Observing a single hydrogen-like ion in a Penning trap at T = 4K

Transcription

1 Hyperfine Interactions 115 (1998) Observing a single hydrogen-like ion in a Penning trap at T = 4K M. Diederich a,h.häffner a, N. Hermanspahn a,m.immel a,h.j.kluge b,r.ley a, R. Mann b,w.quint b,s.stahl b and G. Werth a a Johannes-Gutenberg-Universität, D Mainz, Germany { }@dipmza.physik.uni-mainz.de b GSI Darmstadt, D Darmstadt, Germany { }@gsi.de We describe how a single hydrogen-like ion (C 5+ ) is prepared, cooled with the method of resistive cooling and non-destructively detected with the image-current technique in a cryogenic Penning trap at T = 4 K. The storage time for C 5+ -ions in the cryogenically pumped vacuum chamber is longer than six months. The experimental techniques of preparing, cooling and detecting highly-charged ions in a Penning trap are relevant for precision experiments such as g-factor measurements, mass spectroscopy and laser spectroscopy. Keywords: Penning trap, highly charged ions 1. Introduction A single particle in a trap, stored for a long time and cooled to a low temperature, is the ideal object for high precision experiments in various fields of physics. The first experimental demonstration by Wineland and Dehmelt [1] that a single electron can be stored, cooled and nondestructively detected in a trap has opened the way to a series of exciting experiments with single particles in electromagnetic traps. The measurement of the magnetic moment of the electron in a Penning trap is an outstanding test of QED [2,3]. The direct observation of quantum jumps was made possible with a single laser-cooled Ba + -ion stored in a Paul trap [4]. The quantum nature of light was investigated studying the resonance fluorescence emitted by a single Mg + -ion in a Paul trap [5]. The most accurate method to determine the inertial mass of a particle is to measure its cyclotron frequency in a Penning trap. Recently, mass measurements with single ions in a Penning trap have reached an accuracy of [6]. The electron/positron [7] and the proton/antiproton mass comparisons [8] are among the most stringent tests of CPT symmetry. The mass of the electron in atomic units was measured in a comparison of the cyclotron frequencies of a few electrons and a single C 6+ -ion [9]. In this paper we report the experimental techniques which are used for loading, cooling and detecting a single highly charged ion in a Penning trap. The motivation J.C. Baltzer AG, Science Publishers

2 186 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap for this experiment is the measurement of the magnetic moment (or g-factor) of the bound electron in hydrogen-like ions as a precision test of bound-state QED [10, 11]. The g-factor of the bound electron can be determined by measuring its Larmor precession frequency in the magnetic field of a Penning trap with Dehmelt s quantum jump method [12,13]. 2. Experimental results 2.1. Experimental setup In a Penning trap charged particles are stored in a combination of a homogeneous magnetic field and an electrostatic quadrupole field [3]. The magnetic field confines the particles in the direction perpendicular to the magnetic field lines, and the electrostatic potential in the direction parallel to the magnetic field lines. The three characteristic motions that result are the cyclotron motion (frequency ν + = 24 MHz), the axial motion (parallel to the magnetic field lines, frequency ν z = 340 khz) and the magnetron motion (frequency ν = 2 khz), which is an E B drift motion perpendicular to the magnetic field lines. Here, the numbers refer to a C 5+ -ion in our trap described below. The Penning trap consists of a superconducting magnet (B = 3.8 T) and cylindrical electrodes (inner diameter 7 mm) to create the electrostatic trapping field. The electrodes are housed in an ultra-high vacuum chamber which is sealed by a coldwelded tube. The UHV chamber with the trap electrodes is thermally coupled to a helium dewar (T = 4 K), which is suspended in the vertical bore of the superconducting magnet (see figure 1). The low temperature provides effective cryopumping in the UHV chamber and minimises the electronic noise in the detection circuits. There are three positions in the stack of cylindrical electrodes where ions can be trapped: (i) in the reservoir trap, consisting of three cylindrical electrodes, ions can be parked for later use; (ii) in the production trap neutral atoms are ionised by electron impact. Here, contaminant ions are removed from the trap and the ion number is reduced to one. The single ion is then transported to the (iii) spin flip trap. This trap is equipped with a nickel ring to produce a quadratic component of the magnetic field ( magnetic bottle ) superimposed on the homogeneous field of the superconducting magnet. In the spin flip trap the Larmor precession frequency of the bound electron is measured via spin flips which are induced by a microwave field (at 105 GHz). The spin flips of the bound electron can be detected because the axial frequency of the hydrogen-like ion depends on the spin direction due to the presence of the magnetic bottle (Dehmelt s quantum jump method [14]). The production trap as well as the spin flip trap are harmonic traps consisting of five cylindrical electrodes (see figure 2) [15].

