Adiabatic passage for a lossy two-level quantum system by a complex time method

Abstract

Using a complex time method with the formalism of Stokes lines, we establish a generalization of the Davis–Dykhne–Pechukas formula which gives in the adiabatic limit the transition probability of a lossy two-state system driven by an external frequency-chirped pulse-shaped field. The conditions that allow this generalization are derived. We illustrate the result with the dissipative Allen–Eberly and Rosen–Zener models.

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].…”

“…Subsequently, Sun has devoted to the generalization of the high-order adiabatic approximation method for the NH quantum systems by using perturbation theory and integration by parts, and obtained an adiabaticity condition similar to the Hermitian one with the damping factor and the oscillating factor [28]. Recently, Dridi et al have established a generalization of the Davis-Dykhne-Pechukas formula by the complex time * E-mail: xia-208@163.com method and showed a general adiabatic approximation for lossy two-state models [29,30]. 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].…”

“…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.…”