Adiabatic theorem for non-Hermitian time-dependent open systems

Abstract

In the conventional quantum mechanics (i.e., hermitian QM) the adiabatic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t') formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criteria for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the generation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived. 42.50.Hz, 32.80.Rm

Distinguishing between aligned and randomly oriented polar molecules by using a combination of strong laser field with a weak static field

“…The requirement for envelopes of laser pulses which support more than several optical cycles is based on the adiabatic theorem for open systems [17]. For an excellent agreement between the HGS obtained from wavepacket propagation calculations when short laser pulses are used, and the HGS obtained from Floquet calculations see [18].…”

“…Here we assume that the HGS is obtained by a laser pulse which supports more than 5-10 optical cycles to justify the theoretical study by using Floquet theory (see [17,18]). However, we require also that the pulse is still too short to affect molecular alignment.…”

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

“…Non-Hermitian Hamiltonians are widely used as effective models to describe open quantum and classical systems [4,5,6], or are introduced to provide complex extensions of the ordinary quantum mechanics such as in the PT -symmetric quantum mechanics [7,8,9,10]. The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,…”

“…The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,17,18,22,26,27,32,33] and shortcuts to adiabaticity [30,36,…”

Adiabaticity in a time-dependent trap: The passage near a continuum threshold

“…The question of adiabaticity in bound-to-continuum transitions, studied by various authors, [9][10][11][12] leaves room for further discussion, even in regard to its formulation. As a trapping potential becomes shallower, a bound states is brought closer to the continuum, and eventually joins it.…”