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Kasuari Physics Education Journal (KPEJ)

Fast Forwad and Shortcut to Adiabaticity Methods in Two Level System

Rigo Tambang Apriansyah, Iwan Setiawan, Irwan Koto

Published Jun 11, 2025• 0 citations
Publisher

Abstract

This research examines the fast forwad and shortcut to adiabaticity (STA) method in accelerating adiabatic dynamics applied to two level systems. The fast forwad and shortcut to adiabaticity (STA) method is a strategy developed to accelerate the evolution of quantum systems from the initial state to the final state in a short time. In this method, the acceleration scheme is built by modifying the Hamiltonian through the addition of additional terms to the initial Hamiltonian as regularization terms so that the time-dependent Schrodinger equation is still fulfilled. The formulation of the problem in this study is how to find the regularization term and additional Hamiltonian of the fast forwad and STA methods. The methodology used to obtain regularization terms with adiabatic magnetic field and analysis of wave function solutions and additional Hamiltonians. The results of the study are regularization terms and additional Hamiltonians to shorten the dynamics of the system adiabatically. In the fast forwad method to obtain the regularization term, one energy information of the system is required, while in the STA method all energy information of the system is required

DOI
10.30862/kpej.v8i1.789

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This research examines the fast forwad and shortcut to adiabaticity (STA) method in accelerating adiabatic dynamics applied to two level systems. The fast forwad and shortcut to adiabaticity (STA) method is a strategy developed to accelerate the evolution of quantum systems from the initial state to the final state in a short time. In this method, the acceleration scheme is built by modifying the Hamiltonian through the addition of additional terms to the initial Hamiltonian as regularization terms so that the time-dependent Schrodinger equation is still fulfilled. The formulation of the problem in this study is how to find the regularization term and additional Hamiltonian of the fast forwad and STA methods. The methodology used to obtain regularization terms with adiabatic magnetic field and analysis of wave function solutions and additional Hamiltonians. The results of the study are regularization terms and additional Hamiltonians to shorten the dynamics of the system adiabatically. In the fast forwad method to obtain the regularization term, one energy information of the system is required, while in the STA method all energy information of the system is required
Abstract We study a scheme of accelerated adiabatic quantum dynamics. This scheme was originally proposed by Masuda-Nakamura. The strategy of combining two opposite idea: infinitely-large timemagnification factor and infinitely-small growth rate of adiabatic parameter was elucidated. We apply the proposed method to two dimensional system with electric field and magnetic field using two dimensional Dirac equation. We settle the quasi-adiabatic dynamics (QAD) by adding the regularization terms to the original vector potential and scalar potential and accelerate it with use of a large time-scaling factor which realizes QAD on shortened time scale. These terms multiplied by the velocity function give the counterdiabatic terms that generate the fast forward potential. The fast forward potential can accelerate the dynamics of the system from iniitial state to the final state with the same condition.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
Abstract We study a scheme to accelerate adiabatic quantum dynamics of Dirac particle. This scheme using the strategy of combining two opposite ideas: infinitely-large time-magnification factor (𝛼̅) and infinitely-small growth rate (𝜖) of adiabatic parameter. The accelerated adiabatic state is obtained by obtaining the regularization term and driving potential. We introduce the proposed method to the system of two level systems of Dirac particle by using a (1 + 1) dimension time dependent Dirac equation and obtained the regularization term. By tuning the driving magnetic field, this method to be able to accelerate adiabatic dynamics of electron as a Dirac particle in the ground state that considered as a two level system. This acceleration will preserve the ground state of the wave function from initial to the final time.
This research is a theoretical research by reviewing the literature that discusses the method of accelerating quantum dynamics adiabatically. This method for accelerating quantum dynamics is so- called the fast-forward method. This method was proposed by Masuda and Nakamura in 2010. In this method, the ground state and first excited state wave function is modified by adding an additional term to the wave function which is called the adiabatic phase. This is done so that the time-dependent Schrodinger equation remains fulfilled. The accelerating process is carried out using an adiabatic parameter that goes to zero. Fast-forward method is applied first to get the adiabatic phase. Furthermore, by reviewing the wave function at the ground state and first excited state we get the adiabatic phase which ensures that the harmonic oscillator can move from the initial state to the final state in a shorter time.
This research is theoretical research with a literature study that examines methods to maintain characteristics of electrons when moving in a quantum system at the potential barrier. Attempts to maintain the characteristics of electrons in quantum systems are known as adiabatic. The method used in this research is the fast-forward method. This method was first introduced by Masuda and Nakamura in 2010. The fast-forward method is applied to barrier potential in case of electron energy larger and smaller than the potential barrier. This research focuses on preserving the characteristics of electrons by determining the regularization phase and additional potential of the quantum system at the barrier potential. The wave function solution of the system at the potential barrier is approximated by the Schrödinger equation into three regions for each case. The wave function of each region is regularized to be an adiabatic wave function and an additional term in the form of regularization phase (θ) is obtained. Given the regularized Hamiltonian, the additional potential (Ṽ) is obtained. The obtained regularization phase and additional potential ensure the quantum system at the potential barrier is in the same state from the initial state to the final state
A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.