Multimode Quantum Optomechanics in Solids and Superfluids
Abstract
We consider the space of n n non-Hermitian Hamiltonians (n = 2, 3, ...) that are equivalent to a single n n Jordan block. We focus on adiabatic transport around a closed path (i.e., a loop) within this space, in the limit as the time scale T = 1/epsilon taken to traverse the loop tends to infinity. We show that, for a certain class of loops and a choice of initial state, the state returns to itself and acquires a complex phase that is epsilon -1 times an expansion in powers of epsilon1/n. The exponential of the term of nth order (which is equivalent to the "geometric" or Berry phase modulo 2pi) is thus independent of epsilon as epsilon --> 0; it depends only on the homotopy class of the loop and is an integer power of e2pii/n. One of the conditions under which these results hold is that the state being transported is, for all points on the loop, that of slowest decay.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 19, 2021
- Accession Number
- AD1121629
Entities
People
- Jack Harris
Organizations
- Yale University