CPT symmetry tests with cold math formula and antihydrogen

Authors


  • This is really huge, comparable to the mass of a bacteria

  • The highest energy from the largest accelerator (LHC) is ∼104GeV in the center of mass frame, corresponding to ∼108GeV in the laboratory frame. Even in the case of cosmic rays, it can be as high as 1011GeV.

Corresponding author E-mail: yasunori@riken.jp

Abstract

Precision comparisons of the properties of particles and their corresponding antiparticles are highly relevant because the Standard Model of elementary particle physics, a local, Lorentz-invariant field theory, is necessarily symmetric with respect to the combined CPT operation. This symmetry defines exact equality between the fundamental properties of particles and their anti-images. Any measured and confirmed violation constitutes a significant challenge to the Standard Model. Recent results of different CPT-tests are summarized, with emphasis to the high-precision measurement of the magnetic moment of the proton and the antiproton, as well as the precision investigation of antihydrogen ground state hyperfine splitting.

1 Introduction

Symmetries are an essential concept in modern physics particularly in the Standard Model (SM), and are categorized into global and local symmetries, which are related to conservation laws and forces, respectively [1]. Charge conjugation (C), parity operation (P), and time reversal (T) are the components of discrete symmetry transformations. The CPT symmetry, simultaneous application of all three transformations, is supposed to be the most fundamental symmetry in physics. Actually, it's conservation is theoretically guaranteed by local quantum field theories constructed on a flat space-time, which fulfil the condition of Lorentz invariance and unitarity [2]. Considering the fact that P [3], CP [4], and T [5] have already been found to be violated, the CPT symmetry is the last one still evading our pursuit. If some of the conditions which back-up CPT are not satisfied, the symmetry might be violated, e.g., when space-time is curved by the gravitational interaction, and/or, non-local interactions play a role. It is noted, that the physical origin of the violations of P and CP symmetries in weak interactions is not yet understood in detail [6].

1.1 Gravitational interaction

The Planck mass math formula given by math formulaGeV/c2) is the critical mass of a particle, which in itself becomes a black hole, where ℏ is the Planck constant divided by 2π, c the speed of light, and G the gravitational constant1. When we consider influences of the gravitational interaction on a physics system in question, a possible measure for CPT violation could be the ratio of the particle mass (m) involved in the system and the Planck mass, math formula, math formula. The corresponding energy of the Planck mass is far too high to be accessible by accelerator techniques known until now2, and will probably never be reached even in the distant future. It would therefore make sense to reconsider our strategy in studying the fundamental laws of nature not only by pushing to higher and higher energy, but instead by adopting a softer and humbler way with higher sensitivity. We call such a complementary approach as listen to the whisper of nature. For the proton (p)/antiproton (math formula) system, math formula, which corresponds to math formulaGeV. Although this quantity looks extremely small, in terms of a frequency it corresponds to ∼10 kHz, which might be resolvable, depending on the physical quantities targeted.

1.2 Non-local interaction

Another condition which might violate CPT is a non-local interaction. Actually, the string theory is in its nature non-local, which may provide some proactive prediction to violate CPT [7]. Other Lorentz invariant non-local CPT violating models are proposed and discussed in [8, 9].

1.3 SME

The Standard Model Extension (SME), developed and extended considerably by Kostelecky and his colleagues, is constructed by adding possible CPT violating interactions artificially to the standard CPT conserving Lagrangean of the SM. Based on this approach physical quantities sensitive to CPT violation are discussed3 [10-12]. One of the main statements of the SME is, that CPT violation should be tested by comparing quantities with respect to an absolute energy scale, not by comparing relative accuracies. In general, it would not make much sense to compare different quantities with relative accuracies4.

