Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

Abstract

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and q-deformed binomial statistics.

Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets

“…Simply making the replacements a j = α 2 j t + t, p j = α j β j and rescaling H j in Eqs. (56)(57)(58) does not work. In addition, we have to redefine the parameter η as η = κ 2 t + t, rescale the off-shell Bethe state Φ DO , and redefine the function f .…”

Integrable Time-Dependent Quantum Hamiltonians

“…In a more recent work [43], it was shown that nontrivial solvable models belong to families of mutually commuting Hamiltonians linear or quadratic in t. It was therefore conjectured that quantum integrability understood as the existence of nontrivial time-dependent commuting partners [44][45][46][47] is a necessary condition for the multistate Landau-Zener solvability. In a parallel development, methods to solve and search for new models were discovered [48][49][50] and since then the number of such models has grown rapidly [51][52][53][54].…”

SU(3) Landau-Zener interferometry with a transverse periodic drive

“…four photons in the cavity, the number of steps reduces to two. Therefore, given that diabatic energies are [31,[39][40][41] is integrable and its large positive times asymptotic solutions are written as by-product of the spin-1/2 LZSM formula [1][2][3][4] (see Appendix B).…”

“…In our case, we move from an SU (3) model with a transverse periodic drive and constructed the corresponding "pseudo" SU (5) model with time-independent couplings and remarkably reproduce all the tendencies observed in the SU (3) picture with time-dependent couplings. As a direct consequence to this construction, one may envisage a long time asymptotic solution to the SU (3) through its equivalent counterpart SU (5) by classical multiplication of probabilities 39,42 . The good news is that for finite times, solutions to the SU (5) LZSM problem in the nonadiabatic limit are known in advance for P 2→2 (t) and are given by Eq.…”