Elliptic Rydberg states as direction indicators

Abstract

The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of a hydrogen atom that mimic classical elliptic orbits are the coherent states of the SO(4) rotation group.It is known how to produce these states experimentally. They have minimal dispersions of the two conserved vectors and can be used as direction indicators. We compare the fidelity of this transmission method with that of the idealized optimal method

Optimal measurements for relative quantum information

“…It should be noted that estimating the relative angle between a pair of SU(2) coherent states is of particular importance because estimating the eccentricity of an elliptic Rydberg state of a Hydrogen atom is an instance of the same problem [27]. Rydberg states are significant because they can be prepared experimentally.…”

Quantum information and relativity theory

“…where the explicit expressions for ξ(Λ,k) are given by Lindner, Peres, and Terno (2003) and Bergou, Gingrich and Adami (2003). The superselection rule that was mentioned above makes it impossible to define a reduced density matrix in the usual way Lindner, Peres and Terno, 2003).…”

Transfer of spatial reference frame using singlet states and classical communication

“…In previous work, it was shown that by exchanging a single quantum system between Alice and Bob, a reference frame can be transmitted from Alice to Bob [21,22]. This requires implementing a complex POVM.…”

“…Subsequently, it was realized that a single quantum system, such as a hydrogen atom, can transmit all three axes of a Cartesian coordinate frame [21,22]. In such schemes, the rotation matrix between the predefined reference frame and the local frame is determined by POVM measurements [23] on the exchanged quantum system.…”