Adiabatic approximation for quantum dissipative systems: Formulation, topology, and superadiabatic tracking

Abstract

A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.

Non-Hermitian quantum annealing in the ferromagnetic Ising model

“…Here the critical point, z c , is determined as a solution of the equation, ε k (z c ) = 0, in the complex plane obtained by analytical continuation, t → z [30][31][32][33][34][35][36][37][38]. Similarly, if initially the system was in the excited state: |ψ k (0) = |u + (k, 0) , so that α k (0) = 0 and β k (0) = 1, the result of integration yields…”

Reverse engineering of a nonlossy adiabatic Hamiltonian for non-Hermitian systems

“…However, in practice the quantum system inevitably interacts with the surrounding environment, e.g. the non-Hermitian (NH) systems [20][21][22][23][24][25][26][27][28][29][30][31][32]. In this case, the complicated adiabatic phase factor could not be simply discarded as the common pure phase any more, since it generally is not a pure (real) phase factor.…”

“…In fact, several authors have paid attention to the study of adiabaticity in NH systems [27][28][29][30][31]. For example, Miniatura et al have set a rough estimate of an adiabaticity condition by analogy with the Hermitian counterpart and recognized the importance of the nonadiabatic transition [27].…”

“…More recently, Ibáñez and Muga have generalized the concept of population for NH systems to characterize adiabaticity and worked out an approximate adiabaticity criterion [31]. Indeed, the adiabaticity of a given NH system has been discussed well with those excellent methods [27][28][29][30][31]. However, in principle above methods didn't give a clear quantitative analysis about the dynamics of the bare state in the eigenstate and the adiabatic phase.…”

Landau-Zener problem with decay and dephasing

“…Work on related problems has been reported in Refs. [5,7,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], Refs. [27][28][29] consider a LZ transition for two states coupled to a bath of harmonic oscillators, and Refs.…”