Abstract
Majorana stars are visual representation for a quantum pure state. For some states, the corresponding majorana stars are located on one curve on the Block sphere. However, it is lack of exact curve equations for them. To find the exact equations, we consider a superposition of two bosonic coherent states with an arbitrary relative phase. We analytically give the curve equation and find that the curve always goes through the North pole on the Block sphere. Furthermore, for the superpositions of SU(1,1) coherent states, we find the same curve equation.
Highlights
The Majorana representation (MR), in which a pure state of a spin-j system1,2 can be precisely described as the trajectory of 2j stars on a unit sphere, was proposed by Majorana in 19323
It is interesting to find that the stars displays different topological structures for topologically different phases and the topological structure is closely related to the parity of the system
It was found that the MR provides a very interesting and intuitive way to understand the nonlinear Laudau-Zener tunneling22 and the breakdown of adiabaticity is related to some stars never reaching the South pole of the Bloch sphere
Summary
The corresponding majorana stars are located on one curve on the Block sphere. It is lack of exact curve equations for them. The MR was used to study a multi-band topological systems21 They find a geometric interpretation of the topological phases of inversion-symmetric polymerized models by mapping the Bloch states of the topological system to majorana stars. All the stars for coherent states coincide on one point on the Bloch sphere32 Using this coherent-state approach, we can study star representations of many quantum states including both finite and infinite-dimensional systems. We find an exact curve equation for Majorana stars for a superpositon of two bosonic coherent states (STCS) with an arbitrary relative phase.
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