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In the system with a two-level ion confined both in a linear trap and in a high-Q single-mode cavity, we present a simple scheme to realize the basic two-qubit logic gates such as the quantum phase gate (QPG), the SWAP gate and the controlled-NOT (CNOT) gate beyond the Lamb–Dicke (LD) limit. We realize the three kinds of two-qubit quantum phase gates, i.e. QPG operation involving the cavity mode as well as the vibrational mode of the trapped ion, QPG operation involving the internal states as well as the vibrational mode of the trapped ion and QPG operation involving the internal states of the trapped ion as well as the cavity mode. The controlled-NOT gate can be implemented from a QPG operation through a rotation of the second qubit before and after the QPG operation. We can also perform the SWAP gate operation involving the ionic internal states of the trapped ion and the two-mode bosonic basis. The logic gates involving the cavity mode as well as the vibrational mode of the trapped ion are insensitive to spontaneous emission, and the logic gates involving the internal states as well as the vibrational mode of the trapped ion are insensitive to the decay of the cavity, which is an important feature for the practical implementation of quantum computing. Neither the LD approximation nor the auxiliary atomic level is needed in our scheme. Experimental feasibility for achieving our scheme is also discussed.

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Considering a double JC model with different coupling constants, we investigate the entanglement between the two two-level atoms, and discuss dependence of the atomatom entanglement on the different coupling constants, and the detuning between the atomic transition frequency and the cavity field frequency. The results show when = δ/g is small, with the increase of the relative difference of the two atom-cavity coupling constants γ , the atom-atom entanglement periodically evolves with the amplitude slowly and periodically modulated. What's more interesting is that long-lived entanglement between the two atoms can be obtained when atom A non-resonantly interacts with the cavity field a, and atom B has no coupling with the cavity field b. In this case, the concurrence C AB (t) of the two atoms evolves in form of cosine, and is invariant and equals the initial value when far off resonance. In addition, we find that the so-called entanglement sudden death can occur under appropriate conditions on the detunings and the different coupling constants for different initial atomic states.

A scheme is proposed to implement a two-qubit conditional quantum phase gate for the intracavity field using a single ladder-type three-level atom driven by two modes in a high-Q cavity. The quantum information is encoded on the Fock states of a bimodal cavity. The averaged fidelity of the gate can be expected to reach 99:86%.

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We propose a simple and efficient scheme to generate a nonclassical state of a quantum system, which is composed of the one-dimension trapped-one motion and a single-cavity field mode. We also generate two-mode SU(2) Schrödinger-cat states, entangled coherent states and squeezed cat states. In addition, we show that a quantum swap gate can be implemented if the vibration mode and cavity mode are used to represent separately a qubit. The distinct feature of the scheme is that it operates in the strong-excitation regime (Ω ≫ ν), which greatly enhances operation speed.