1.4 Relation with Big Bang

The Big Bang scenario is quite successful and powerful in explaining various astronomical observations such as Hubble's law, cosmic microwave background radiation, abundance of primordial elements, galactic evolution and distribution, etc. On the other hand, it is still a mystery how matter survives escaping full annihilation with antimatter, because it is generally assumed that the same amount of matter and antimatter existed at the early stage of the hot universe. One interesting idea is that the universe might be a patchwork consisting of distinct regions of matter and antimatter still keeping the same amount of both, and we are just located on one of the matter patches. If this is the case, the universe as a whole is symmetric with respect to matter and antimatter. However, in this scenario the amount of annihilation near regional matter-antimatter boundaries is not negligible, and the observed cosmic γ ray spectrum would be considerably distorted, depending on the size of the patches. Actually, possible energy spectra were simulated as a function of the patch size. By comparing astronomical observations with these simulations, it was concluded that the size of the patch should be comparable to the size of the entire universe. This is considered to be rather unlikely, and thus, a matter-antimatter symmetric universe is unfavored [13]. The most recognized model to explain the matter dominant universe was proposed by Sakharov. It requires (1) baryon number non-conserving processes, (2) C- and CP violation, and (3) interactions far from thermal equilibrium conditions [14]. Although the CP symmetry is experimentally found to be violated for neutral mesons, which qualitatively supports the idea of Sakharov, the level of violation which is known is by far too small to explain the amount of matter observed in the present universe. Considering these facts, although speculative, CPT violation might be another possibility to drill a hole in the mystery of the matter dominant universe (see math formula, refs. [8, 15, 16]).

2 Experiments to test CPT Symmetry

An important consequence of the CPT symmetry is that the mass, the total lifetime, the absolute values of the charge and the magnetic moment of an antiparticle should be exactly the same as those of the corresponding particle. In addition, the spectroscopic properties of a complex anti-particle such as antihydrogen should again be exactly the same as those of the corresponding complex particle such as hydrogen. These facts provide potential schemes to test the CPT symmetry. Particularly when the particle is stable, observation time can be infinitely long, and accordingly, the mass/energy of particle conjugates in question can potentially be determined with arbitrarily high precision. In usual high precision measurements, experimental results are compared with predictions of precise and reliable theories taking into account all known interactions trying to find some finite deviations. Once successful, the residue can be attributed to a hidden interaction and/or to some important dynamics which need to be considered. In the case of CPT symmetry tests, the taste of the experiment can be qualitatively different from other high precision experiments described above, because detailed theoretical predictions are NOT necessary. As soon as a difference between matter and antimatter is observed, CPT violation is automatically confirmed. The research can be done purely experimentally, i.e., the CPT test is performed and concluded in a model independent way. On the other hand, no quantitative predictions are available from theory, and thus, experimentalists need to fix various experimental parameters as the physical quantities to be measured as well as their precision in a blind way, employing their full intuitions and sixth sense. In the following subsections, experiments on (K0, math formula), p/math formula and H/math formula are summarized and discussed, with special emphasis on p/math formula magnetic moments and H/math formula ground state hyperfine splittings.

2.1 math formula

As is well-known, research on math formula and math formula revealed for the first time that the CP symmetry is violated, which was one of the key findings to ignite theory to predict a three generation quark model [17]. At the same time, the CPT symmetry was reported to be verified with an accuracy as high as math formula [18]. Although this is often cited as the most stringent test of the CPT symmetry, there is still a reservation on the way how it is discussed. In terms of energy, math formulaGeV is obtained. Kobayashi et al. discussed that this small value just implies that CPT violating interaction, if any, is very weak compared to the strength of QCD. Considering the fact that math formula requires both CP and CPT violations, it is more appropriate to compare the strength of possible CPT violation to the strength of CP violation [19]. Actually, the CP violation level of K0 and math formula is Immath formulaGeV, i.e., the CPT violation could still be as large as a few % of the CP violation [20]. It is also noted that the accuracy above is comparable to the level of possible violation related with the gravity discussion (see Sec.1). It is evident that the experiments should be done with higher accuracy and also complementary experiments are necessary.

2.2 math formula and math formula related experiments

Proton (p) and antiproton (math formula), as well as hydrogen (H) and antihydrogen (math formula) are all stable, and thus meet the requirements to be observed for macroscopic time-scales and thus, perform high resolution spectroscopy.

Table 1 shows several comparisons of properties of conjugated particles such as the mass, the charge, and the g-factor for (math formula) and (p, math formula). As a reference, some information of (math formula), (p, e), and (math formula) conjugates is given as well. It is seen, that the CPT symmetry of these particles with respect to mass and charge has already been tested to the level of 10math formula, corresponding to math formulaGeV for p/math formula and math formulaGeV for math formula. The g-factor of the (p, math formula) pair is known with a precision of 4.4· 10−6. Actually, the g-factor measurements of an isolated proton [21] or an antiproton [22] just became possible very recently (See Sec. 3.2).

