Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and Theoretical

Time-dependent perturbation treatment of independent Raman schemes

Benedetto Militello, Paolo Aniello, ANTONINO MESSINA

Published Apr 17, 2007• 2 citations
Publisher

Abstract

The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur

DOI
10.1088/1751-8113/40/18/011

Related papers

Perturbative Treatment of the Evolution Operator Associated with Raman Couplings

Benedetto Militello

A novel perturbative treatment of the time evolution operator of a quantum system is applied to the model describing a Raman-driven trapped ion in order to obtain a suitable 'effective model'.It is shown that the associated effective Hamiltonian describes the system dynamics up to a certain transformation which may be interpreted as a 'dynamical dressing' of the effective model.

arXiv:quant-ph/0605091•Symmetry Integrability and Geometry Methods and Applications•May 10, 2006•1 citation

Evolution operator for time-dependent non-Hermitian Hamiltonians

Bijan Kumar Bagchi

The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available. In this paper, we make use of a procedure, originally developed by A.R.P. Rau [Phys.Rev.Lett, 81, 4785-4789 (1998)], in the context of deriving the solution of Liuville-Bloch equations in the product form of exponential operators when time-dependent external fields are present, for the evaluation of U(t) in the interaction picture wherein the corresponding Hamiltonian is time-dependent and in general non-Hermitian. This amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition.

arXiv:1809.09377•Sep 25, 2018•0 citations

Coarse grained and fine dynamics in trapped ion Raman schemes

B Militello, P Aniello, A Messina

A novel result concerning Raman coupling schemes implemented using trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamic. The second is a suitable correction restoring the fine dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level. The case where a decoherence source is present is also studied.

arXiv:quant-ph/0310162•Journal of Physics A Mathematical and General•Aug 5, 2004•3 citations

Time-dependent Hamiltonian

Efstratios Manousakis

Abstract This chapter discusses how to treat the case of a perturbation which depends on time. It also discusses the case of the so-called real-time evolution and the adiabatic process which has received more recent attention because of experiments on quantum dynamics in trapped cold atoms.

•Nov 1, 2015•1 citation

Coarse grained and fine dynamics in trapped ion Raman schemes

Benedetto Militello, Paolo Aniello, ANTONINO MESSINA

A novel result concerning Raman coupling schemes implemented using trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the fine dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.

•Jan 1, 2008•5 citations

A new perturbative expansion of the time evolution operator associated with a quantum system

Paolo Aniello

A novel expansion of the evolution operator associated with an—in general, time-dependent—perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.

arXiv:quant-ph/0508017•Journal of Optics B Quantum and Semiclassical Optics•Nov 15, 2005•10 citations
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur
The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available. In this paper, we make use of a procedure, originally developed by A.R.P. Rau [Phys.Rev.Lett, 81, 4785-4789 (1998)], in the context of deriving the solution of Liuville-Bloch equations in the product form of exponential operators when time-dependent external fields are present, for the evaluation of U(t) in the interaction picture wherein the corresponding Hamiltonian is time-dependent and in general non-Hermitian. This amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition.
A novel result concerning Raman coupling schemes implemented using trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamic. The second is a suitable correction restoring the fine dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level. The case where a decoherence source is present is also studied.
A novel result concerning Raman coupling schemes implemented using trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the fine dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.