3 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap 187 Figure 1. Experimental setup with superconducting magnet and cryogenic Penning trap. Figure 2. Sketch of the cylindrical triple trap configuration.

4 188 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap Figure 3. Mass spectrum of trapped highly-charged ions before (upper curve) and after (lower curve) removal of contaminant ions Creating highly-charged ions Light hydrogen-like ions are created in the production trap by electron impact (see figure 2). The electrons are emitted from a cold tungsten field emission point. The strong magnetic field of the Penning trap confines the electron beam radially. The beam is reflected onto itself by the reflection electrode. After multiple reflections, the diameter of the electron beam increases due to space charge, and finally the electrons hit the anode, which has a carbon coating. Neutral atoms, mostly carbon and oxygen, which are released from this surface, are successively ionised in the production trap. Clouds of ions containing bare carbon and oxygen ions are created applying an electron current of 5 na for 500 ms with an electron energy of 2 kev (see figure 3, upper curve). Unwanted ions are then removed by excitation of their axial eigenmotion and a reduction of the trapping potential for a short period, until only hydrogen-like ions remain in the trap (see figure 3, lower curve) Detection and cooling of trapped ions The trapped ions are nondestructively detected with high sensitivity via the image currents they induce in the trap electrodes by their oscillatory motion [16]. These electronic signals are picked up by LCR resonant circuits, which are tuned to the eigenfrequencies of the ions, and amplified by low noise broadband amplifiers. Through the image currents the trapped particles are in thermal contact with the resonant circuits. In this way the particles are cooled to the temperature of the resonant circuits which are kept at 4 K (resistive cooling). For high-precision experiments the cooling of the trapped ions to low temperatures is of great importance to minimise the line shift and

5 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap 189 Figure 4. Distinct peaks in the cyclotron frequency spectrum representing individual C 5+ -ions, the left graph showing six ions, the right two ions. broadening due to inhomogeneities of the magnetic field and anharmonicities of the electrostatic trapping field Reducing the ion number To reduce the ion number to one, the cyclotron motion of the ions is excited by applying a drive frequency from an rf synthesizer to one half of a split trap electrode. Due to the Coulomb interaction between the trapped ions their axial energy is also increased. When the trapping potential is lowered from 10 V to 2 V, the hot ions boil out of the trap [8]. As soon as only about 20 ions remain in the trap, distinct peaks become visible in the cyclotron frequency spectrum, each peak representing a single ion. The cyclotron frequencies of the individual ions differ because they travel on different cyclotron orbits around the trap center in the slightly inhomogeneous magnetic field (a typical orbit has a radius of 100 µm). Figure 4 shows, as an example, two snap shots of cyclotron frequency spectra with six and then two C 5+ -ions in the trap. When only a single ion is left in the trap, the trapping potential is increased to 10 V Detecting a single ion at T = 4K The cyclotron energy and the axial energy of a single C 5+ -ion are resistively cooled to T = 4 K with a normal conducting resonant circuit (cooling time constant 30 s) and with a superconducting resonant circuit (cooling time constant 200 ms), respectively. The magnetron orbit of the ion is centered with a side band drive at the frequency ν z + ν [17]. It is possible to detect the single C 5+ -ion, which is in thermal equilibrium with the resonant circuit at T = 4 K, nondestructively without exciting its eigenmotions with an external drive. At its axial frequency, the cooled ion acts as a short-circuit parallel to the resonant circuit and reduces the thermal Johnson noise of the circuit [16]. Thus

6 190 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap Figure 5. Measurement of the axial frequency of a single C 5+ -ion in the spin flip trap. The ion is in thermal equilibrium with the resonant circuit at T = 4K. the axial frequency of the single C 5+ -ion is measured as a minimum in the frequency spectrum of the thermal noise of the resonant circuit (see figure 5). The width of this minimum is given by the axial cooling time constant τ z : ν z = 1/2πτ z. The elegance of the described measurement technique lies in the fact that it allows the detection of a single trapped ion and the nondestructive measurement of its axial frequency while it is at a temperature of 4 K. At this low temperature its oscillation amplitudes in the trap are strongly reduced. We plan to use this detection method in measurements of the g-factor of the bound electron in hydrogen-like ions. The Larmor precession frequency of the electron is measured with a single hydrogen-like ion in the spin flip trap. Quantum jumps of the spin of the electron are induced with a microwave field resonant with the Larmor frequency and detected via a small shift of the ion s axial frequency due to the magnetic bottle. The possibility of observing the quantum jumps with the trapped ion at T = 4 K minimises systematic errors due to magnetic field inhomogeneities Storage time of trapped highly charged ions In a long-term test we stored about 34 C 5+ -ions in the trap for 16 days in order to estimate the storage time. In this measurement, the number of trapped ions is determined in an analysis of the minimum in the noise signal of the axial resonant circuit (as described in the previous section). For small ion numbers, the width of

