Superposition, entanglement, and raising Schrödinger's cat

Experimental control of quantum systems has been pursued widely since the invention of quantum mechanics. In the first part of the 20th century, atomic physics helped provide a test-bed for quantum mechanics through studies of atoms’ internal energy differences and their interaction with radiation. The advent of spectrally pure, tunable radiation sources such as microwave oscillators and lasers dramatically improved these studies by enabling the coherent control of atoms’ internal states to deterministically prepare superposition states, as for example in the Ramsey method (Ramsey, 1990). More recently this control has been extended to the external (motional) states of atoms. Laser cooling and other refrigeration techniques have provided the initial states for a number of interesting studies, such as Bose-Einstein condensation. Similarly, control of the quantum states of artificial atoms in the context of condensed-matter systems is achieved in many laboratories throughout the world. To give proper recognition to all of these works would be a daunting task; therefore, I will restrict these notes to experiments on quantum control of internal and external states of trapped atomic ions. The precise manipulation of any system requires low-noise controls and isolation of the system from its environment. Of course the controls can be regarded as part of the environment, so we mean that the system must be isolated from the uncontrolled or noisy parts of the environment. A simple example of