Table 1. Differences of mass, charge, and g-factor between electron and positron, and between proton and antiproton [18, 21, 38]
 math formulamath formulamath formula
e vs e+math formula10 −9math formula10 −8(−0.5 ± 2.1) × 10−12
p vs math formulamath formula10−9math formula 10−9math formula 10−6
math formula vs math formula  math formula
p vs math formula math formula 
n vs math formula(9 ± 6) × 10−5

Table 2 shows spectroscopic properties of the hydrogen atom, which are among the most precisely known quantities in atomic physics. The 1S-2S and ground state hyperfine transitions are experimentally determined with the fascinating precision of math formula (∼ 10 Hz) and math formula (∼1mHz), respectively [23]. On the other hand, as shown in Table 2, for the 1S-2S transition the theoretical accuracy is limited to 10−11 (10 kHz) and in case of the ground state hyperfine splitting to 10−5 (10 kHz). Once a math formula beam is available, an experiment can be conducted which would beat the limit of theoretical precision by two orders of magnitude. In the non-relativistic framework, the 1S-2S transition energy of hydrogen is given by

display math(1)

where math formula and math formula are the electron and proton masses, respectively, and α the fine structure constant defined by math formula, where math formula and math formula are the electron and proton charges, respectively, ε0 the vacuum dielectric constant, and c the speed of light. The electron mass defines the transition frequency at leading order, while the proton mass contributes at the level of 10−3. Taking relativistic and QED effects into account brings shifts at the 10 ppm level. The present theoretical limit of 10−11 is due to the ambiguity on the proton charge radius. In the case of the ground state hyperfine transitions, it originates from the interaction between the magnetic moments of the proton and the electron, i.e., this effect increases with the overlap of proton and electron wave-functions, like in the case of S states, particularly 1S state. The transition frequency between the singlet (F=0) and the triplet (F=1) states of hydrogen in its ground state is given by

display math(2)

which approximates the proton as a point-like particle. Here math formula and math formula are the magnetic moments of electron and the Bohr magneton, respectively, and math formula and math formula are the magnetic moments of proton and nucleon, respectively. The hyperfine transitions are directly proportional to the magnetic moment of proton as well as to that of electron. Thus, from a measurement of the ground state hyperfine splitting of math formula an independent value for the magnetic moment of math formula is obtained (see also section 3. 2). This is in contrast with 1S-2S transition, where the electron mass primarily determines the transition energies. Considering that math formula is −1.0011596521811 and math formula is 2.7928473565, the observed transition frequency can be reproduced with a precision of 10−5, which is further improved to 3.5math formula when the charge and magnetization radius of proton is taken into account. Again, the prediction level is limited by the uncertainty of charge and magnetization distribution of the proton [24]. Considering the fact that the 1S-2S transition and the hyperfine transitions are both reproduced by the CPT conserving theories to the level of 10 kHz, any experiment which aims for the discovery of the CPT violation should exceed this accuracy. Until now, it is not known which transition (i.e., 1S-2S or hyperfine) is more sensitive for the CPT symmetry test. However, in the first order perturbation theory of the SME, in case of the 1S-2S transition the CPT violating energy shift cancels exactly. Thus, higher sensitivity to CPT violation is expected in case of the hyperfine transition [10]. In addition, a beam-based hyperfine transition experiment has higher potential to reach better resolution than 1S-2S transition of trapped math formula. It is noted that the hyperfine transition measurements of math formula and magnetic moment measurement of the bare math formula yield complementary and important information on the magnetic moment of math formula, since the hyperfine transition reflects the magnetization distribution inside math formula probed by a positron and the spin transition frequency of bare math formula reflects the overall magnetic moment probed by a macroscopic external magnetic field.

Table 2. Spectroscopic properties of hydrogen
 experiments (Hz)math formulamath formula
math formula2,466,061,413,187,035 (10)4 × 10−151 × 10−11
math formula1,420,405,751.7667 (9)6 × 10−13(3.5 ± 0.9) × 10−6

3 Precision Investigation of the Proton and the Antiproton

3.1 (Anti)proton charge and mass

The charge-to-mass ratios math formula of the p and the math formula were compared with a fractional precision of 9math formula, which corresponds to math formula [25]. Assuming math formula, the accuracy in energy is about 0.08 eV. This fascinating test of the CPT symmetry was reported by the TRAP collaboration, which compared the free cyclotron frequencies math formula of an H-ion and a single antiproton stored in a cryogenic Penning trap setup. Such a trap is a superposition of a homogeneous magnetic field B in the axial direction and an electrostatic quadrupolar potential. The trajectory of a particle stored in such a superposition of electric and magnetic fields is shown in Fig. 1.

Figure 1.

