubit states used for these experiments are the ²S_1/2|F = 0, m_f = 0〉 and ²S_1/2|F = 1, m_f = 0〉 hyperfine ground states (denoted |0〉 and |1〉, respectively) of the ¹⁷¹Yb⁺ ion. These 'clock' states are chosen for their insensitivity to magnetic field fluctuations (to first order) enabling long coherence times (figure 2). Manipulation and detection of the ¹⁷¹Yb⁺ hyperfine qubit have been well documented in [36]. Coherent transfer between qubit states can be accomplished using a resonant microwave field at Δ_HF = 12.6 GHz, or by stimulated Raman transition using two laser beams with a frequency difference of Δ_HF (figure 2).

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The electronic state of the ¹⁷¹Yb⁺ hyperfine qubit is measured by applying near-resonant light (∼ 100 mW cm⁻²) for the ²S_1/2|F = 1〉 → ²P_1/2|F = 0〉 transition of the ion [36]. The beam excites ²S_1/2|F = 1〉 → ²P_1/2|F = 0〉 transitions while the ²S_1/2|F = 0〉 state remains unchanged. The ²P_1/2|F = 0〉 state decays back down to one of the ²S_1/2|F = 1〉 Zeeman states and the excitation can be repeated many times. The transition between the ²S_1/2|F = 0〉 state and the ²P_1/2|F = 0〉 state is forbidden by atomic selection rules, leaving the ²S_1/2|F = 0〉 state dark throughout the detection process. For a given polarization of the excitation beam, linear superposition states of the ²S_1/2|F = 1〉 sublevels that are decoupled from the pump beam, known as coherent dark states [37] are formed. To prevent the ion from remaining in such dark states, a magnetic field of 3–5 G is provided by wire coils located outside the vacuum chamber to lift the degeneracy of the ²S_1/2|F = 1〉 states and thus 'destabilize' the coherent dark states over time [38]. Due to the small possibility of the ion going from the ²P_1/2|F = 0〉 state to the ²D_3/2|F = 1〉 state (not shown in figure 2) a 935 nm laser is used to pump the ion back into the $^2{\mathrm { P}}_{1/2}{|F\!=\!0\rangle } \leftrightarrow {^2{\mathrm { S}}_{1/2}}{|F\!=\!1\rangle }$ manifold. Sidebands are placed on the 935 nm laser to ensure any population in the ²D_3/2 state sublevels (not shown in figure 2) is also pumped out. This scheme results in ion fluorescence if the ion is in the ²S_1/2|F = 1〉 state, while the ion remains dark if it is in the ²S_1/2|F = 0〉 state.

Continuous wave external cavity diode lasers are used to cool, initialize and detect the state of the qubit. The diode laser addressing the main transition (369.5 nm) is frequency locked to a transfer cavity resonant at both 369.5 and 780 nm wavelengths. The transfer cavity length is locked to a 780 nm diode laser which is frequency stabilized to a rubidium vapor cell using saturated absorption spectroscopy.

State initialization is performed by adding a 2.1 GHz sideband onto the cooling beam via a resonant electro-optic modulator (EOM). After several scattering events the ion is pumped into the |0〉 state [36]. For Doppler cooling, a 14.7 GHz blue sideband on the cooling beam is needed to pump the ion from the dark ²S_1/2|F = 0〉 state to the ²P_1/2|F = 1〉 state. This is accomplished using the second order sideband produced by a bulk resonant EOM driven at 7.37 GHz.

Frequency combs from phase-locked ultrafast lasers are well suited for driving Raman transitions between the hyperfine qubit states due to their ability to span large frequency gaps while providing very fine frequency tuning [27]. For our experiments a picosecond titanium–sapphire laser with a center frequency near 739 nm and 76 MHz repetition rate (ω_rep/2π) is used. The output is frequency doubled to yield a central frequency near 369.5 nm, red-detuned by δ = 395 GHz from the ion resonance. The repetition rate of the pulsed laser is stabilized to ensure that the frequency difference between the two Raman beams plus an integer multiple of the repetition rate spans Δ_HF.

The repetition rate of the mode-locked laser is stabilized by monitoring the beat frequency between the 166th harmonic of the laser repetition rate with a stable oscillator near Δ_HF, and controlling the cavity length with the error signal (figure 3(a)). The Raman transition is driven by first splitting the frequency comb into two beams, then shifting the frequency of each beam using acousto-optic modulators (AOMs) (figure 3(c)).

