⇦Chinese Physics Letters, 2020, Vol. 37, No. 9, Article code 093701 Significantly Improving the Escape Time of a Single $^{40}$Ca$^+$ Ion in a Linear Paul Trap by Fast Switching of the Endcap Voltage Peng-Peng Zhou (周朋朋)1,2, Shao-Long Chen (陈邵龙)1, Shi-Yong Liang (梁世勇)1,2, Wei Sun (孙伟)1, Huan-Yao Sun (孙焕尧)1, Yao Huang (黄垚)1, Hua Guan (管桦)1*, and Ke-Lin Gao (高克林)1,3* Affiliations 1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China Received 6 May 2020; accepted 21 July 2020; published online 1 September 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 11934014, 11622434 and 11804373), the Scientific Instrument Developing Project of the Chinese Academy of Sciences (Grant No. YZ201552), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB21030100 and XDB21030300), CAS Youth Innovation Promotion Association (Grant Nos. Y201963 and 2018364), and the Hubei Province Science Fund for Distinguished Young Scholars (Grant No. 2017CFA040).
*Corresponding author. Email: guanhua@wipm.ac.cn; klgao@wipm.ac.cn Citation Text: Zhou P P, Chen S L, Liang S Y, Sun W and Sun H Y et al. 2020 Chin. Phys. Lett. 37 093701    Abstract Sympathetic cooling is a method used to lower the kinetic energy of ions with complicated energy-level structures, via Coulomb interactions with laser-cooled ions in an ion trap. The ion to be sympathetically cooled is sometimes prepared outside of the trap, and it is critical to introduce this ion into the trap by temporarily lowering the potential of one endcap without allowing the coolant ion to escape. We study the time required for a laser-cooled ion to escape from a linear Paul trap when the voltage of one endcap is lowered. The escape time is on the order of a few microseconds, and varies significantly when the low-level voltage changes. A re-cooling time of a maximum of 13 s was measured, which can be reduced to approximately one hundred of milliseconds by decreasing the duration of the low-level voltage. The measurement of these critical values lays the foundation for the smooth injection and cooling of the ion to be sympathetically cooled. DOI:10.1088/0256-307X/37/9/093701 PACS:37.10.Ty, 37.10.-x © 2020 Chinese Physics Society Article Text An ion trap containing ultracold ions is a useful research object for quantum computation,[1] optical frequency standards,[2,3] and high-precision spectroscopy.[4,5] To date, the availability of laser sources and the complexity of energy-level structures have limited the ion species capable of being laser cooled directly. However, sympathetic cooling can circumvent these limits by confining two or more ion species in a trap simultaneously, and using the laser-cooled ion species as a coolant to decelerate other ion species by way of their mutual Coulomb interaction.[6–11] Due to its versatility, sympathetic cooling has played an increasingly important role in scientific research, and is routinely performed in multiple laboratories. In practice, coolant ions are often selected according to their charge-to-mass ratio, as well as other parameters;[12] the most frequently used ions include Ca$^+$,[6,13] Rb$^+$,[14] Be$^+$,[7–9] Mg$^+$,[10,11] and Ba$^+$.[12,15] The ions to be sympathetically cooled can be prepared directly in the trap center, e.g., as an isotope or hydride of the laser-cooled ion species.[11] In other cases it is necessary to guide the ions into the trap from the external ion source where they are produced. For instance, some studies have used highly charged ions (HCIs) generated in electron beam ion traps (EBITs),[7,16] molecular ions generated during electrospray ionization (ESI),[16] and metastable lithium ions.[17,18] Due to their large space and convenience for potential control, linear Paul traps are always used in sympathetic cooling, a process whereby externally produced ions can be axially injected by lowering the endcap voltage. A reduction in the endcap voltage alters the axial parabolic potential field used to confine the precooled ions. Under the new potential distribution, the precooled ions move towards the lower potential side, and may escape from the ion trap. In order to realize sympathetic cooling, one prerequisite is that the implantation time for the external ions should be less than the escape time of the precooled ions. Therefore, it is very important to study to what degree the time required for precooled ions to escape from the trap is dependent upon the electrode voltages. Molecular ions[15,19] and highly charged ions[7,20] have been implanted into ion traps via the fast switching of trap voltages without the loss of coolant ions. Zhang et al.