We report that methane, CH4, can be used as an efficient F-state quenching gas for trapped ytterbium ions. The quenching rate coefficient is measured to be (2.8 ± 0.3) × 106 s−1 Torr−1. For applications that use microwave hyperfine transitions of the ground-state 171Y b ions, the CH4 induced frequency shift coefficient and the decoherence rate coefficient are measured as δν/ν = (−3.6 ± 0.1) × 10−6 Torr−1 and 1/T2 = (1.5 ± 0.2) × 105 s−1 Torr−1. In our buffer-gas cooled 171Y b+ microwave clock system, we find that only ≤10−8 Torr of CH4 is required under normal operating conditions to efficiently clear the F-state and maintain ≥85% of trapped ions in the ground state with insignificant pressure shift and collisional decoherence of the clock resonance.

Singly ionized, trapped ytterbium ions have been widely utilized in developing stable microwave clock,1 optical clock,2 quantum computing,3 and quantum information4 applications. With a nuclear spin of I = 1/2, the 171Y b+ ion has a simple ground-state hyperfine structure compared to many species used in ion trapping. This simple structure allows nearly perfect state preparation in the F = 0 state and the use of an optical cycling transition for state detection. The long coherence time between the hyperfine ground states that can be realized in practice is ideal for microwave clock applications1,5 by using the clock transition between state |F = 0, m = 0〉 and |F = 1, m = 0〉. The Yb+ ion, however, has a notoriously long-lived internal electronic state, the so-called “F-state,” (4f13(2F0)6s2) which has a natural lifetime of approximately 8 years6 owing to the very weak electric octupole (E3) coupling to the ground state (4f146s). After an electric-dipole, optical excitation to the lowest P orbital (4f146p), there is an finite branching ratio (∼0.005) causing the ion to decay to a lower-lying D orbital (4f145d), which has a natural lifetime of 53 ms.7 Collisions with background gas atoms can cause ions in the P and D orbitals to decay to an even lower-lying F orbital.8 Figure 1 illustrates the associated internal atomic states of the 171Y b+ ion. Except for Yb-ion optical clocks that utilize the octupole transition between the ground state and this F-state, Yb-ion applications would like to avoid the population trapping in the F-state, because ions in the F-state do not contribute to the signal and reduce the SNR (signal to noise ratio). Usually, a laser at 760 nm, 638 nm, or 864 nm is introduced to clear the population in out of the F-state.

FIG. 1.

(a) Relative energy levels of a 171Y b+ ion. The electron configuration for each atomic state is indicated in the parentheses. In the ground state 2S1/2, the 171Y b+ microwave clock transition occurs between the hyperfine-split sublevels at frequency f0. The optical cycling transition is achieved via 369 nm and 935 nm transitions. The 760 nm transition is used for clearing the 2F7/2 state. (b) The population in the F-state is determined by the effective pumping speed, RP, to the F-state and the total relaxation rate, RF, from the F-state.

FIG. 1.

(a) Relative energy levels of a 171Y b+ ion. The electron configuration for each atomic state is indicated in the parentheses. In the ground state 2S1/2, the 171Y b+ microwave clock transition occurs between the hyperfine-split sublevels at frequency f0. The optical cycling transition is achieved via 369 nm and 935 nm transitions. The 760 nm transition is used for clearing the 2F7/2 state. (b) The population in the F-state is determined by the effective pumping speed, RP, to the F-state and the total relaxation rate, RF, from the F-state.

