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

arXiv:1607.02499

Quantum control in nearly non-degenerate qubits interacting with light

Wolff, J., C. Newell, A. Martin, J. H. McGuire

Published Jul 8, 2016• 0 citations
arXivHTMLPDF

Abstract

We consider the time evolution of nearly degenerate two-state systems with an external interaction. Conditions in which full population transfer is possible when the two-states become degenerate are considered. A new variation of the coupled differential equations for the probability amplitudes suggests a possible singularity in the time evolution of the system. The singularity occurs at the point in time where full control in the degenerate limit is achieved. We solve this new variation to derive more information about non-degenerate population control. The new results of numerical calculations for occupational probabilities of non-degenerate systems are presented and interpreted. These results are used to understand how population control breaks down as the photon energy and the energy of the system are changed. Applications are discussed, with an emphasis on interactions of twisted-vortex and plane-wave photons with a variety of targets, including macroscopic gas cells of atoms, of large single crystals, and of molecules.

DOI
10.48550/arxiv.1607.02499

Related papers

Population control of 2s−2p transitions in hydrogen

Kh. Kh. Shakov, James H. McGuire

We consider the time evolution of the occupation probabilities for the $2s\ensuremath{-}2p$ transition in a hydrogen atom interacting with an external field $V(t).$ A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Schr\"odinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.

arXiv:quant-ph/0306160•Physical Review A•Mar 21, 2003•13 citations

Complete Control of Population Transfer between Clusters of Degenerate States

Ioannis Thanopulos, Petr Král, Moshe Shapiro

We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.

Physical Review Letters•Mar 18, 2004•47 citations

Quantum time ordering and degeneracy. II: Coherent population transfer between degenerate states

Kh. Yu. Rakhimov, Shakov, Kh. Kh., James H. McGuire

We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate $n$-state atom, where transitions are caused by an external interaction. In systems with degenerate states there is no time ordering. Analytic expressions have been found for transition probabilities in a degenerate $n$-state atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple $n^{th}$ order equation to determine eigenvalues of dressed states, the method is entirely analytic. These expressions may be used to control electron populations in degenerate $n$-state atoms. Examples are given for $n=2$ and $n=3$.

arXiv:quant-ph/0308015•Aug 2, 2003•0 citations

Control of population transfer in degenerate systems by nonresonant Stark shifts

François Légaré

Two simple schemes are presented for the selective population transfer in systems where the target state is degenerate with a second level. Both states are coupled with the ground state via a one photon resonance. The schemes use a combination of two laser pulses. The first pulse breaks the degeneracy of the levels by inducing a Stark shift. The second pulse is chirped across the new levels. The idea is illustrated by numerical simulations of the time-dependent Schr\"odinger equation for a four-level system. The efficient population transfer is explained using a dressed state representation. In conclusion, applications for molecules are suggested.

Physical Review A•Dec 10, 2003•5 citations

Controllability of population transfer to degenerate states: Analytical and numerical results for a four-level system

Suhail P. Shah, David J. Tannor, Stuart A. Rice

We examine, both numerically and analytically, the limits of controllability and the dynamics of population transfer in systems with degenerate target states embedded in a finite manifold of states. An analysis of the dressed eigenstates of coupled field-matter systems is combined with the theory of the controllability of invariant systems on Lie groups to show the existence of a control scheme using a pair of shaped laser pulses acting upon a four-state system with intermediate degenerate states and a diamond-shaped array of transition moments $({\ensuremath{\mu}}_{12},{\ensuremath{\mu}}_{24},{\ensuremath{\mu}}_{13},{\ensuremath{\mu}}_{34}\ensuremath{\ne}0,{\ensuremath{\mu}}_{14},{\ensuremath{\mu}}_{23}=0).$ The limits of the controllability of these systems are linked to the symmetry of the transition dipole moments connecting the states. A broken symmetry of the transition dipole moments $({\ensuremath{\mu}}_{12}/{\ensuremath{\mu}}_{24}\ensuremath{\ne}{\ensuremath{\mu}}_{13}/{\ensuremath{\mu}}_{34})$ permits complete population transfer to one of the pair of degenerate states. Numerical simulations of the optimized population transfer to one of a pair of degenerate states in the system agree quantitatively with the analytically predicted limits of population transfer in different regimes in the joint material-field characteristics of the system. The applicability of the four-state model to selective population transfer in vibrationally mediated photodissociation experiments is discussed.