Trajectory of a single particle in a Penning trap, which is a superposition of three uncoupled harmonic oscillators.

It can be described as the superposition of three uncoupled harmonic oscillators, one at the modified cyclotron frequency math formula, which is math formula slightly modified by the trapping potential, another at the axial frequency math formula, and a third one at the magnetron frequency math formula. The free cyclotron frequency is obtained by measuring math formula and math formula, and application of the so called invariance theorem [26]

display math(3)

The eigenfrequencies are measured non-destructively via image current detection. To achieve this high precision measurement several pioneering techniques were invented, as catching of antiprotons from the CERN Low Energy Antiproton Ring (LEAR) [27], electron cooling of antiprotons [28], and trapping of a single antiproton for arbitrarily long time [29].

In addition to these experiments, high precision laser spectroscopy of exotic math formulaHe+ atoms has achieved impressive progress. These experiments allow for the measurement of the antiproton related Rydberg constant, which is proportional to math formula. Thus, by combining the results of laser spectroscopy with the measured charge-to-mass ratio, the mass and the charge of the antiprotons can be extracted independently, and compared with those of the proton. Recently, Hori et al. reported on an agreement of both values at the sub-ppb level [30]. It is an amazing fact that once the used laser spectroscopy techniques slightly improve, the mass of the antiproton can be determined with higher accuracy than that of the proton. It is noted that in order to extract mass and charge of antiprotons, the experimentally obtained transition frequencies have to be compared with challenging theoretical three body calculations. For CPT tests at even higher precision, theoretical methods have to be improved significantly.

3.2 (Anti)proton magnetic moment

Among the numerous comparisons of different fundamental particle properties, one quantity has not yet been compared with high precision: the magnetic moment of the proton math formula and the antiproton math formula. Here, math formula, where math formula is the Landé g-factor, and math formula the (anti)proton charge-to-mass ratio. The magnetic moment of the proton is known with a fractional accuracy of 8.2math formula [31]. This value is based on hyperfine spectroscopy data of an atomic hydrogen maser in a magnetic field, from which the magnetic moment ratio of the proton and the electron bound in atomic hydrogen math formula was extracted at that level. The g-value of the free proton

display math(4)

is calculated, where the g-factor of the electron math formula, and the proton-to-electron mass ratio math formula are known at a level of math formula [32] and math formula [33], respectively. The theoretical correction terms math formula and math formula are reviewed in [34, 35] and are also known at the level math formula, resulting in [36]

display math(5)

limited by the experimental precision achieved in the hydrogen-maser experiment [31]. In contrast, the magnetic moment of the antiproton is only known with moderate precision. Currently two collaborations, a part of ATRAP and BASE, are pushing their efforts to measure the (anti)proton magnetic moment with sub-ppb precision. These experiments are based on spectroscopy with single particles stored in a Penning trap at 4 K. A major step towards this goal was achieved in 2011. Spin flips of a single trapped proton were observed for the first time [21, 37]. Recently, diSciacca et al. (ATRAP) reported on a 4.4math formula measurement of the antiproton magnetic moment [22], which corresponds to a 680-fold improvement of the formerly best value [39]. In this experiment the particle's magnetic moment was measured in units of the nuclear magneton math formula

display math(6)

by determination of the free cyclotron frequency math formula, and the spin precession frequency math formula of a single antiproton. While the measurement of math formula is straight forward [40], the determination of the spin precession frequency math formula is a major challenge. It is based on the application of the continuous Stern-Gerlach effect, which has already been applied in the widely recognized math formula comparisons of the electron and the positron [41]. However, these measurements involved magnetic moments at the level of the Bohr magneton. In contrast the magnetic moments of the proton/antiproton system are at the level of the Nuclear magneton, which is about 660 times smaller. This complicates the (anti)proton magnetic moment measurement significantly. A magnetic inhomogeneity

display math(7)

is superimposed to the Penning trap, where B2 characterizes its strength. This adds a spin dependent magnetic potential math formula to the axial electrostatic potential, and consequently, the axial oscillation frequency becomes spin dependent. Compared to a magnetic moment-down particle, a magnetic moment-up particle has a lower oscillation frequency math formula. Thus, the determination of the spin eigenstate is reduced to a non-destructive frequency measurement. The spin precession frequency math formula is determined by the following sequence: first the axial frequency is measured, and subsequently a spin flip is driven by a magnetic radio-frequency drive with field vector math formula perpendicular to B0 at a frequency math formula, which is close to the Larmor frequency math formula. Afterwards the axial frequency is measured again. The detection of an axial frequency shift indicates a spin quantum jump. By repeating this sequence for several 100 times and different drive frequencies math formula, the spin flip probability is obtained as a function of math formula. From the well understood line-shape the Larmor frequency can be extracted with high precision. However, the axial frequency shift induced by an (anti)proton spin flip, is