[19] introduced rhodamine molecular ions prepared by ESI into Ba$^+$ ion crystals to achieve sympathetic cooling by reducing the endcap electrode potential. In their experiment, the endcap voltage was also used to control the flow of implanted molecular ions. Schmöger et al.[20] built a device to prepare, decelerate, and sympathetically cool HCIs. Two electrostatic mirror electrodes in a coaxial arrangement were rapidly pulsed to facilitate the implantation and export of the ions to be sympathetically cooled. The fast switching of trap voltages was also used in a penning trap by Andelkovic et al.[21] However, to our knowledge, there has to date been no detailed analysis of the behavior of precooled ions in an ion trap in the process of ion implantation, although this topic is very important in relation to sympathetic cooling. In this Letter, we introduce a method to prepare a single $^{40}$Ca$^{+}$ ion, with temperatures on the order of mK, in a segmented linear ion trap. For a single ion confined in the trap, we analyze the acceleration effect resulting from a decrease in the endcap voltage. The duration of the low-level voltage is used to determine the escape time of the $^{40}$Ca$^{+}$ ion, which is generally only a few microseconds. Where the ion does not escape from the trap, the re-cooling time is determined using a statistical method by inspecting the fluorescence signal. Our experimental results indicate that the escape time primarily depends on the axial potential of the ion trap, and is only slightly affected by other factors such as the radio-frequency (rf) amplitude and the frequency of the cooling laser with a power of $\sim $1 mW.
cpl-37-9-093701-fig1.png
Fig. 1. (a) Schematic diagram of the linear Paul trap and rf field. (b) Axial electrostatic potential distribution before and after the pulse signal is triggered. $V_{\rm right}$ and $V_{\rm left}$ denote the voltages of the right and left endcaps of the trap, respectively. $V_{\rm low}$ and $V_{\rm high}$ denote the voltages of the low- and high-level pulses, respectively.
In our experiment, the segmented linear ion trap is housed in a vacuum chamber with a background pressure lower than $1 \times 10^{-8}$ Pa. A schematic diagram is given in Fig. 1(a). An rf signal with a frequency of 2.31 MHz is used to radially trap the $^{40}$Ca$^{+}$ ions in the trap region. The eight electrodes at the two ends are used as the endcaps for axial confinement of the ions. Only the direct current (dc) potential controlled by the pulse output (50% duty cycle) of a signal source is applied to the right endcap [the red end in Fig. 1(a)]. An rf with a superimposed dc potential is applied to the remaining left endcap and central electrodes. The triggering of the pulse is programmable, so as to allow the switching of the right endcap potential between high-level ($V_{\rm high}$) and low-level ($V_{\rm low}$) voltages, as shown in Fig. 1(b). Half of the pulse period is regarded as the duration of $V_{\rm low}$, which is denoted by $T_{\rm end}$. All rf- and dc- carrying wires pass through two vacuum feedthroughs, and are attached to the electrodes by screws. In addition, two oscilloscopes are used to monitor the rf and dc potentials. The calcium ions are generated by laser ablation with a 532 nm pulse laser.[22] To improve the cooling efficiency, the wavelengths of the cooling laser at 397 nm and the repump laser at 866 nm, semiconductor lasers are locked to a wavelength meter (WS-7, accuracy 60 MHz), calibrated using a stabilized 729 nm laser.