Energy levels of 40 Ca + employed for the ion trap 

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... shown in Fig. 2, our linear ion trap is encap- sulated in a vacuum chamber connected to a 40 L/s ion pump (Varian) plus a titanium sublimation pump (Varian). to the blades with the tunable power from 0.5 W to 15 W. The ions are produced in the trap centre by the electron bombardment on an atomic beam from the calcium oven. After loading 40 Ca + ions in the trap, we cool them by two diode lasers with wavelengths 397 nm (DL100 Toptica) and 866 nm (home made). The two laser beams are overlapped and focused on the centre of the trap, where the power and the beam waist are 50 μ W and 50 μ m respectively for 397 nm laser, and 200 μ W and 100 μ m respectively for 866 nm laser. The laser scheme could be found in Fig. 3. The detection is made by both photon counting and imaging. The photon counting system consists of a set of microscope objective with an enlargement factor of 7, a photo multiplier tube (PMT) (9893QSB, EMI) plus a fast preamplifier (SR445A, Stanford research systems) and a photon counter (SR400, Stanford research systems). The fluorescence is collected by the microscope objective, and then focused onto a 1.2 mm-diametre pinhole in front of the PMT. The data are recorded by the PMT and finally stored by a computer system. The imaging system shares the same microscope objective with the PMT, and demonstrates the image of the ions by an electron- multiplying coupled-charge device (EMCCD) (Pho- tonMax: 512B, PI) camera. The successful trapping of the ions could be evidenced by both the PMT and the EMCCD camera. In order to study the property of the ion clouds, we have loaded hundreds of 40 Ca + ions and radiated them by cooling lasers, where the 397 nm laser was scanned from 1 GHz red detuning to the near resonance and the 866 nm repumping laser was always at the resonance. Under appropriate trapping condition, the ions stay stably as a cloud, whose fluorescence collected by the EMCCD presents the image shown in Fig. 4. We have changed the trapping potential in the trap by adjusting the voltages on the compensation electrodes, the blades and the tips. Since the ion cloud always moves toward the lowest energy point of the potential, we could fully control the position of the ion cloud in the trap. To fully confine the ions, however, we have to make sure that the ions stayed in the stability re- gion. This means that the stability parameters a and q should satisfy a q < 1. On the other hand, as the shape of the ion cloud depends on the balance between the trapping potential and the Coulomb repulsion, our adjustment of the external voltages could determine the size and the shape of the cloud. This is the prerequisite of QIP with the trapped ions. A series of images of such ion cloud were taken with the varied trapping parameters. Figure 5 is the two-dimensional Gaussian fitting for these images on the EMCCD, from which we could know accurately the sizes of the ion clouds. Figures 6(a) and 6(b) present the ellipticities of the ion clouds varied with the trapping voltages. To understand the changes, we have made some calculations to fit the experimental values, where the good fittings imply the high-quality of the trapping potential in our setup. The small deviation is probably due to the thermal fluctuation of the ions’ motion and the inhomogeneous potential caused by the deposit of the material patches from the oven beam on the electrodes. To eliminate these imperfection, we will further cool the ions to the Doppler cooling limit and clean the trap as much as we can. Alternatively, we will replace the electron bombardment by photoionization in the future for more efficiently producing the calcium ions, which would largely reduce the deposit of the patches on the electrodes. Since our trap works well and the trapped ions are fully under our control, we could measure the secular motion frequency of the ions by the RF field resonance method. [16 , 17] After loading the ions, we carefully ad- justed the compensation voltages to push the ions to the potential centre where the excess micromotion is minimum and the Doppler cooling works more efficiently. Then we applied a weak RF voltage to a tip electrode or a compensation electrode for driving the ions’ motion. By scanning the frequency of the driving RF field (produced by Agilent 33220A), we have observed the signal of the resonant fluorescence, which implies the resonance between the weak RF driving and the secular motion of the ions. The ions were heated up at the resonance