Physical Review A•Sep 27, 2002•19 citations

Modeling of quantum beats of the state populations of a molecule

V. A. Morozov

Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.

Russian Journal of Physical Chemistry B•May 1, 2017•0 citations
We consider the time evolution of nearly degenerate two-state systems with an external interaction. Conditions in which full population transfer is possible when the two-states become degenerate are considered. A new variation of the coupled differential equations for the probability amplitudes suggests a possible singularity in the time evolution of the system. The singularity occurs at the point in time where full control in the degenerate limit is achieved. We solve this new variation to derive more information about non-degenerate population control. The new results of numerical calculations for occupational probabilities of non-degenerate systems are presented and interpreted. These results are used to understand how population control breaks down as the photon energy and the energy of the system are changed. Applications are discussed, with an emphasis on interactions of twisted-vortex and plane-wave photons with a variety of targets, including macroscopic gas cells of atoms, of large single crystals, and of molecules.
We consider the time evolution of the occupation probabilities for the $2s\ensuremath{-}2p$ transition in a hydrogen atom interacting with an external field V(t).V(t).V(t). A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Schr\"odinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.
We present an analytic solution to the "degenerate quantum control problem," which enables the transfer of any desired fraction of population between arbitrary initial and final pure wave packets, made up of nearly degenerate energy eigenstates. It consists of two two-photon adiabatic passage steps, in which the population of the initial wave packet is first transferred, via a number of nondegenerate intermediate states, to a single eigenstate and then returned to a different target superposition state. We demonstrate the approach by executing a stepwise isomerization of three Jahn-Teller states of the Al3O molecule, where a proper optical coupling can easily be established.
We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate nnn-state atom, where transitions are caused by an external interaction. In systems with degenerate states there is no time ordering. Analytic expressions have been found for transition probabilities in a degenerate nnn-state atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple nthn^{th}nth order equation to determine eigenvalues of dressed states, the method is entirely analytic. These expressions may be used to control electron populations in degenerate nnn-state atoms. Examples are given for n=2n=2n=2 and n=3n=3n=3.
Two simple schemes are presented for the selective population transfer in systems where the target state is degenerate with a second level. Both states are coupled with the ground state via a one photon resonance. The schemes use a combination of two laser pulses. The first pulse breaks the degeneracy of the levels by inducing a Stark shift. The second pulse is chirped across the new levels. The idea is illustrated by numerical simulations of the time-dependent Schr\"odinger equation for a four-level system. The efficient population transfer is explained using a dressed state representation. In conclusion, applications for molecules are suggested.
We examine, both numerically and analytically, the limits of controllability and the dynamics of population transfer in systems with degenerate target states embedded in a finite manifold of states. An analysis of the dressed eigenstates of coupled field-matter systems is combined with the theory of the controllability of invariant systems on Lie groups to show the existence of a control scheme using a pair of shaped laser pulses acting upon a four-state system with intermediate degenerate states and a diamond-shaped array of transition moments $({\ensuremath{\mu}}_{12},{\ensuremath{\mu}}_{24},{\ensuremath{\mu}}_{13},{\ensuremath{\mu}}_{34}\ensuremath{\ne}0,{\ensuremath{\mu}}_{14},{\ensuremath{\mu}}_{23}=0).$ The limits of the controllability of these systems are linked to the symmetry of the transition dipole moments connecting the states. A broken symmetry of the transition dipole moments $({\ensuremath{\mu}}_{12}/{\ensuremath{\mu}}_{24}\ensuremath{\ne}{\ensuremath{\mu}}_{13}/{\ensuremath{\mu}}_{34})$ permits complete population transfer to one of the pair of degenerate states. Numerical simulations of the optimized population transfer to one of a pair of degenerate states in the system agree quantitatively with the analytically predicted limits of population transfer in different regimes in the joint material-field characteristics of the system. The applicability of the four-state model to selective population transfer in vibrationally mediated photodissociation experiments is discussed.
Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.