[23] Fluorescence photons at 397 nm are guided through several imaging lenses and mirrors before being split into two beams, detected by a photomultiplier tube (PMT, Thorlabs PMT2100) and an electron multiplying charge-coupled device (EMCCD, Andor DU970P). Filters are placed in front of the PMT and the EMCCD to filter out indoor and other stray light. Subsequent to the alteration in the endcap voltage, the axial parabolic potential is disrupted, and a new potential distribution is formed with a gradient pointing out of the ion trap as shown in Fig. 1(b), which results in the escape of the precooled ions. The axial gradient of the new potential distribution vanishes when $V_{\rm low}$ is equal to the voltage of the trap center $V_{\rm effect}$, and points into the trap region if $V_{\rm low}$ is greater than $V_{\rm effect}$. When the axial potential field is approximated by a linear function of position near the trap center, the motion of a single ion can be treated as an accelerated motion, where the initial velocity is zero, and the acceleration is $$\begin{align} a = \frac{q}{m}\frac{V_{\rm effect} - V_{\rm low}}{k},~~ \tag {1} \end{align} $$ where $k$ denotes the length factor, $q$ is equal to the elementary charge for $^{40}$Ca$^+$, and $m$ is the ion mass. To detect ion signals, two conditions must be met: the energy of the ion must be lower than that of the axial potential well, and the ion must be located within the trap volume. Therefore, there are two conditions in which single $^{40}$Ca$^{+}$ ion can escape before the end of the low-level voltage duration: the $^{40}$Ca$^{+}$ ion can escape from the trap region before the voltage of the endcap returns to a higher level, or the ion obtains sufficient kinetic energy to overcome the initial parabolic potential barrier, even if it is still in the trap volume. The escape time can then be written as $$\begin{align} T_{\rm limit}=\sqrt{\frac{m}{q} \frac{2 Z_{\rm limit} k}{(V_{\rm effect} - V_{\rm low})}},~~ \tag {2} \end{align} $$ and $$\begin{align} T_{\rm limit}=\frac{{km}}{q} \frac{\sqrt{(2 D_{\rm limit}/m)}}{({V_{\rm effect} - V_{\rm low}})},~~ \tag {3} \end{align} $$ for the limited axial displacement and the limited potential well, respectively. The parameters $V_{\rm effect}$ and $k$ in both equations are determined by fitting to our experimental data. Here, $Z_{\rm limit}$ is the length of the central electrode, and $D_{\rm limit}$ denotes the potential difference between the average voltage of four central electrodes and the average voltage of both endcaps after the pulse. In practice, fast switching of the endcap voltage can be used to remove ions for the preparation of a single ion. When the pulse voltage of the endcaps is set to a lower level, the number of removed ions is controlled by the low level and duration of $V_{\rm low}$. Figure 2(a) shows the fluorescence counts during the process of reducing the number of ions from four to one. The green arrow A indicates the initial ablation process, after which the fluorescence counts go through four steps (shown as dashed red lines) and reach a stable state from the background level. The red arrows represent the procedure of preparing a single ion by triggering a series of voltage pulses. The procedures marked by E, F, G, and B do not reduce the number of ions, due to the short duration of $V_{\rm low}$, whereas the procedures marked by C, D, and H do reduce the number of ions at the appropriate settings. The brief dips appearing in the figure are caused by the transitory heating of ions due to collisions with the background gas. The number of required pulses and $T_{\rm end}$ are directly proportional to the number of initial ions inn order to prepare a single ion. Figure 2(b) shows the process in which the number of ions in the trap decreases significantly with an increasing number of pulses, and how the crystalline structure of the ions evolves from an ellipsoid to a chain shape, ultimately obtaining the state of a single $^{40}$Ca$^{+}$ ion.
cpl-37-9-093701-fig2.png
Fig. 2. (a) Fluorescence counts in the process of ablation, and the procedure for preparing single $^{40}$Ca$^+$; (b) EMCCD imaging in the procedure for preparing a single $^{40}$Ca$^+$ ion.