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To manipulate the qubit states without affecting the ion's motion, co-propagating Raman beams can be used. The two combs can be combined in a single beam by driving a single AOM with two modulation frequencies. For qubit manipulation that involves changes in the ion's motional degree of freedom, we use two beams with a finite k-vector difference Δk = k₁ − k₂ to impart a change in the ion's momentum. The two beams are aligned such that Δk lies perpendicular to the trap RF axis, allowing for addressing of the radial modes of motion within the trap.

To load ions into the trap, an oven with solid metallic Yb is resistively heated to provide a beam of neutral Yb atoms to the trapping volume. A 399 nm diode laser (intensity ⩾250 W cm⁻²) along with the 370 nm cooling laser is used to resonantly photoionize the neutral atoms. Typically the ovens are heated for no longer than 5 min to trap a single ion. Once the atom is ionized in the trapping volume it is immediately cooled with Doppler cooling light (∼ 325 mW cm⁻²) detuned 20–30 MHz from the ²S_1/2|F = 1〉 → ²P_1/2|F = 0〉 resonance with constant 935 nm re-pumping. In this system ion lifetimes of greater than 10 h are routinely observed while performing experiments, provided Doppler cooling is applied with a duty cycle of greater than 20%. Without cooling, ion lifetimes as long as 20 min are observed.

3.2.1. Trap frequencies

3.2.2. Micromotion

Micromotion of the ion is a result of the misalignment of the RF null and DC nulls in the x–z plane (as shown in figure 1(b)), where the ion's motion is driven at the RF frequency by the residual RF field at null defined by the RF and DC fields. Elimination of the micromotion is critical for the realization of multi-qubit gates. There are three detection mechanisms used to determine if the nulls are overlapping. The first method is to monitor the lineshape of the transition between the ²S_1/2|F = 1〉 and ²P_1/2|F = 0〉 states. The presence of micromotion causes a spread in the velocity of the ion, which results in a Doppler broadening of its natural Lorentzian lineshape. This method provides a rough measure of the offset between the RF and DC nulls.

A more sensitive measure of micromotion correlates the time of arrival of the scattered photons with the phase of the applied RF voltage [39]. An ion located away from the RF null experiences an oscillating force at the RF frequency. For this method, the cooling laser is tuned roughly one linewidth away from the atomic resonance, where the scattering rate depends strongly on the detuning so that the ion brightness difference between when the ion sees a red or blue Doppler shift is maximized. Since the ion is more likely to scatter a photon when it is moving toward the beam (blue shifted) than away (red shifted), we see a modulation in the photon arrival time measured with respect to the RF phase. The measure that quantifies micromotion is the contrast of this time-correlated photon arrival fringe. This method is only sensitive to micromotion along the laser propagation direction. We are unable to detect micromotion along the z-axis (perpendicular to the electrode surfaces) using this method.

To detect micromotion along the z-axis, a third method is used to resonantly excite the micromotion [40]. Similar to the setup used to determine trap frequencies, we add an additional excitation signal onto the RF signal applied to the trap. The mixing of the excitation signal and the RF signal at the trap results in an extra modulation force on the ion at the difference frequency of the two. If the ion is positioned slightly off the RF null it will experience this force exciting the ion's motional degree of freedom, while it will remain unaffected if located at the RF null. When a red-detuned cooling beam is used, the resonant excitation is translated into ion brightness. By sweeping the frequency of the excitation signal, we see an increase in the ion brightness when the frequency of the added excitation signal approaches ω_RF ± ω_trap. As we change the DC voltages to bring the DC null closer to the RF null, the micromotion is reduced and the ion brightness enhancement is reduced (figure 4(a)). Under reduced micromotion amplitude, the excitation signal power must be increased to see a similar change in brightness (figure 4(b)).

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Using these methods we were able to fully compensate for micromotion only in the trap containing capacitors on all DC electrodes. For traps without on-package filter capacitors, residual RF voltage is coupled to the DC electrodes. If the RF signal pick-up at the DC electrodes involves a finite phase shift, residual RF voltage appears at the RF null and the micromotion cannot be fully compensated. All DC electrodes must therefore be filtered to eliminate any residual RF pick-up.

