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

Abstract

We generalize the quantum adiabatic theorem to the non-Hermitian system and build a strict adiabaticity condition to make the adiabatic evolution non lossy when taking into account the effect of adiabatic phase. According to the strict adiabaticity condition, the non-adiabatic couplings and the effect of the imaginary part of adiabatic phase should be eliminated as much as possible. Also the non-Hermitian Hamiltonian reverse engineering method is proposed for adiabatically driving an artificial quantum state. Concrete two-level system is adopted to show the usefulness of the reverse engineering method. We obtain the desired target state by adjusting extra rotating magnetic fields at a predefined time. Furthermore, the numerical simulation shows that certain noise and dissipation in the systems are no longer undesirable, but play a positive role in the scheme. Therefore, the scheme is quite useful for quantum information processing in some dissipative systems.

Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup

“…To extend Noether's theorem to PT -symmetric systems, the biorthogonal quantum mechanics [55][56][57][58] is applied. In biorthogonal quantum mechanics, the inner product is defined as…”

“…In this work, we extend Noether's theorem to a class of significant PT -symmetric non-Hermitian systems and introduce a generalized expectation value of a time-independent operator based on biorthogonal quantum mechanics [55][56][57][58]. For the PT -symmetric systems considered here, the eigenvalues of the PT -symmetric Hamiltonian ĤPT change from purely real numbers to purely imaginary numbers.…”

Work statistics in non-Hermitian evolutions with Hermitian endpoints

“…Non-Hermitian systems occur in various fields of physics and are experimentally accessible [1][2][3][4][5][6][7][8][9][10]. Many fascinating phenomena related to non-Hermiticity were discovered in, e.g., topological systems [11][12][13][14][15], many-body systems [16,17], adiabatic passage [18][19][20][21][22][23], nonreciprocal scattering [24][25][26], and localizationdelocalization transitions [27][28][29][30]. Many works have introduced non-Hermiticity to well-known systems, especially those already shown to have novel properties in the Hermitian cases.…”

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,…”