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Kasuari Physics Education Journal (KPEJ)

Fast Forward Method on Single Spin with Rabi Frequency

Rinarti Raja Gukguk, Iwan Setiawan, Andik Purwanto

Published Dec 25, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.30862/kpej.v7i2.756

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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.

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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.
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.
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
Abstract We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity function together with the original Hamiltonian give fast-forward driving for adiabatic states. We apply our method to XY spin model by considering three spin systems on the Kagome lattice. In this model, we obtained the XY pair-wise exchange interaction of nearest neighbors and next-nearest neighbors should be added to the original Hamiltonian as a driving interaction to accelerate the adiabatic motion. This pair-wise driving interaction in the fast-forward scheme guarantees the complete fidelity of accelerated states.
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.
Quantum computers have data in the form of quantum bits (qubits), which are 0 and 1 simultaneously. This 0 and 1 state is the electron spin state on the quantum computer, namely spin up and spin down. Qubits are very sensitive to environmental disturbances, so it is necessary to accelerate the adiabatic dynamics so that the system's coherence is not disturbed by environmental interactions. These spin dynamics can be accelerated using the fast forward method, which uses an additional phase to drive the spin adiabatically. The adiabatic state is a state where the dynamics of a system have the same characteristics as the initial state after the dynamics take place. This research was conducted by qualitatively reviewing physical theory and conducting literature studies on previous research on the fast-forward method and the Landau-Majorana-Zener system. The results of this study obtained wave function solutions, regularization terms, and additional Hamiltonians in the Landau-Majorana-Zener system to accelerate adiabatic spin dynamics so that spin dynamics on quantum computers are not disturbed by the environment. After adding additional Hamiltonian adiabatic dynamics in the Landau-Majorana Zener system can be maintained but requires considerable energy. The magnetic field needed to create the same graph as the wave function graph before adding Hamiltonian, B0 = 100 Tesla. The energy required to accelerate the adiabatic spin dynamics is large, so the cost is also quite large. Therefore, efforts are needed to minimize the energy required to accelerate the adiabatic spin dynamics.