3.2.3. Heating rate

It is generally observed that ions in surface traps are more susceptible to an increase in motional quanta, commonly referred to as ion heating, when compared to their macroscopic counterparts [41, 42]. Uncontrolled changes in the motional quanta will degrade the fidelity of multi-qubit gates that utilize the motional degree of freedom, and must be minimized. Compared to macroscopic traps, the ions are typically trapped much closer to the trap electrodes in surface traps, increasing the effect of fluctuating fields from the trap electrodes on the ion motion. Additionally, trap frequencies in microfabricated traps tend to be lower since they cannot typically tolerate the high RF voltages used on macroscopic traps, leading to higher heating rates when subject to the same heating source. A sensitive measurement of the ion heating rate can be performed by cooling the ion close to the ground state of motion, allowing the ion to heat for a controlled amount of time, and then measuring the average number of motional quanta contained in the system. The heating rate of the trap containing capacitors on all of the DC electrodes was measured using this approach.

The ion is brought close to the motional ground state by Raman sideband cooling using optical frequency combs, as described in section 2.4 [43]. The optical frequency comb produced by the repetition-rate-stabilized pulsed laser is divided into two beams, and the frequency is shifted in each beam by an AOM. The difference frequency between the driving signals for the AOMs is tuned such that pairs of comb teeth, one from each beam, exactly match the energy difference between the |0〉 and |1〉 states (Δ_HF) plus or minus the trap frequency along an axis on which Δk has a projection (see figure 3(c)). Each beam has an average intensity of 335 W cm⁻² with a detuning of 395 GHz from resonance.

To perform Raman sideband cooling, first 2.1 GHz sidebands are added onto the red detuned Doppler cooling light for a time sufficient to pump the ion to the |0〉 state (∼ 20 μs). Then, the frequency combs are turned on, tuned to the first red motional sideband of the ²S_1/2|F = 0〉 to ²S_1/2|F = 1〉 transition for a π-time which has a finite probability to subtract a motional quantum from the system. The ensuing pumping that places the ion back in the |0〉 state on average leaves the motional state unchanged. This sequence (motional transition, pump to |0〉) is repeated many times on both transverse motional modes (1.5 and 2.1 MHz) to condense the motional distribution near the ground state.

The average number of motional quanta in the system at a given time is determined by examining the motional sideband amplitudes. This is accomplished by examining the first Rabi cycle on both the first red and first blue motional sideband, where the ion, initially in the dark (|0〉) state, is driven to the bright state (|1〉) by subtracting and adding a motional quantum, respectively (figure 5(b)). The maximum probability of measuring the ion to be in the bright (|1〉) state is equivalent to the amplitude of that motional sideband. The maximum probability of bright state measurement during Rabi flopping for the first red and blue motional sidebands can be used to calculate the average number of motional quanta in the trap potential by [44]

$$\begin{equation} \bar{n} = \frac{A_{\rm red}}{A_{\rm blue}-A_{\rm red}}, \end{equation} \tag{ 1 }$$

where A_red and A_blue are the maximum amplitude of a Rabi cycle of the red (|n〉 to |n − 1〉) and blue (|n〉 to |n + 1〉) motional sideband, respectively.

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Measurements were performed on the higher frequency radial motional mode (2.1 MHz), with an RF drive frequency ω_RF/2π = 27.8 MHz. After Doppler cooling we observe $\bar {n}=4.5$ (figure 5(a)). Raman sideband cooling is used to cool the ion below the Doppler limit. The average number of motional quanta present after 50 iterations of Raman sideband cooling is $\bar {n}=0.5$ (see figure 5(b)). To measure the heating rate, the ion is placed in the dark for up to 1 ms after Raman sideband cooling, then the Rabi oscillations for both the blue and red sideband are obtained to estimate $\bar {n}$ after the ion has heated (figure 5(c)).