After a single ion is prepared in the trap, compensation for excess micromotion is achieved by monitoring the average ion position using the imaging system as the rf potential is raised and lowered, and by observing the fluorescence profile.[24,25] During the escape time measurement process, the optimized voltage of the four central electrodes remains constant. When the voltage of the right endcap is rapidly switched to the low level, the EMCCD imaging disappears, and the fluorescence counts simultaneously drop to the background level. This is because the ion no longer interacts with the laser under the electric field. When the low-level voltage period ends, the EMCCD and PMT signals are observed to recover to the levels of the single ion. The minimum duration of $V_{\rm low}$ to facilitate the ion's escape from the trap, where the ion signals of EMCCD and PMT disappear permanently, may therefore be referred to as the escape time ($T_{\rm limit}$) under a given condition, and is determined by scanning the pulse period ($2T_{\rm end}$). To analyze the correlation between the escape time and the pulse amplitude of the endcap, we measure the escape time under different low-level voltages. As shown in Fig. 3(a), the $T_{\rm limit}$ for a single ion is observed to increase with increasing $V_{\rm low}$, and tends to infinity at a critical voltage. This critical voltage is anticipated to equal $V_{\rm effect}$. The same trends are detected for each initial voltage of both endcaps in Fig. 3(b). Equations (2) and (3) are used to fit our experimental data within the boundary of $V_{\rm low} = -1$ V. The fitted curve overlapping our experimental data indicates the acceleration effect of a single ion under the new potential distribution. As shown in Table 1, the values of the parameters $V_{\rm effect}$ (in V) and $k$ (in mm) are obtained from the fitted curve in Fig. 3(b). Here, $V_{\rm effect}$ indicates the minimum of the parabolic potential after the escape of single ions, which increases with the increasing voltage of both electrodes. In addition, $k$ denotes the axial position where the potential is $V_{\rm low}$, which approximates the distance from the endcap center to the trap center. These two parameters are inserted into Eq. (1) to reflect the electric field applied to the ion, which is not a real value, since the actual electric field is not invariable. The parametric inconsistency for different equations may result from the hypothesis that the constant electric field has different degrees of fitness for these two conditions, the effect of the stray field and the ground potential. The real axial motion of a single ion will need to be further analyzed in the future.
cpl-37-9-093701-fig3.png
Fig. 3. (a) Plot of the escape time, showing its tendency to increase with increasing $V_{\rm low}$. The blue curve corresponds to Eq. (2), which is derived under the condition that the maximal displacement of a single ion is the length of the central electrode ($Z_{\rm limit} = 3$ mm) prior to escape. The red curve corresponds to Eq. (3), which is derived under the condition that the maximal energy of a single ion is the depth of the potential well prior to escape. $V_{\rm left} = 1.34$ V and $V_{\rm high} = 1.3$ V. (b) Relation between $T_{\rm limit}$ and $V_{\rm low}$ under different $V_{\rm left}$ and $V_{\rm high}$. As with (a), the data are fitted via Eq. (2) when $V_{\rm low} \geq -1$ V, and the data in the inset are fitted via Eq. (3) when $V_{\rm low} < -1$ V. (c) Plot of the escape time data at the difference peak-peak voltage ($V_{\rm pp}$) of the rf field, where $V_{\rm low} = -1$ V. (d) Plot of the escape time for different frequency detunings of the cooling laser when $V_{\rm low} = -4$ V. For details, see the text.
Table 1. List of parameters $V_{\rm effect}$ and $k$ obtained from Fig. 3(b) for different $V_{\rm left} - V_{\rm high}$.
$V_{\rm left}-V_{\rm high}$ ${Z_{\rm limit}}^{\rm a}$ ${D_{\rm limit}}^{\rm b}$
(V) $V_{\rm effect}\,{\rm (V)}$ $k({\rm mm})$ $V_{\rm effect}$ (V) $k$ (mm)
1.34$-$1.3 0.511(4) 8.44(12) 1.69(24) 13.9(6)
1.49$-$1.4 0.577(1) 8.92(4) 1.92(11) 13.5(3)
1.75$-$1.6 0.617(4) 9.38(9) 2.41(5) 13.7(1)
1.99$-$1.8 0.669(1) 9.99(2) 2.39(7) 13.0(1)
$^{\rm a}Z_{\rm limit}=3$ mm when $V_{\rm low} \geq-1$.
$^{\rm b}D_{\rm limit}$ is 0.620 V, 0.745 V, 0.975 V and 1.195 V for the difference $V_{\rm left}-V_{\rm high}$ when $V_{\rm low} < -1$.