display math(8)

which is for typical experimental parameters (math formula 600 kHz to 1 MHz) in the order of a few hundred nHzmath formula. Thus, to obtain a clearly detectable spin flip induced axial frequency jump, a very strong B2 (300000 T/m2) has to be used [21, 38]. Under these extreme conditions a spin quantum jump shifts the axial frequency by about 150 mHz to 200 mHz out of 600 kHz to 1 MHz.

The strong magnetic inhomogeneity constitutes a major challenge. In addition to the spin magnetic moment it couples as well the radial magnetic moments of the cyclotron mode and the magnetron mode to the axial frequency, which is shifted by

display math(9)

where math formula and math formula are the quantum numbers of the modified cyclotron and the magnetron mode, respectively. A cyclotron quantum jump math formula corresponds to a radial energy change of math formulaneV and causes an axial frequency shift of math formulamHz. A transition of the magnetron quantum number math formula leads to math formulaHz. Changes of both radial quantum numbers math formula are due to easily driven electric dipole transitions. Spurious electrical field noise with amplitudes in the order of only a few 10 nV· mmath formulaHzmath formula cause fluctuations of math formula, which are large enough to avoid the unambiguous detection of single (anti)proton spinflips. However, with the axial frequency stability reached by the two experiments [21, 38] it was possible to measure the (anti)proton magnetic moment in the strong B2 by means of a statistical detection technique. Once spin flips are driven, the corresponding axial frequency shifts math formula add up to the axial frequency fluctuation math formula, which is defined as the rms-value of the difference of two subsequent axial frequency measurements math formula, in a statistical way

display math(10)

By measuring math formula for different drive frequencies math formula, the spin flip probability math formula is obtained as well. The result of the first Larmor resonance curve ever measured with this technique [21] is shown in Fig. 2. The asymmetry of the resonance curve is easy to understand. While a spin flip is driven, the particle is in contact with the axial detection system, which leads to Boltzmann distributed fluctuations of the particle's axial energy math formula. As a consequence the Larmor frequency fluctuates since

display math(11)

and thus, the resonance is a convolution of the unperturbed spin transition-line with the asymmetric Boltzmann profile math formula, where math formula is the temperature of the axial detection system. From a best fit to these data math formula is obtained with 100 ppm precision. With an improved apparatus BASE obtained meanwhile a Larmor frequency resolution of 1.8math formula [42], while the Harvard group reached a precision of 1.7math formula [38]. For the determination of the g-factor, the cyclotron frequency is measured by using the same principle as in the case of the Larmor line, but with an electrical dipole drive tuned to the modified cyclotron frequency. The drive amplitude is chosen weak enough to avoid a significant increase of math formula, but it clearly affects the axial frequency fluctuation as a function of the drive frequency. Again math formula is obtained from a best fit and

display math(12)

is extracted. The precision of this value is limited by the cyclotron frequency determination [42]. However, another order of magnitude can be gained easily by more accurate sampling of the cyclotron resonance line. This strategy was applied by di Sciacca et al., who obtained [38]

display math(13)
Figure 2.

Larmor resonance curve measured with a single trapped proton.

By further improvement of the experimental setups the results of the statistical detection method may be improved by another order of magnitude, but as a matter of principle a limit is set by the strong magnetic bottle which produces an unavoidable line-width. To reach even higher precision, a group at Mainz developed the elegant double-trap method [43], in which the precision frequency measurements and the detection of the spin state are separated to two traps: a precision trap (PT) with a very homogeneous magnetic field, and an analysis trap (AT) with the strong superimposed magnetic inhomogeneity. Such a setup is shown in Fig. 3. The two traps are connected by transport electrodes. Voltage ramps applied to these electrodes are used to shuttle the particle between the traps. A magnetic moment measurement starts with the determination of the spin state in the analysis trap. Subsequently the particle is transported to the precision trap, where the cyclotron frequency is measured, while a spin flip drive is injected to the trap. Afterwards the particle is transferred back to the AT and the spin state is analyzed again. This measuring sequence is very similar to the g-factor measurement which has already been described above, with one major difference: Spin flips are driven in a magnetic field which is about a factor of 100000 more homogeneous than in the analysis trap. This reduces the line-shape dramatically and boosts experimental precision. This method has been applied successfully in experiments for the high precision determination of the magnetic moment of the electron bound to hydrogen-like ions [44, 45], for precise tests of bound state quantum electrodynamics. In these experiments precisions at the level of 0.5 ppb were achieved. The successful application of this method to measure the magnetic moment of the antiproton would provide a 1000-fold improved test of the CPT symmetry with baryons.

