Abstract:
We show that entanglement of multiple atoms can arise via resonant interaction with a displaced thermal field with a macroscopic photon-number. The cavity field acts as the catalyst, which is disentangled with the atomic system after the operation. Remarkably, the entanglement speed does not decrease as the average photon-number of the mixed thermal state increases. The atoms may evolve to a highly entangled state even when the photon-number of the cavity mode approaches infinity.

Abstract:
We show that a cavity field can evolve from an initial displaced mixed thermal state to a macroscopic superpositions of displaced thermal states via resonant interaction with a two-level atom. As a macroscopic system (meter) is really in a mixed state before coupling with the microscopic system at some temperature, our result is important for studying the quantum measurement problem and decoherence under real conditions. For the two-mode case, entanglement of displaced thermal states between the modes can be obtained.

Abstract:
We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange.

Abstract:
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.

Abstract:
We propose a scheme for generating entangled states for two or more multi-level atoms in a thermal cavity. The photon-number dependent parts in the effective Hamiltonian are canceled with the assistant of a strong classical field. Thus the scheme is insensitive to both the cavity decay and the thermal field. The scheme does not require individual addressing of the atoms in the cavity. The scheme can also be used to generate entangled states for many hot multi-level ions.

Abstract:
We propose a scheme for realizing two-qubit quantum phase gates with atoms in a thermal cavity. The photon-number dependent parts in the evolution operator are canceled with the assistant of a strong classical field. Thus the scheme is insensitive to the thermal field. In the scheme the detuning between the atoms and the cavity is equal to the atom-cavity coupling strength and thus the gates operate at a high speed, which is also important in view of decoherence. The scheme can be generalized to generate multiatom entangled states with a thermal cavity.

Abstract:
We propose a scheme for direct measurement of the Wigner function for a cavity mode. In the scheme the cavity field resonantly interacts with an atomic ensemble. Under certain conditions, the state of the cavity mode is transferred to the atomic system. After a displacement the measurement of the parity of the atomic excitation number directly yields the Wigner function of the initial state of the cavity mode.

Abstract:
We propose a scheme for implementing conditional quantum phase gates for two four-state atoms trapped in a cavity. The two ground states of the atoms are coupled through two Raman processes induced by the cavity mode and two classical fields. Under certain conditions nonresonant Raman processes lead to two-atom coupling and can be used to produce conditional phase gates. The scheme is insensitive to cavity decay, thermal photons, and atomic spontaneous emission. The scheme does not require individual addressing of the atoms.

Abstract:
This paper proposes a scheme for generation of superpositions of coherent states of the effective bosonic mode in a collection of atoms. In the scheme an atomic sample interacts with a slightly detuned cavity mode and a resonant strong classical field. Under certain conditions the atomic system evolves from a coherent state to a superposition of coherent states.