We consider a single-mode Bose-Einstein condensate with an arbitrary initial density matrix. This mode is coupled to another condensate mode via a quantized optical-field. We describe a method for transferring the diagonal elements of the initial density matrix in a number state basis to the optical-field's density matrix.
We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.
We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.
We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49 atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data.