Figure 3.

Schematic of a double Penning trap setup [21]. The system consists of two Penning traps which are connected by transport electrodes. The central ring electrode of the analysis trap is made of ferromagnetic material. The lower graph shows the magnitude of the magnetic field along the z-axis. For further details see text.

To apply this technique, single spin flip resolution is required, i. e., it is crucial to clearly identify the spin eigenstate of the particle in the analysis trap. So far this was not possible due to the limited axial frequency stability, but recently important progress towards a first application of this technique has been reported [46]: single spin flips were clearly resolved for the first time with a significantly improved apparatus and the application of an elegant Bayesian analysis. The spin state of a single trapped proton was identified with a fidelity of about 90math formula. Based on these results BASE demonstrated the application of the double Penning-trap method [47] for the first time, which paves a path to measure the magnetic moment of both, the proton and the antiproton, with ppb precision.

4 Precision Spectroscopy of Antihydrogen

4.1 math formula synthesis and manipulation

Synthesis of antihydrogen (math formula) atoms has been intensively studied in the last decades [48, 49] to make stringent tests of the CPT symmetry via high precision spectroscopy either of the 1S-2S transition [50, 51] or of ground state hyperfine transitions [52-54]. Recently, studies on the gravitational interaction of antimatter (math formula) and matter (the earth), the so-called weak-equivalence principle, were also proposed [55, 56]. The cold antihydrogen research celebrated the first milestone in 2002, when ATHENA and ATRAP successfully synthesized cold math formula atoms in a uniform magnetic field [57, 58]. Both groups aimed for 1S-2S high precision laser spectroscopy, and accordingly the next critical step was to prepare ultra-cold math formula atoms (< 1 K) in the low-field-seeking states and to trap them in the Ioffe-Pritchard trap or a variant of it having minimum B field configurations [59, 60]. math formula atoms were not really controlled, and the synthesis was only confirmed by annihilation signals, math formula, it was a kind of archaeological approach, which confirmed that math formula atoms existed some time before the detection of their annihilation. After several years of experimental developments, ALPHA realized the second milestone in 2010, the success of trapping 39 math formulas [61]. Just one month later, the ASACUSA-CUSP group reported on the successful synthesis of math formula atoms in a non-uniform magnetic field, a so-called cusp trap, which was a major step to extract an math formula beam to a field-free region for high precision microwave spectroscopy. This is essential for high resolution microwave spectroscopy of math formula hyperfine transitions [62] (see Sec 4.2). In 2011, ALPHA succeeded in trapping antihydrogen atoms for more than 1000s [63]. In presence of a magnetic field, the ground state hyperfine levels of H/math formula split into four sub-states, as shown in Fig. 4. Two of them become higher with increasing magnetic field, i.e., they are attracted towards lower magnetic fields, and are named as low-field seeking (LFS) states. The other two levels are lowered, i.e., they are attracted towards high magnetic fields, and are named high-field seeking (HFS) states. Figure 4 also shows, that the potential energy corresponding to the magnetic field difference of 0.2 T amounts to ∼3GHz. In other words, even for a magnetic trap with a magnetic field difference of 1 T, the trap depth is only about 0.7 K (∼14GHz).

Figure 4.

Frequency diagram of 1S-2S and ground state hyperfine transitions together with the variation of hyperfine levels as a function of magnetic field.

