Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

Hiromichi Nakazato; Alessandro Sergi; Agostino Migliore; Antonino Messina

doi:10.3390/e25010096

Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

Hiromichi Nakazato, Alessandro Sergi, Agostino Migliore, Antonino Messina^*

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator (Formula presented.) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of (Formula presented.) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any (Formula presented.) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.

Original language	English
Article number	96
Journal	Entropy
Volume	25
Issue number	1
DOIs	https://doi.org/10.3390/e25010096
Publication status	Published - 2023 Jan

Keywords

control field
geometric methods
quantum dynamical invariants
qubit
time-dependent SU(2) Hamiltonian models

ASJC Scopus subject areas

Information Systems
Mathematical Physics
Physics and Astronomy (miscellaneous)
Electrical and Electronic Engineering

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10.3390/e25010096

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title = "Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian",

abstract = "We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator (Formula presented.) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of (Formula presented.) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any (Formula presented.) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.",

keywords = "control field, geometric methods, quantum dynamical invariants, qubit, time-dependent SU(2) Hamiltonian models",

author = "Hiromichi Nakazato and Alessandro Sergi and Agostino Migliore and Antonino Messina",

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T1 - Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

AU - Nakazato, Hiromichi

AU - Sergi, Alessandro

AU - Migliore, Agostino

AU - Messina, Antonino

PY - 2023/1

Y1 - 2023/1

N2 - We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator (Formula presented.) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of (Formula presented.) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any (Formula presented.) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.

AB - We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator (Formula presented.) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of (Formula presented.) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any (Formula presented.) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.

KW - control field

KW - geometric methods

KW - quantum dynamical invariants

KW - qubit

KW - time-dependent SU(2) Hamiltonian models

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ER -

Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

Abstract

Keywords

ASJC Scopus subject areas

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