The electric-field noise power spectral density (S_E(ω)) is typically used to compare the ion heating rate between different traps and ion species [41, 45, 46], and is given by

$$\begin{equation} S_{\mathrm{E}}(\omega)=\frac{4m\hbar\omega}{q^2}\dot{\bar{n}}. \end{equation} \tag{ 2 }$$

The electric-field noise power spectral density is normalized by the ion mass m and charge q, and the frequency of the motional mode (ω) under investigation. The integrated electric-field noise power for this system was found to be ωS_E(ω) = 6.3 × 10⁻⁴ V² m⁻² corresponding to $\dot {\bar {n}} = 0.8\pm 0.1\,{\mathrm { quanta}}\,{\mathrm { ms}}^{-1}$, shown in figure 5(c). This value is significantly lower than previous measurements by Allcock et al [47] in a nearly identical ion trap, and is consistent with measurements obtained from various non-cryogenic ion traps [45]. The lowest heating rate was observed in the trap with a gold coated surface which contained in situ capacitive filters that enabled complete compensation of micromotion. For this trap, the NEG pump was placed a few millimeters away from the trap surface. The proximity of the pump to the trap may have assisted in decreasing the ion collision rate with background gas molecules, an important factor in achieving exceptionally long trapping times.

High fidelity state detection is crucial for quantum information processing experiments. Here we employ standard state-dependent fluorescence detection. The ion fluorescence is collected using a custom objective with a numerical aperture of 0.26, and is directed through a bandpass (BP) filter (Semrock FF01-370/6, 6 nm width) to a photo-multiplier tube (PMT) (Hamamatsu 10682-210). Ideally no photons are scattered when the ion is in the |0〉 state while many photons are scattered from an ion in the |1〉 state. In reality, there are detector dark counts and background counts arising from detection light scattered off the trap surface that are collected. By analyzing the distributions of the number of photons during the detection interval for the bright and dark states, a threshold of 1.5 photons is determined. If the PMT collects 0 or 1 photon counts during the detection interval, the ion is determined to be in the |0〉 state. If the PMT collects more than 1 photon count during the detection interval, the ion is then determined to be in the |1〉 state. This yields a best detection fidelity of 98.8 ± 0.3% for a detection interval of 1 ms (see figure 6).

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The largest source of error for detection of the |1〉 state can be attributed to off-resonant excitation of the |1〉 state to the ²P_1/2|F = 1〉 state during the detection process (2.1 GHz detuned), which can decay to the |0〉 state and quench the fluorescence. The state detection fidelity could be improved by increasing the photon collection and detection efficiency, and decreasing the detector dark counts and background counts [36, 48].

By addressing the Δ_HF = 12.6 GHz energy splitting between the qubit states directly with a resonant microwave field, we can perform single qubit rotational gates on the hyperfine qubit. This is accomplished by aligning a microwave horn to the ion from outside the vacuum chamber.

After Doppler cooling, the ion is initialized to the |0〉 state. A 12.6 GHz microwave field resonant with the |0〉 to |1〉 transition is then applied for a variable amount of time, followed by state detection. The probability to find the qubit in the |1〉 state as a function of the duration of the applied microwave field is shown in figure 7. After the microwave field is applied for  ∼ 0.1 ms the state of the qubit is fully transferred from |0〉 to |1〉. More efficient microwave coupling can be accomplished using trap chips with integrated microwave waveguides [23].

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The qubit–microwave coherence time is characterized by a Ramsey experiment. In this experiment the ion is first placed in a superposition state of |0〉 and |1〉 by a π/2 pulse (∼ 50 μs). This pulse is followed by a time delay, then another π/2 pulse with an adjustable phase. The probability to find the qubit in |1〉 state as a function of the phase of the second pulse results in a fringe (figure 7(b)). The fringe visibility as a function of time delay is fit to a Gaussian function to deduce a coherence time of 780 ± 101 ms (figure 7(c)).

To remove dephasing errors arising from a discrepancy between the ion clock and the local microwave oscillator, a sequence of three microwave pulses can be used, provided this dephasing occurs at a rate slower than the time required for one experiment [49, 50]. Applying this spin-echo technique increases the measured coherence time to 1883 ± 44 ms.

A Ramsey experiment was also performed using a single-path pulsed laser beam modulated by an AOM at two frequencies with an average intensity of 523 W cm⁻² at the ion. The beam has σ polarization such that the transition, as shown in figure 2 (light and dark red and blue) is accomplished. A Ramsey experiment yields a qubit coherence time of 1433 ± 37 ms with a single spin-echo pulse. The reduced coherence time observed for the Raman gates in comparison with the microwave gates is attributed to the residual intensity fluctuation of the Raman beams at the ion.