4.2 Cusp trap scheme to extract math formula for microwave spectroscopy

For high resolution microwave spectroscopy, a weak and uniform magnetic field is essential. In order to make this practically feasible, a potential scheme had been invented employing a pair of anti-Helmholtz coils [52], which is called the cusp trap scheme. This opens for the first time a path to realize high precision microwave spectroscopy of antihydrogen ground state hyperfine transitions [52, 62]. Figure 5 shows a conceptual drawing of the experimental setup, which consists of the unique cusp trap (the combination of superconducting anti-Helmholtz coils and a stack of multiple ring electrodes (MRE)), a microwave cavity, a sextupole magnet, and an math formula detector. The cusp trap provides the minimum B field configuration still maintaining axially symmetric magnetic and electric fields, which enables stable manipulation of both math formulas and math formulas such as trapping, cooling, compression, and mixing [64, 65]. Further, once math formula atoms are formed by mixing math formula and math formula in the cusp trap, math formula atoms in low-field-seeking (LFS) states are preferentially focused along the cusp trap axis whereas those in high-field-seeking (HFS) states are strongly defocused, resulting in the formation of an intensity-enhanced spin-polarized math formula beam [52]. The microwave cavity is installed downstream of the cusp trap along the beam line in a weak, highly uniform magnetic field, which is carefully shielded from parasitic stray fields. A preliminary simulation revealed that the spin-polarization of a 50 K math formula beam amounts to about 30 % [66]. The microwave induces hyperfine transitions from LFS to HFS states when the microwave frequency matches with one of transition frequencies. The sextupole magnet sorts out math formula atoms in HFS states from those in LFS states. By recording the antihydrogen signal as a function of the drive frequency applied to the microwave cavity, the hyperfine structure becomes accessible. Figure 6(a) schematically shows the central part of the setup. It consists of the math formula catching trap [67], the e+ accumulator, the cusp trap, and the 3D track detector to monitor math formula/math formula annihilation near the cusp trap.

Figure 5.

A conceptual experimental setup for the ground-state hyperfine transition measurements of math formula atoms with the cusp trap (see the text for more details).

Figure 6.

(a) A schematic drawing of the present experimental setup, which consists of the math formula (math formula) catching trap, the compact positron (e+) accumulator, the cusp trap for math formula synthesis, the 3D track detector, and the math formula detector downstream of the cusp trap. (b) The central part of the cusp trap, which consists of a superconducting solenoid coils, a cryogenic UHV bore tube, and an MRE installed in the bore tube.

Antiprotons of 5.3 MeV from the Antiproton Decelerator (AD) at CERN are extracted into the ASACUSA area, slowed down to math formula by a radio frequency quadrupole decelerator (RFQD). Subsequently they are injected into the math formula catching trap. Typically, math formulas are accumulated and electron-cooled. The math formula cloud is then radially compressed [68] which ensures efficient particle transfer to the cusp trap. Figure 6(b) shows the central part of the cusp trap structure, which consists of superconducting coils (math formula=2.7 T), a UHV cryogenic bore tube (6K), an MRE at the center of the coils. Figure 7 shows an example of the math formula intensity variation since the start of the mixture of 3 math formulas in 3 × 106 positrons [62]. The number increased in the first 30 s and then slowly decreased in the next 80 s yielding totally 70 events per mixture. The total number of math formula atoms in high Rydberg states was estimated to be about 7 × 103 per mixture.

Figure 7.

The number of field-ionized antihydrogen atoms accumulated in the field ionization trap. For this measurement the trap was opened every 5 s.

As already mentioned in section 2.2, from a measurement of the ground state hyperfine transition frequency at the ppm level together with an independent measurement of the magnetic moment of the antiproton at the same level (see section 3.2), constraints on antiproton substructure are obtained.

4.3 math formula trapping for 1S-2S spectroscopy

In contrast to the beam concept applied in ASACUSA, ALPHA and ATRAP plan to perform spectroscopy with trapped antihydrogen atoms. Figure 8 (a) schematically shows the central part of the ALPHA setup used to synthesize and trap math formula atoms [61]. The octupole coil provides a strong magnetic field gradient in the radial direction, and the pair of mirror coils produce a field gradient in the axial direction. A magnetic bottle is formed by the combination of these fields, which is an Ioffe-Pritchard type trap but employing an octupole coil instead of a usually used quadrupole. The magnetic field difference is about 0.7T, which can trap antihydrogen at temperatures up to 0.5 K. It is noted that the azimuthal uniformity of the usual Ioffe-Pritchard trap near the magnetic field axis is poor, which results in an instability in storing math formulas and positrons, the ingredients of antihydrogen. In order to match the interaction energy of math formulas and math formula sensitively, so that potentially colder antihydrogen is synthesized, a so-called auto-resonance scheme had been employed. This can exclusively induce a center of mass motion, which doesn't affect the internal temperature of the math formula cloud [69].

Figure 8.

