Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Hamiltonians in the Quantum Rabi Problem   We revisit the theoretical description of the ultrastrong light-matter
interaction in terms of exactly solvable effective Hamiltonians. A perturbative
approach based on polaronic and spin-dependent squeezing transformations
provides an effective Hamiltonian for the quantum Rabi model up to the second
order in the expansion parameter. The model consistently includes both rotating
and counter-rotating terms, going therefore beyond the rotating wave
approximation. Analytical and numerical results show that the proposed
Hamiltonian performs better than the Bloch-Siegert model when calculating
operator averages (e.g.\, the mean photon number and number of excitations).
This improvement is due to a refined calculation of the dressed states within
the present model. Regarding the frequency shift induced by the qubit-photon
interaction, we find a different sign from the Bloch-Siegert value. This
influences the eigenstates structure in a non-trivial way and ensures the
correct calculation of the number of excitations associated to a given dressed
state. As a consistency check, we show that the exactly solvable independent
boson model is reproduced as a special limit case of the perturbative
Hamiltonian.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph