Eigenstates Transition without Undergoing an Adiabatic Process

Abstract

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to shortcut to adiabaticity (DASA). In particular, in our proposed 2 × 2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of the eigenvalues helps us to exponentially decay the population in an undesired eigenfunction or amplify the population in the desired state while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonians have a much simpler form with a lower thermodynamic cost. Furthermore, we show that DASA can be extended to higher dimensions using the parameters associated with our 2 × 2 Hamiltonians. Our proposed Hamiltonians not only have application in DASA but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics. PACS numbers:The current transition of technological advancements from classical to quantum systems, makes the quantum adiabatic theorem an important matter beyond a conceptual curiosity with widespread applications in atomic and molecular physics [1][2][3][4][5][6], quantum Hall physics [7,8], the physics of geometric phase [9], quantum computation [10-12], quantum annealing [13][14][15], and quantum simulations [16]. The adiabatic theorem in its earliest form [17] states that a quantum system with a timedependent Hamiltonian H( t) and non-degenerate discrete states will remain in its instantaneous ground state (GS) if it is initially prepared in its GS and its Hamiltonian changes sufficiently slow in time, namely → 0. Apart from some inconsistency for certain Hamiltonians [18][19][20], while there is no doubt about the correctness of adiabatic theorem, in practice it is very difficult, if not impossible, to satisfy its necessary conditions due to the competition between the scan time and decoherence time resulted from the existence and unavoidable undesired non-adiabatic channels. To overcome this problem and improve the population transfer from the GS of the original system to the GS of the final system [21] without disturbing other states some techniques have been proposed including nonlinear level crossing [22], amplitudemodulated and composite pulses [23,24], and parallel adiabatic passage [25]. Another growing approach is the so-called "shortcuts to adiabaticity" where one looks for fast processes with the same outcome as an ideal and yet infinitely slow process. The common approach in the shortcuts to adiabaticity is to nullify the non-adiabatic coupling by introducing the so-called counter-diabatic extra field [26][27][28][29][30]. The shortcut to adiabaticity originally studied in Hermitian systems and has been extended to non-Hermitian systems [31][32][33]. The rapid adiabatic passage in the above methods comes with a fundamental problem, namely the cost of increasing the coupling in the Hermitian case...

Unconventional steady states and topological phases in an open two-level non-Hermitian system

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Unconventional steady states and topological phases in an open two-level non-Hermitian system

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