(a) A schematic drawing of antihydrogen synthesis and trapping region. The atom-trap magnets, the modular Si annihilation detector and some of the Penning trap electrodes are shown. An external solenoid (not shown) provides a 1 T magnetic field for the Penning trap. (b) Measured t-z distribution for annihilations obtained with no bias (circles), left bias (triangles), right bias (inverted triangles). The gray dots are from a numerical simulation of antihydrogen atoms at ground state. The simulated atoms have a maximum kinetic energy of 0.1 meV.

When the antihydrogen synthesis reactions are more or less over (about 1s after the mixing started), math formulas and positrons are cleaned up by applying voltages on the MRE. Then, the octupole coil and the pair of mirror coils are quenched to open the magnetic bottle. As soon as the magnetic bottle is opened, trapped math formulas are released, if any, and annihilate hitting the inner-wall of the MRE near the magnetic bottle. The red inverted triangles, the blue triangles, and the green circles in Fig. 8(b) shows such events as functions of the annihilation position and the time of annihilation since the quench of the magnetic bottle. Different symbols correspond to different electric fields applied. As is seen, the annihilation position did not depend on the electric field configurations. The fine gray dots in Fig. 8(b) show the results of simulation assuming antihydrogen atoms were trapped in the magnetic bottle. Repeating such runs, totally 38 trapped antihydrogen events were identified in 335 trials. The ATRAP collaboration also reported on successful trapping of math formula [70].

The next step is to laser-cool trapped math formulas and to make laser spectroscopy. The Zeeman broadening due to magnetic field distribution in a magnetic bottle affects the spectroscopic resolution, which could amount to as high as 106 Hz. Donnan et al. reported that math formulas can be cooled just by a one directional pulsed laser as low as 20 mK [71], which would improve resolution. Recently, hyperfine transitions of math formula trapped in a magnetic bottle have been successfully induced by a microwave drive in the right frequency range [72].

5 summary

In this article a brief motivation on tests of the CPT symmetry and their significance in physics was given. Particularly the experimental progress on tests with math formula and math formula was reviewed. Penning trap based experiments to measure the magnetic moments of a single proton and an antiproton have recently become possible, and in preamble experiments a precision in the order of 10−6 was achieved. The recently resolved single proton spin flips, and the first demonstration of the double Penning trap technique with a single proton are a major step towards another factor of 1000 improvement.

A cusp trap scheme for the efficient extraction of a spin-polarized math formula beam to a magnetic-field-free region has been developed. In the cusp antihydrogen atoms were synthesized successfully. This development allows for the first time a high precision ground state hyperfine spectroscopy of math formula. By combining these quantities, constraints on the internal structure (magnetization distribution) of math formula are obtained, which constitutes another stringent test of the CPT symmetry. Successful trapping of math formula in a magnetic bottle has been demonstrated recently, which will soon allow first laser spectroscopy of the 1S-2S transition of antihydrogen atoms. Further cooling of trapped antihydrogen atoms would become an important issue to realize high resolution spectroscopy. Cold math formula research is now at a stage where first experiments to precisely investigate fundamental symmetries can start.

  1. 1

    The SME also suggests sidereal-variation tests in the matter sector.

  2. 2

    For example, as shown in table 1, the relative precision of 1S-2S transition of hydrogen is reported to be math formula. If the hydrogen mass is used in the denominator, this quantity may become math formula

  3. 3

    This does not necessarily exclude a possibility that the lifetime of a specific decay channel can be different between the paired particle and antiparticle

  4. 4

    The charge radius extracted from the pmath formula Lamb shift measurement [24] is reported to be 5σ away and smaller than the currently accepted CODATA value.

Biographies

  • Image of creator

    Yasunori Yamazaki was a professor of the University of Tokyo from 1993 to 2011. In 1997, he was joint-appointed as a Chief Scientist of RIKEN, and then continues his carrier at RIKEN as a Distinguished Senior Scientist from 2011. He was the International Chairperson of ICPEAC from 2005 to 2007. He has been studying fundamental physics via antimatter as well as radiation biology via micro irradiation on living cells. He was awarded the Fellow of American Physical Society in 2011, 15th Matsuo Foundation Hiroshi Takuma Memorial Award in 2011, and 52nd Toray Science and Technology Prize in 2012.

  • Image of creator

    Stefan Ulmer received his PhD in 07/2011 at the University of Heidelberg for the first observation of spin flips with a single trapped proton. As a post-doctoral fellow he joined the ASACUSA CUSP collaboration and worked on the production of a polarized antihydrogen beam. Since 04/2012 he is leading a RIKEN initiative research unit as well as the international BASE collaboration at CERN, which intends to measure the magnetic moment of the antiproton with high precision.