Erratum to: “A proposal of quantum logic gates using cold trapped ions in a cavity” (original) (raw)

We propose a scheme for implementation of logical gates in a trapped ion inside a high-Q cavity. The ion is simultaneously interacting with a (classical) laser field as well as with the (quantized) cavity field. We demonstrate that simply by tuning the ionic internal levels with the frequencies of the fields, it is possible to construct a controlled-NOT gate in a three step procedure, having the ion's internal levels as well as vibrational (motional) levels as qubits. The cavity field is used as an auxiliary qubit and basically remains in the vacuum state. 32.80.Lg, The coherent manipulation of simple quantum systems has become increasingly important for both the fundamental physics involved and prospective applications, especially on quantum information processing. Entanglement between two or more subsystems is normally required in order to have conditions for "quantum logical" operations to be performed. Two-level systems are natural candidates for building quantum bits (qubits), which are the elementary units for quantum information processing. We may mention single ions interacting with laser fields [1], atoms and field modes inside high-Q cavities [2], and molecules (via NMR) [3], as quantum subsystems which have shown themselves suitable for coherent manipulation. Regarding the atoms (or ions), both internal (electronic) as well as vibrational motion states may be readily used for performing quantum operations, e.g., a controlled-NOT gate , and a phase gate . It is therefore important to explore other combinations of (experimentally available) physical systems. An interesting set up is a single trapped ion inside a cavity. The quantized field couples to the oscillating ion so that we have three quantum subsystems: the center-of-mass ionic oscillation, the ion's internal degrees of freedom, and the cavity field mode. One of the advantages of such a system is the high degree of control one may achieve in trapped ions, allowing, for instance, long interaction times with the cavity field. A few papers may be found, in which it is investigated the influence of the field statistics on the ion dynamics [5,6], quantum state transfer [7], as well as a scheme to generate Bell-type states of the cavity-field and the vibrational motion . More recently, we may find propositions of other schemes involving the combination of trapped ions with cavity QED [9,10]. On the experimental side, a single trapped ion has been succesfully coupled to a cavity field , an important step towards the use of trapped ions for quantum computing and quantum communication purposes .