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Undergraduate texts in physics

Coherent State on a Beam Splitter

Ray LaPierre

Published Jan 1, 2022• 1 citation
Publisher
DOI
10.1007/978-3-031-12432-7_11

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Abstract A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.
Using the linear entropy as a measure of entanglement, we investigate the effect of a beam splitter on the Perelomov coherent states for the q-deformed Uq(su(2)) algebra. We distinguish two cases: in the classical q → 1 limit, we find that the states become Glauber coherent states as the spin tends to infinity; whereas for q ≠ 1, the states, contrary to the earlier case, become entangled as they pass through a beam splitter. The entanglement strongly depends on the q-deformation parameter and the amplitude Z of the state.