The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms

Intensity-dependent quantum Rabi model: spectrum, supersymmetric partner, and optical simulation

“…At this point, we can follow an argument identical to that found in [18] and find that despite that the modified evolution operatorÛ ± = e −i(Ĥ ± +ω 0 /2)t is apparently unitary, the value of ±, j|Û ± |±, k diverges at any finite time for g ≥ ω/2 and, thus, the model seems to be valid just for values of g < ω/2.…”

“…reduces the parameter range where the model is well defined to g < ω/2 due to the underlying su(1, 1) symmetry [16,18].…”

Spectral Analysis of Selfadjoint Jacobi Matrices with Periodically Modulated Entries

“…The class of J's induced by the above sequences {l n }, {q n } provides (as will become clear) many interesting and new examples of operators with complicated spectral behaviour with respect to perturbation of parameters {b n }, {c n } and the parities of M and N. Our interest in this class was partially inspired by noticing very particular but nice examples of Jacobi matrices with linear (in n) entries discussed from the point of view of group theory by Masson and Repka in [9] and Edward in [8]. Unbounded Jacobi matrices also appear in recent works on quantum optics devoted to the Jaynes-Cumming model with counterrotating terms [20,21]. The paper [16] was devoted to the very special case when M=1, m n =n a , a ¥ (0, 1], r n =dm n .…”

Phase state and related nonlinear coherent states

“…A theoretical program emerged to approach linear dissipative processes in quantum optical systems related to phase modulation and photon echo [37]. Even purely theoretical models such as the Buck-Sukumar model [25,38] and the anharmonic oscillator [39,40] have shown the benefits of using the SU(1, 1) formalism in quantum optics although care must be exerted depending on the particular circumstances [41][42][43].…”