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b'This work reports on experiments in which antihydrogen atoms have been produced in cryogenic Penning traps from antiproton and positron plasmas by two different methods\\nand on experiments that have been carried out subsequently in order to investigate the antihydrogen atoms.\\n\\nBy the first method antihydrogen atoms have been formed during the process of positron cooling of antiprotons in so called nested Penning traps and detected via a field ionization method. A linear dependence of the number of detected antihydrogen atoms on the number of positrons has been found. A measurement of the state distribution\\nhas revealed that the antihydrogen atoms are formed in highly excited states. This suggests along with the high production rate that the antihydrogen atoms are formed\\nby three-body recombination processes and subsequent collisional deexcitations. However current theory cannot yet account for the measured state distribution. Typical\\nradii of the detected antihydrogen atoms lie in the range between 0.4 \\xb5m and 0.15 \\xb5m.\\nThe deepest bound antihydrogen atoms have radii below 0.1 \\xb5m. Antihydrogen atoms with that size have chaotic positron orbits so that for the first time antihydrogen atoms\\nhave been detected that cannot be described by the GCA-model. The kinetic energy of the weakest bound antihydrogen atoms has been measured to about 200 meV, which\\ncorresponds to an antihydrogen velocity of approximately 6200 m/s. A simple model suggests that these atoms are formed from only one deexcitation collision and methods\\nthat might lead to a decrease of the antihydrogen velocity are presented.\\n\\nBy the second method antihydrogen atoms have been synthesized in charge-exchange processes. Lasers are used to produce a Rydberg cesium beam within the cryogenic Penning trap that collides with trapped positrons so that Rydberg positronium atoms are formed via charge-exchange reactions. Due to their charge neutrality the Rydberg positronium atoms are free to leave the positron trapping region. The Rydberg positronium atoms that collide with nearby stored antiprotons form antihydrogen atoms in charge-exchange reactions. So far, 14 +/- 4 antihydrogen atoms have been detected background-free via a field-ionization method.\\n\\nThe antihydrogen atoms produced via the two-step charge-exchange mechanism are expected to have a temperature of 4.2 K, the temperature of the antiprotons from which\\nthey are formed. A method is proposed by which the antihydrogen temperature can be determined with an accuracy of better than 1 K from a measurement of the time delay\\nbetween antihydrogen annihilation events and the laser pulse that initiates the antihydrogen production via the production of Rydberg cesium atoms. First experiments have\\nbeen carried out during the last days of the 2004 beam time, but the number of detected antihydrogen annihilations has been too low for a determination of the antihydrogen\\ntemperature.\\n\\nTrapped antiprotons have been directly exposed to laser light delivered by a Titanium:Sapphire laser in order to investigate if the laser light causes any loss on the trapped antiprotons. Experiments have shown that no extra loss occurs for laser powers of less than 590 mW. This is an important result against the background of the future plan to confine antihydrogen atoms in a combined Penning-Ioffe trap and then to carry out laser spectroscopy on these atoms, since it reveals that laser light does not cause an increase of the pressure in the trapping region to the extend that annihilations with the background gas become noticeable.\\n\\nThe ATRAP Collaboration plans to precisely investigate antihydrogen atoms. The ultimate goal is to test the CPT-theorem by a high precision measurement of the 1S-2S transition of antihydrogen and a comparison with the precisely known value of the corresponding transition in hydrogen. This thesis presents the achievement of the first\\nstep towards this challenging goal: the production of cold antihydrogen itself.'