Creating adiabatic cat states of topologically coupled quantum modes

The simplest topological pump consists in a two level system periodically driven in time at two

frequencies [1, 2]. We consider a quantum analog of such a pump: two quantum electromagnetic

modes strongly coupled to a qubit. We show that any initial state of this system decomposes into

a pair of adiabatic states. In a generic adiabatic state, the qubit is entangled with the two quantum

modes. We characterize this entanglement in terms of a quantum metric tensor of the model. The

time evolution of each adiabatic state induces a topologically quantized energy transfer either from

mode 1 to mode 2, or from 2 to 1. Hence, as a consequence of this topological pumping, the pair of

adiabatic states splits into states with distinguishable energy content of mode 1 and mode 2, thereby

realizing a new kind of cat state [3].

[1] I. Martin, G. Refael, and B. Halperin, Phys. Rev. X 7, 041008 (2017).

[2] J. Luneau, C. Dutreix, Q. Ficheux, P. Delplace, B. Douçot, B. Huard, and D. Carpentier, Phys. Rev. Research 4, 013169 (2022).

[3] J. Luneau, B. Douçot, and D. Carpentier, to be published.