טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLindner Netanel
SubjectElliptic Rydberg States as Direction Indicators
DepartmentDepartment of Physics
Supervisor Mr. Asher Peres (Deceased)


Abstract

The information about a spatial direction cannot be represented by a sequence of symbols, unless the emitter (Alice) and the receiver (Bob) have prearranged a common coordinate system for specifying the numerical values of relevant angles. A quantum system with large spin can transmit a single direction or a Cartesian frame (three axes). This can be either a single quantum system such as a hydrogen atom, or a large number of particles with intrinsic spin. In order to achieve this task with maximal precision, the system has to be prepared in a superposition of states belonging to different irreducible representations of the rotation group.


In this work we show how to transmit a Cartesian frame by using the elliptic Rydberg states of a hydrogen atom. These are the quantum mechanical analogs of classical Keplerian orbits which have two vectorial constants of motion: the angular momentum and the Herman-Laplace-Runge-Lenz vector. Mathematically, the elliptic Rydberg state are the coherent states of SO(4), and it is known how to produce them experimentally. Elliptic Rydberg states, just as their classical counterparts, define three orthogonal directions in space, and have minimal dispersion of the two conserved vectors. They are thus natural candidates for encoding a Cartesian frame.


We shall compare the precision achieved by using the angular momentum or Laplace-Runge-Lenz vector to indicate a direction, and see that their performance falls below the well studied optimal method for encoding one direction in an atomic state. However, for transmission of full Cartesian frames, the elliptic Rydberg states will be shown to touch the bound for maximal precision.