Atomic Quantum Computer

The current proposals for the realization of quantum computer such as NMR, quantum dots and trapped ions are based on the using of an atom or an ion as one qubit. In these proposals a quantum computer consists from several atoms and the coupling between them provides the coupling between qubits necessary for a quantum gate. We discuss whether a {\it single} atom can be used as a quantum computer. Internal states of the atom serve to hold the quantum information and the spin-orbit and spin-spin interaction provides the coupling between qubits in the atomic quantum computer. In particular one can use the electron spin resonance (ESR) to process the information encoded in the hyperfine splitting of atomic energy levels. By using quantum state engineering one can manipulate the internal states of the natural or artificial (quantum dot) atom to make quantum computations.