The Geometric Phase Of A Two-level Atom In A Kerr Spacetime

Relativistic quantum information is a new cross theory which integrates rela-tivity,quantum theory,classical information theory,quantum field theory and so on.The main research problems of this theory include the following two aspects:one is to study how the relativistic effect and curved spacetime affects the quan-tum resources and the transmission of quantum information;the other is to study how to use quantum resources,quantum information and other quantum method to detect the relativistic effect and the structure of spacetime.In this paper,we study the geometric phase of a two-level atom in a Kerr spacetime by using the open quantum system approach,and reveal the Hawking effect of a Kerr black hole in terms of the geometric phase.In the framework of open quantum system,we study the geometric phase of an open two-level atom coupled with a massless scalar field prepared in the Unruh and Candelas-Chrzanowski-Howard vacuum state in the background of a Kerr black hole.Due to the interaction between the atom and the fluctuating massless scalar field in the black hole spacetime,the information about the black hole will be reflected in the geometric phase of the atom.Then by comparing the geometric phase of the black hole spacetime with that of the flat spacetime,the information about the black hole will be extracted.In this way,we can reveal the Hawking effect of the black hole.In the specific study,we consider two kinds of atoms with different states of motion,namely the static atom and the stationary atom.We use a static atom to study the geometric phase of the atom outside the infinite redshift surface,but it can not exist inside the engosphere of the black hole.Therefore,in order to study the geometric phase of the atom in the engosphere,we introduce a stationary atom which rotates with the black holeIt is found that for the static atom locating outside the infinite redshift surface,the geometric phase in the Unruh vacuum is modified by the thermal factor,which means that the atom behaves as if it was immersed in a thermal bath,and the temperature of the thermal bath is exactly the Hawking temperature of the Kerr black hole.Moreover,we find that this kind of thermal correction is disappearing at infinity.In the Candelas-Chrzanowski-Howard vacuum,the geometric phase of the atom is also modified by the thermal factor.But unlike the Unruh case,there is still a thermal correction even at infinity.With the help of a stationary atom,we study the geometric phase of the atom locating inside the ergosphere.We find that the results of the stationary atom in two kinds of vacua are similar to those in static case,which also shows that the atom behaves as if it was immersed in a thermal bath with a Hawking temperature of the black hole.The difference from the static case is that the stationary atom has an angular velocity which rotates with the black hole,so it also has a certain influence on the geometric phase.Our study shows that,we can reveal the Hawking effect of the Kerr black hole from the correction of the geometric phaseFinally,we make the conclusions and prospects of this work.