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INDONESIAN JOURNAL OF APPLIED PHYSICS

Kajian Literatur Fase Adiabatik untuk mempercepat Dinamika Kuantum Adiabatik pada Osilator Harmonik

Mayasari Katrina Hutagalung, Iwan Setiawan, Dedy Hamdani

Published Apr 30, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.13057/ijap.v12i2.65252

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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.
AbstrakPenelitian ini membahas metode percepatan dinamika kuantum adiabatik pada sistem spin tunggal yaitu dinamika spin yang bergerak pada keadaan awal up (atas) akan bergerak ke down (bawah) pada keadaan akhir. Metode ini disebut skema fast forward. Metode ini pertama kali di usulkan oleh Masuda dan Nakamura. Dalam metode ini, skema percepatan dibangun dengan menambahkan suku interaksi penggerak ke Hamiltonian awal dan mempercepatnya dengan menggunakan faktor penskalaan waktu yang bernilai besar dan parameter adiabatik yang menuju nol (0) dan bertujuan mewujudkan dinamika kuantum adiabatik pada waktu yang singkat dan dengan penambahan medan magnet penggerak. Hamiltonian penggerak dan medan magnet penggerak ini menjamin spin tunggal dapat bergerak dari keadaan awal ke keadaan akhir dalam waktu yang singkat tanpa mengubah karakteristik awalnya. Kata kunci: Adiabatik, Dinamika Kuantum, Spin tunggal AbstractThis study discusses the method of accelerating adiabatic quantum dynamics in a single spin system, namely the dynamics of a spin that moves in the up initial state will move down in the final state. This method is called a fast forward scheme. This method was first proposed by Masuda and Nakamura. In this method, the acceleration scheme is constructed by adding the driving interaction term to the initial Hamiltonian and accelerating it by using a large time scaling factor and adiabatic parameter towards zero (0) and aims to realize adiabatic quantum dynamics in a short time and by adding a driving magnetic field. The driving Hamiltonian and the driving magnetic field ensure that a single spin can move from its initial state to its final state in a short time without changing its initial characteristics. Keywords : Adiabatic, Quantum Dynamics, Single Spin
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.
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
We study a scheme of fast-forward adiabatic quantum dynamics of a (2 + 1) Dirac particle. This scheme was originally proposed by Masuda and Nakamura. In this scheme, we include the adiabatic parameter that maintains the adiabatic motion of the particle and fast forward its motion by introducing a time scaling parameter. The fast forward adiabatic state is obtained by determining the regularization term and driving potential. We introduce the proposed method to the system with the Dirac particle using a (2 + 1) dimensiontime- dependent Dirac equation and obtain the regularization term, the driving scalar potential VFF and the driving vector potential AFF . By tuning the driving electric field, this method can accelerate the adiabatic dynamics of an electron as a Dirac particle trapped in the ground state in the plane xy and an electric field in the x direction and a constant magnetic field in the y direction. This acceleration will preserve the ground state of the wave function from the initial time to the final time.
We propose a method to accelerate adiabatic dynamics of wave functions (WFs) in quantum mechanics to obtain a final adiabatic state except for the spatially uniform phase in any desired short time. In our previous work, acceleration of the dynamics of WFs was shown to obtain the final state in any short time by applying driving potential. We develop the previous theory of fast-forward to derive a driving potential for the fast-forward of adiabatic dynamics. A typical example is the fast-forward of adiabatic transport of a WF, which is the ideal transport in the sense that a stationary WF is transported to an aimed position in any desired short time without leaving any disturbance at the final time of the fast-forward. As other important examples, we show accelerated manipulations of WFs, such as their splitting and squeezing. The theory is also applicable to macroscopic quantum mechanics described by the nonlinear Schrödinger equation.