Close modal

For the development of a buffer-gas cooled miniature Yb+ ion clock with low-power consumption5,9 (the application motivating this work), the requirement of a laser for clearing the F-state is highly undesirable. It is favorable if the F-state can be efficiently quenched back to the ground state via a collisional process using an atom or molecule with negligible influence on the internal atomic states of the ions. We can in-principle design a system to maintain a sufficient amount of the quenching gas in the ion-trapping environment. A previously known efficient F-state quenching gas for Yb+ ions is nitrogen (N2).10 In a sealed vacuum system, the vacuum is usually maintained by a passive getter pump. Many gas getters, however, pump nitrogen. We have found that methane (CH4) can quench the F-state at a rate similar to that of nitrogen for trapped Yb+ ions with sufficiently small perturbations to the ground-state hyperfine sublevels. Advantageously, methane is not pumped by most getter materials below 300C, making it an excellent choice for use in a sealed, passively pumped vacuum system.

To study the F-state quenching and other characteristics of Yb+ ions due to the presence of CH4 gas, we have set up an experiment to trap and probe Yb+ ions while introducing buffer gases. The details of the experimental apparatus are sketched in Fig. 2. Inside the vacuum chamber, a linear Paul-trap assembly with four 2-cm long trap electrodes (2-mm spacing) and two small hollow cylinder end-caps, which allows the laser beams to propagate along the long-axis of the trap. The chamber volume (∼ 1L) with the trap assembly can be sealed by a valve with a passive getter pump (SEAS Capacitorr D400-2) inside. A gas manifold is constructed for introducing different gases to the vacuum chamber. There are an ion gauge and an RGA (residual gas analyzer) on the system for measuring the buffer-gas pressure and the gas composition inside the chamber. There are four laser sources used in the experiment: a 369-nm laser of ∼200 μW at the ion-trap is used for optical pumping; a 935-nm laser of ∼2.5 mW at the ion-trap is used for repumping ions out of the D state; a 760-nm laser of ∼3 mW at the ion-trap is used for clearing the F-state; and a 399-nm laser of ∼4 μW at the ion trap with the 369-nm laser are used for ionizing the neutral Yb atoms to load ions into the trap. All the laser beams are focused down to a few hundred microns in diameter at the ion trap. The neutral Yb atom source is provided by the two handmade Yb ovens next to the trap assembly. Lasers are switched on and off with optical shutters, which are controlled by a computer or function generator. Fluorescence from neutral and ionized Yb is detected with an imaging system including a CCD camera and a PMT (photomultiplier tube). The CCD camera is used for optical alignment and observing fluorescence when the 399-nm laser is interacting with the neutral Yb atoms. The PMT with band-pass filters is mainly for detecting the trapped ion signals at 369 nm (spontaneous decay from 2P1/2 to 2S1/2) or 297 nm (spontaneous decay from 3[3/2]1/2 to 2S1/2). For studying 171Y b+ ions, a microwave horn and a frequency synthesizer are used to probe the ground-state hyperfine transitions.

FIG. 2.

The experimental apparatus includes laser sources, optics, a vacuum system, a gas manifold, a microwave source, and a computer control system.

FIG. 2.

The experimental apparatus includes laser sources, optics, a vacuum system, a gas manifold, a microwave source, and a computer control system.

Close modal

While conducting the experiments, the RF trap electrodes are driven at 4 MHz, 360 Vp−p. The end-caps are maintained at 10 V. This allows the ion trap to keep about 105 Yb+ ions with a trap depth ∼ 1 eV. The trapped ions are buffer-gas cooled to 1000 K by a few microtorr helium. With the experimental conditions of this work, the lifetime of the ion in the trap is on the order of a day. During ion loading period, a handmade ceramic oven containing natural abundance Yb is heated to 450–500C to send hot Yb vapor through the trap volume, and both 399-nm and 369-nm lasers propagate through the trap. The 399-nm laser is tuned for a selected Yb isotope (λ = 399.4109 nm for 172 and λ = 399.4106 nm for 171 in vacuum). With the given 399-nm laser power, it takes about 10 minutes to fully load ions into the trap. The buffer-gas pressure is controlled by the flow rate from the source and the pump rate through a turbo pump. Once the desired partial pressures of different buffer gases are obtained, we measure the ion signals. Normally the valve for the ion-trap volume is open. This valve can be closed to test the effects of the getter pump on the buffer gases and the lifetime of the trapped ions. While probing the ion signals, we usually detect trapped ions using their fluorescence at 297 nm for good background rejection. This requires both the 369-nm laser and the 935-nm to interact with the ions together. Depending on the experimental procedure, different lasers and the microwave are introduced at the time of demand. The 369-nm, 935-nm, and 760-nm laser wavelengths in vacuum as measured by our wavemeter (Bristol Instruments, 621 Series) are 369.5243 nm, 935.1872 nm, 760.0716 nm for the 172 Yb+ ions and 369.5259 nm, 935.1876 nm, 760.0744 nm for the 171Y b+ ions.

