Macroscopic Entanglement Generation In Bose-Einstein Condensates And Its Applications In Quantum Information

The ability to control macroscopic qubits that are encoded in the systems such as cold atomic ensembles and Bose-Einstein condensates promises to be an important direc-tion in quantum information.Physically,such a system can be realized,for example,in multi trap atom chips or atomic ensembles trapped in glass cells.Furthermore,using macroscopic qubits allows for a more robust way of storing the quantum infor-mation due to the duplication across 10~3-10~8or more atoms in the atomic ensemble.One of the fundamental operations that is required for such a quantum computing platform is the ability to create entanglement efficiently in a deterministic manner.In this thesis,we have addressed this issue from the perspective of entanglement generation and its applications.We have analyzed experimentally realistic schemes for producing entangled states using the coherent interactions between cold atoms in two bimodal Bose Einstein condensates.This can be engineered by introducing atom-atom correlations,which generate spin squeezing that reduces the quantum fluctuation in certain linear combinations of the spin variables leading to entangled states.In particular,we introduce the two-axis two-spin squeezing interaction that minimizes the noise and generates a correlated state.We use photons to mediate a collective measurement between atomic clouds in an alternative scheme that has already been experimentally demonstrated in hot atomic ensembles.Quantum nondemolition(QND)measurements on the photon detection outcomes collapse the atomic state into an entangled state.Due to the many-body nature of the quantum states in the ensembles,after a single QND measurement,a non-maximally entangled state is produced.We have analyzed a sequence of QND measurements and found that it can enhance the entanglement between two atomic ensembles or BECs.This leads to one of the main results of this thesis,which in-troduces a scheme to prepare a macroscopic maximally entangled state between two atomic ensembles using adaptive QND measurements.The procedure performs a local unitary spin rotation conditionally on the QND measurement outcome.This proce-dure is repeated such that the state converges deterministically towards the maximally entangled state.A numerical analysis of the protocol demonstrates the generation of a maximally entangled state with unit fidelity.We have also discussed the effect of potential decoherence sources such as atom and photon loss on the entanglement generation scheme and find that with a careful choice of parameters,the detrimental effects can be minimized.This shows that QND measurements are a powerful tool for quantum computing with ensembles of atomic qubits.Finally,we have discussed an essential application of maximally entangled states that serves as a resource state in the remote state preparation(RSP)protocol.Overall we conclude that using atomic ensembles is an experimentally viable and powerful way of accomplishing quantum computing.