In addition, the two opposing trends occurring with the change in $V_{\rm left}$ and $V_{\rm high}$, as shown in Fig. 3(b) may also be attributed to the different limiting conditions for different $V_{\rm low}$ when $V_{\rm effect}$ is increased, as shown in Table 1. Under the condition $V_{\rm low} \geq -1$ V, the length of the trap region is invariable. Therefore, $T_{\rm limit}$ decreases, due to the larger $V_{\rm effect}$ when the initial voltage of the endcaps is increased. However, when $V_{\rm low} < -1$ V, the augmentation of the axial potential well weakens the effect of the larger $V_{\rm effect}$ on $T_{\rm limit}$. Consequently, a longer time is required to overcome the potential well. Moreover, the effects of the frequency and power of the 397 nm laser and rf amplitude on $T_{\rm limit}$ are analyzed, and no obvious dependency is observed within the statistical margin of error, as shown in Figs. 3(c) and 3(d). The variation in $T_{\rm limit}$ shown in Fig. 3(c) may result from the variability of micromotion when the rf amplitude is altered. In cases where the ion does not escape from the trap when the endcap voltage is at a low level, the ion is pushed back to the trap region and re-cooled by the laser when the endcap voltage returns to the higher level. The re-cooling time required to recover a sign of the $^{40}$Ca$^{+}$ ion reflects the time scale of reducing its kinetic energy, resulting from the acceleration effect. The sample background level after triggering the pulse is used to measure the re-cooling time, multiplying it by the sampling time. The re-cooling time curves for different low-level voltages are shown in Fig. 4. These curves have a trend similar to that of the escape time curves shown in Figs. 3(a) and 3(b). However, $T_{\rm re-cooling}$ can reach approximately 13 s and is one million times larger than $T_{\rm limit}$. With the reduction in the low-level duration, the kinetic energy obtained from the acceleration process is lower. Therefore, the re-cooling time can be reduced to less than one second by decreasing the duration of the low-level voltage. Due to the lower efficiency of a near-detuned cooling laser in relation to high speed ions, adding a far-detuned cooling laser represents an alternative approach to reducing the re-cooling time.
cpl-37-9-093701-fig4.png
Fig. 4. Re-cooling time curve, corresponding to the duration of the low-level voltage under different $V_{\rm low}$.
In summary, we have reported a technique to prepare and discern single $^{40}$Ca$^{+}$ ions. Experimentally, we confirm that the axial potential distribution has an important role in accelerating precooled ions. The escape time of a single precooled $^{40}$Ca$^{+}$ ion is obtained by applying pulses of different periods on the right endcap, which is generally several microseconds. The escape time can be used to analyze the minimum kinetic energy of an externally produced sympathetic ion before injection into the ion trap. In addition, the re-cooling time can be decreased to the order of a few hundreds of milliseconds from the order of tens for more efficient sympathetic cooling by adjusting the low-level voltage and its duration. These experimental results lay the foundation for further research on the sympathetic cooling of metastable Li$^+$ ions and HCI using a precooled ion, and sympathetic cooling is an important step towards Li$^+$ precision spectroscopy and novel HCI optical clocks. The authors thank Tingyun Shi and Xin Tong for their help and discussion. References Quantum Computations with Cold Trapped Ions Ca + 40 ion optical clock with micromotion-induced shifts below 1 × 10 − 18 Improvement of Stability of 40 Ca + Optical Clock with State PreparationSpectroscopy Using Quantum LogicPrecision spectroscopy with a single 40 Ca + ion in a Paul trapTrapping and sympathetic cooling of single thorium ions for spectroscopyCoulomb crystallization of highly charged ionsProduction of Ultracold Trapped Molecular Hydrogen IonsSympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasmaSimulations of the rf heating rates in a linear quadrupole ion trapProbing Isotope Effects in Chemical Reactions Using Single IonsMolecular dynamics simulation of sympathetic crystallization of molecular ionsPreparation of Ultracold Li + Ions by Sympathetic Cooling in a Linear Paul TrapMeasurement of the Low-Energy Rb + –Rb Total Collision Rate in an Ion-Neutral Hybrid TrapSympathetic Cooling of Complex Molecular Ions to Millikelvin TemperaturesA low-energy compact Shanghai-Wuhan electron beam ion trap for extraction of highly charged ionsSaturated fluorescence spectroscopy measurement apparatus based on metastable Li + beam with low energyDeceleration of Metastable Li + Beam by Combining Electrostatic Lens and Ion Trap TechniqueDeceleration, precooling, and multi-pass stopping of highly charged ions in Be + Coulomb crystalsLaser cooling of externally produced Mg ions in a Penning trap for sympathetic cooling of highly charged ionsLaser ablation and two-step photo-ionization for the generation of 40 Ca +Long-Term Frequency Stabilization of Multi-Lasers Based on WavemeterMinimization of ion micromotion in a Paul trapCompensating for excess micromotion of ion crystals
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