For trapped Yb+ ions, the transition rate equations between different energy levels without the hyperfine structures can be written based on Fig. 1(a).

(1)

where NS, NP, ND, and NF are the relative population of the related S1/2, P1/2, D3/2, and F7/2 states. The sum of the total relative population is one. According to Refs. 7 and 8, there are two collisional decay paths to the F7/2 state, one going from the P1/2 state to the D5/2 followed by an electric dipole transition to the F7/2 state and the other going from the D3/2 state to the F7/2 state. The rates for these two paths are nearly equal. In our model we ignore the decay from the P1/2 to the D5/2 state because the population in the P1/2 state is much smaller than the D3/2 state. Based on the laser power and the laser-beam diameters, oscillator strengths of the optical transitions,11 and the decay rates reported previously,7,8 we estimate the values of the parameters in the Eq. (1): the optical excitation rate R369 > 105 s−1; the P to D branching ratio α ∼ 0.005; the spontaneous decay rate γP ∼ 108 s−1 of the P state; the spontaneous decay rate γD ∼ 20 s−1 of the D state; the effective repump rate R935 > 104 s−1; the D to F effective decay rate RDF ∼ 10 s−1 due to the helium buffer gas; and the F-state total relaxation rate RF = R760 + RQ, where R760 ∼ 1 s−1 when the 760-nm laser is on. Here RQ is the F-state quenching rate. With the presence of the 935-nm laser, both P and D states have much faster relaxation rates and reach quasi-equilibrium quickly. The system then evolves into the slowest decay mode. We find the quasi-steady solutions for P and D states to be NP = R369NS/γP and ND = αγPNP/(γD + R935 + RDF) when NP < ND ≪ 1. Hence, Eq. (1) turns into a much simpler two-level equations as illustrated in Fig. 1(b):

(2)

Here, RP = αRDFR369/(γD + R935 + RDF) is the effective pumping rate into the F-state. One can see that RP can be minimized by maximizing R935 that is proportional to the 935-nm laser intensity. When the 935-nm laser is absent, Eq. (2) is not very accurate, because ND is saturated. Nevertheless, the system quickly ends up with a maximum NF and minimum NS without the 935-nm laser.

To characterize F-state relaxation experimentally, we first block the 935-nm and 760-nm lasers to pump the Yb ions into the F-state. Then we restore the 935-nm laser to greatly reduce the pumping rate to the F-state. The 760-nm laser is restored or not depending on the experiment. When the 935-nm laser is restored, the ion signal starts to recover due to the reduced pumping rate RP into the F-state. Since the 935-nm laser is present, Eq. (2) is well satisfied during the recovery. The time-dependent ground-state population NS after turning on the 935-nm laser can be calculated by solving Eq. (2).