and thereby a drop in the fluorescence spectrum was observed, this is demonstrated as an example in Fig 7 for ω . Using the measured values of the secular motion frequencies ω r and ω z , we may obtain the stability parameters and the geometric correction factors. Some of our results are listed in Tables 1 and 2. Since the geometric correction factors are almost constant, the values obtained here will be employed in our future experiments for QIP. In order to calculate the value of q and α ac , we have to measure the accurate value of the rf voltage applied to the trap. As shown in Fig. 8, the RF voltage is generated by a signal generator (Rohde & Schwarz 1000 kHz. SMX) followed by an amplifier (Mini-Circuits LZY-1). The power of the helical res- onator as well as the reflected power are measured by a power meter (Diamond SX-200). The helical res- onator is installed between the power meter and the RF electrodes, which is used for further RF amplifi- cation and for impedance matching of the open-ended circuit. To measure the RF voltage on the RF electrodes, we applied the RF signal to the capacitance di- vider and read the voltage values on the oscilloscope. As shown in Fig. 9, we have measured the high voltage up to 2000 V, and also fitted the experimental data by a theoretical formula. The imperfection in the fitting comes from the power loss in the RF transmission. Based on the above measurements, we have anal- ysed in Table 3 the space charge density and the ion number in Fig. 5, using the equations in Subsection 2.1. For each loading, the numbers of the trapped ions are fixed. We may enlarge or decrease the ion density by changing the trapping potential. Since the ion trap could provide a clean and nearly isolate space for confinement, the trapped ions are good qubit carriers for QIP. There are more than 25 groups worldwide working with trapped ion for QIP, where the most leading groups are in NIST, USA for 9 Be +[3] and in Innsbruck, Austria for 40 Ca + . [5] Besides, some other groups are exploring other candi- date ions, such as 111 Cd + , [18] , 171 Yb + , [19 , 20] 43 Ca + , [6] 138 Ba +[21] and 88 Sr + . [22] Moreover, the scalable QIP with the trapped ions could be hopefully carried out by moving the ions from one zone to another in a multi-trap device [23] or by entangling spatially separated ions using photonic emission. [7] Since these works are based on linear ion traps, it is believed that the individual linear ion trap is the basic component and includes the key technique for future large-scale ion trap QIP. To have the ions doing more QIP tasks, we will further cool the ions by sideband cooling technique down to the vibrational ground state. Due to the Coulomb repulsion and the RF heating, the trapped ions collide strongly with each other in the trap. So only when the cooling rate is much larger than the heating rate, will the ion cloud turn to the ion crys- tallization, which will allow us to encode and manipu- late qubits individually in separated trapped ions for accomplishing some interesting QIP tasks. [24 − 26] In summary, a cloud of laser-cooled 40 Ca + ions have been loaded and manipulated in our home-built linear trap, which could be employed as an ensemble to store quantum information and to accomplish quantum gating. We have tried to optimise the trap- ping condition using external voltages, based on which we have measured the secular motion frequency of the trapped ions and studied the space charge density in our trap. These are the prerequisites for carrying out QIP with our setup. As the ion cloud is well con- trolled, we are confident that the QIP implementation will soon be on the way. We acknowledge thankfully for Guan Hua, Guo Bin, Chen Liang and Liu Qu for discussion and help, and we are grateful to Prof. Zhan Mingsheng and Prof. Gao Kelin for their support and ...

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... we cool them by two diode lasers with wavelengths 397 nm (DL100 Toptica) and 866 nm (home made). The two laser beams are overlapped and focused on the centre of the trap, where the power and the beam waist are 50 µW and 50 µm respectively for 397 nm laser, and 200 µW and 100 µm respectively for 866 nm laser. The laser scheme could be found in Fig. 3. The detection is made by both photon counting and imaging. The photon counting system consists of a set of microscope objective with an enlargement factor of 7, a photo multiplier tube (PMT) (9893QSB, EMI) plus a fast preamplifier (SR445A, Stanford re- search systems) and a photon counter (SR400, Stan- ford research systems). The ...