7 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap 191 Figure 6. Determination of the ion number using the axial signal. The graphs show the signals of about 34 C 5+ -ions at the beginning and end of a 16 day storage period. No loss of ions is observed. this minimum in the frequency spectrum depends on the total charge Q and the total mass M of the trapped particles and is proportional to the ion number N: ν z Q2 M N. The ion number N is extracted from the shape of the measured frequency spectrum in a fitting procedure using an analytic formula which represents the trapped ion as an equivalent LC circuit [18]. No loss of C 5+ -ions was observed during the storage period of 16 days (see figure 6). In addition, we sought for charge exchange products of C 5+,suchasC 4+ or C 3+, by recording mass spectra (similar to the measurements shown in figure 3) after storing the C 5+ -ions for 16 days. No charge exchange products were found, although single ions can be detected in such spectra. Taking into account the experimental uncertainty in the determination of the numberofstoredc 5+ -ions a lower limit of six months for the storage time (defined as the 1/e decay time, 95% confidence level) of C 5+ -ions is deduced from this measurement (a similar measurement yielded a lower limit of 3.4 months for the storage time of trapped antiprotons [19]). The experimentally determined lower limit for the ion storage time can be converted to an upper limit for the vacuum pressure of mbar in the UHV chamber using assumed charge exchange cross sections [20]. The long ion storage time clearly demonstrates the effectiveness and the cleanliness of the method of cryopumping, with no external vacuum pump connected to the sealed UHV chamber which is cooled to the temperature of liquid helium (T = 4K). 3. Conclusions and outlook We demonstrated that a single hydrogen-like carbon ion (C 5+ ) can be prepared in a cylindrical Penning trap and cooled to a temperature of T = 4 K with the method of

8 192 M. Diederich et al. / Observing a single hydrogen-like ion in a Penning trap resistive cooling. The single ion is transported between two adjacent potential minima in the cylindrical electrode structure, the production trap and the spin flip trap. The axial frequency of the C 5+ -ion is measured with a nondestructive electronic detection technique, while the particle is in thermal equilibrium with the resonant circuit at a temperature of T = 4 K. We showed that the storage time for C 5+ -ions in the cryogenically pumped UHV chamber is longer than six months. References [1] D. Wineland, P. Ekstrom and H. Dehmelt, Phys. Rev. Lett. 31 (1973) [2] R. Van Dyck, P. Schwinberg and H. Dehmelt, Phys. Rev. Lett. 59 (1987) 26. [3] H. Dehmelt, Rev. Mod. Phys. 62 (1990) 525. [4] W. Nagourney, J. Sandberg and H. Dehmelt, Phys. Rev. Lett. 56 (1986) [5] F. Diedrich and H. Walther, Phys. Rev. Lett. 58 (1987) 203. [6] F. DiFilippo, V. Natarajan, M. Bradley, F. Palmer and D. Pritchard, Phys. Scripta 59 (1995) 144. [7] P. Schwinberg, R. Van Dyck and H. Dehmelt, Phys. Lett. A 81 (1981) 119. [8] G. Gabrielse, D. Phillips, W. Quint, H. Kalinowsky, G. Rouleau and W. Jhe, Phys. Rev. Lett. 74 (1995) [9] D. Farnham, R. Van Dyck and H. Dehmelt, Phys. Rev. Lett. 75 (1995) [10] W. Quint, Phys. Scripta 59 (1995) 203. [11] H. Persson et al., Phys. Rev. A 56 (1997) R2499. [12] K. Hermanspahn et al., Hyp. Interact. 99 (1996) 91. [13] K. Hermanspahn et al., Acta Phys. Pol. 27 (1996) 357. [14] H. Dehmelt, Proc. Nat. Acad. Sci. U.S.A. 83 (1986) [15] G. Gabrielse, L. Haarsma and S.L. Rolston, Int. J. Mass Spectr. Ion Proc. 88 (1989) 319; 93 (1989) 121. [16] D. Wineland and H. Dehmelt, J. Appl. Phys. 46 (1975) 919. [17] D. Wineland and H. Dehmelt, Int. J. Mass Spectr. Ion Phys. 16 (1975) 338. [18] S. Stahl, Diploma thesis, Universität Mainz (1994, unpublished). [19] G. Gabrielse et al., Phys. Rev. Lett. 65 (1990) [20] R. Mann, Z. Phys. D 3 (1986) 85.