(3)

where 0 ≤ A ≤ 1. In the end of signal recovery the F-state population reaches

(4)

By measuring the signal recovery when varying the quenching gas pressure, we can determine the F-state quenching rate coefficient and the steady-state F-state population by using Equation (3) and (4). Figure 3 summarizes the experimental results of the signal recovery measurements for both 171Y b+ and 172Y b+ ions, with and without the F-state clearing laser. At relatively high CH4 pressure, the F-state relaxation rate is dominated by the collisional quenching rate RQ. We calculate the quenching rate coefficient to be (2.8 ± 0.3) × 106 s−1 Torr−1 independent of the choice of Yb isotopes. This is comparable to the N2 quenching rate coefficient ∼5 × 106 s−1 Torr−1 reported previously.10 We also measure the relative population in the F-state as a function of the CH4 pressure for both ion species as plotted in Fig. 4. The fitted curves use Eq. (4) and assume that RQ linearly depends on the CH4 pressure. The insets in Fig. 3 and Fig. 4 show the examples of the experimental recovery signals of trapped ions, which can be fitted with exponential curves. To normalize the relative ground-state population, we use the signals with presence of the 760-nm laser as the reference of nearly 100% ground-state population. For the measurements with 171Y b+ ions, due to the presence of the ground-state hyperfine structure, we radiate a strong microwave field at the hyperfine splitting frequency ∼12.6 GHz to scramble the populations in the hyperfine sublevels and avoid the ground-state optical pumping effect. Results in Fig. 3 and Fig. 4 indicate some differences between 171Y b+ and 172 Yb+ ions with the same experimental conditions. This is mainly owing to the fact that in 171Y b+ all orbital states have hyperfine structure, but 172Y b+ does not. This leads to different R369, R935, and R760 for these two different isotopes.

FIG. 3.

The signal recovery rate (RF + RP) of the 171Y b+ and 172Y b+ ions as a function of the CH4 pressure with and without the F-state clearing laser. Above 10−7 Torr, the CH4F-state quenching rate is faster than that of the F-state clearing laser used in our experiment. The inset shows the recovery signals with and without the 760-nm laser at relatively high CH4 pressure. The ion signals are detected at 297 nm.

FIG. 3.

The signal recovery rate (RF + RP) of the 171Y b+ and 172Y b+ ions as a function of the CH4 pressure with and without the F-state clearing laser. Above 10−7 Torr, the CH4F-state quenching rate is faster than that of the F-state clearing laser used in our experiment. The inset shows the recovery signals with and without the 760-nm laser at relatively high CH4 pressure. The ion signals are detected at 297 nm.

Close modal
FIG. 4.

The fraction of the 171Y b+ and 172Y b+ ions in the F-state as functions of the CH4 pressure. The inset shows the recovery signals with and without the 760-nm laser at relatively low CH4 pressure. The ion signals are detected at 297 nm.

FIG. 4.

The fraction of the 171Y b+ and 172Y b+ ions in the F-state as functions of the CH4 pressure. The inset shows the recovery signals with and without the 760-nm laser at relatively low CH4 pressure. The ion signals are detected at 297 nm.

Close modal

For microwave clock applications using trapped 171Y b+ ions, it is important to know how the CH4 gas shifts the clock resonance frequency that corresponds to the hyperfine transitions between F = 0 and F = 1 manifolds in Fig. 1(a). To measure this gas induced frequency shift, we lock our microwave frequency synthesizer to the 171Y b+ clock resonance and measure its frequency shift by comparing with a commercial cesium beam reference (Symmetricom 5071A). The results are shown in Fig. 5 and we obtain a relative clock frequency shift coefficient δν/ν = (−3.6 ± 0.1) × 10−6 Torr−1. This value is roughly a factor of two larger than the value previously reported in Ref. 12. In our experiment, the CH4 pressure was determined with two ion gauges and one RGA. We used calibration data from the manufacturers to correct the CH4 pressure readings for both ion gauges and the RGA, and they delivered consistent results. Still, there can be an overall systematic error to the pressure measurements.

FIG. 5.

The relative frequency shift of the 171Y b+ microwave clock transition versus CH4 pressure at room temperature.

FIG. 5.

The relative frequency shift of the 171Y b+ microwave clock transition versus CH4 pressure at room temperature.

