Quantum Entanglement And Quantum Coherence Created By Atomic Ensembles In Optical Cavity

Quantum coherence and entanglement are widely renounced as the most fundamental con-cepts of quantum mechanics. Although coherence can be explained classically, no such ex-planation could be done for entanglement which exhibits non-local interaction properties that cannot be performed and explained classically. In this thesis, we investigate coherence and en-tangled properties of various systems composed of atomic ensembles interacting with cavity modes. The work is motivated by a desire to provides models for creation of entanglement in continuous variable systems that could be realised in practice.We consider a ring cavity as a practical model to study the relation between coherence and entanglement. We first investigate a system composed of a spatially extended single atomic ensemble interacting with counter-propagating modes of the ring cavity and find that several in-teresting coherence and entangled behaviour occur when the size of the atomic ensemble is not taken to the thermodynamic limit. In particular, we find that collective bosonic modes are not in general orthogonal to each other. We present solutions for the second-order statistical moments of different modes of the system and find that the mode nonorthogonality gives rise to phase locking between the cavity counter-propagating modes, which leads to interesting first-order coherence effects that the counter-propagating cavity modes, although in the thermodynamic limit are mutually incoherent and exhibit no one-photon interference, the modes become mu-tually coherent and exhibit interference after interacting with a finite-size atomic ensemble. A study of the second-order correlation functions of the counter-propagating modes shows that the nonorthogonality may lead to the super-bunching effect and can create correlations that are necessary for squeezing and entanglement between the cavity modes. However, we find that the correlations created are not strong enough to violate the Cauchy-Schwartz inequality and to produce squeezing between the modes. We therefore consider spectral distributions of the field variances and logarithmic negativity and find that the two-mode squeezing and the entanglement can actually be created between spectral components of the output cavity fields.We show connections between coherences and entanglement of effective bosonic modes of a nano-mechanical cavity composed of an oscillating mirror and containing an optical lat-tice of regularly trapped atoms. We introduce a polariton model of the system and find that the generation of the first-order coherence between two modes is equally effective in destroy-ing entanglement between these modes. There is no entanglement between the independent polariton modes when both modes are simultaneously coupled to the mechanical mode by the parametric (squeezing-type) interaction. There is no entanglement between the polaritons even if the oscillating mirror is damped by a squeezed vacuum field. The intermediate mechanical mode effectively creates the first-order coherence between the modes. We find that in order to effectively entangle independent modes, one of the modes should be coupled to the interme-diate mode by a parametric interaction but the other should be coupled by the linear-mixing (beamsplitter-type) interaction.In addition, we present two schemes involving four atomic ensembles that could serve as potential sources for creation of four-mode cluster states. In the first scheme, we discuss the entanglement generation among four atomic ensembles inside two separated two-mode cavities, each containing two atomic ensembles. The two cavities are coupled by optical fiber in a cascad-ed way. The time-dependent behavior of the four atomic ensembles in two different cavities is analyzed. It is found that the four atomic ensembles in two different nodes can be prepared in a mixed cluster states. In the second scheme, we propose a procedure which generates four-mode cluster states in a single step of the preparation. We show that this procedure could be done only by a proper driving of atomic ensembles composed of four-level atoms located in four distant cavities connected by an optical fibre. With the aid of the cavity damping, the simultaneous driving of the atomic ensembles with laser pulses of suitably chosen Rabi frequencies and phas-es, a linear four-mode cluster state can be unconditionally created. The scheme could be easily extended to the case of N-mode cluster states.