Close modal

In addition to the gas induced frequency shift, we also experimentally investigate the ground-state hyperfine relaxation rate (1/T1) and the decoherence rate (1/T2) due to the presence of the CH4 gas. We utilize the on-resonance microwave Rabi oscillation between |F = 0, m = 0〉 and |F = 1, m = 0〉 to determine T1 and T2. From detailed density-matrix modeling, we find the normalized Rabi oscillation signal to be

(5)

Here, ωR is the angular Rabi oscillation frequency. Generally, the T1 relaxation mechanism is caused by a spin destruction (S-damping) process, and the T2 relaxation mechanism is caused by both a spin destruction process and a Carver-damping process13 (the former introduces random spin flips from collisions and the later introduces a random hyperfine frequency modulation via collisions). To experimentally measure a microwave Rabi oscillation of the clock state, we implement two consecutive 369-nm laser pulses with a delay time T, and each pulse has a few hundreds of milliseconds duration. The first pulse optically pumps 171Y b+ ions into |F = 0, m = 0〉 sublevel, and the second pulse is used to detect the portion of ions in F = 1 manifold as using the 369-nm transition illustrated in Fig. 1(a). Between the two pulses, the on-resonance microwave field is introduced to excite Rabi oscillations. By varying T, we can map out the fringes of Rabi oscillation. Both 935-nm and 760-nm lasers are active during the entire procedure to make sure no F-state trapping occurs. The inset of Fig. 6 shows typical Rabi oscillation data. We use Eq. (5) with two additional fitting parameters (the overall scaling and the offset) to fit the data and extract the values of 1/T1 and 1/T2. The CH4 pressure-dependence of (1/T1) and (1/T2) is summarized in Fig. 6 and Fig. 7.

FIG. 6.

171Y b+ hyperfine relaxation rate 1/T1 between F = 0 and F = 1 manifold as a function of CH4 pressure. The inset shows an example data of the microwave Rabi oscillation between the two sublevels of the clock state.

FIG. 6.

171Y b+ hyperfine relaxation rate 1/T1 between F = 0 and F = 1 manifold as a function of CH4 pressure. The inset shows an example data of the microwave Rabi oscillation between the two sublevels of the clock state.

Close modal
FIG. 7.

171Y b+ hyperfine decoherence rate 1/T2 of the clock superposition state as a function of CH4 pressure.

FIG. 7.

171Y b+ hyperfine decoherence rate 1/T2 of the clock superposition state as a function of CH4 pressure.

Close modal

F-state clearing using efficient quenching gases is especially useful for the buffer-gas cooled microwave Yb ion clock. In our miniature Yb ion clock device,9 the 369-nm laser intensity is much lower than the value we use for this experiment, and therefore there is lower pumping rate RP to the F-state. According to the results shown in Fig. 4, we will only need ≤10−8 Torr of CH4 to maintain ≥85% of ions in the ground state. With this condition, the relative frequency shift caused by CH4 will be ≤3.6 × 10−14. The short-term uncertainty of this gas induced shift will be on the order of 10−15 or less. Also the ground-state relaxation rate and the decoherence rate are negligible at this pressure. Although the CH4 molecule is in-principle not pumped by the gas getter below 300C, we have not performed a long-term test to verify that there will be no further physical or chemical reactions of the CH4 gas inside a sealed, getter-pumped vacuum chamber. More investigation will be needed to determine the long-term pressure stability of CH4 in a sealed system. While we have shown the efficacy of methane for quenching the F-state, it is possible that other hydro-carbon molecules could serve as well with potentially better properties. In summary, we have experimentally verified that CH4 has an ability similar to N2 for quenching the F-state. The amount of methane gas needed for the microwave Yb ion clock application produces little perturbation of the ground-state hyperfine sublevels.

We would like to thank Dr. John Prestage for useful discussions. This work is supported by DARPA under the Integrated Micro Primary Atomic Clock Technology program (IMPACT). The views, opinions, and/or findings contained in this article are those of the authors and should not be interpreted as representing the official views or policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the Department of Defense. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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