A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via $N$ nondegenerate intermediate states, to one arbitrary member of $M\phantom{\rule{0.3em}{0ex}}(M\ensuremath{\leqslant}N)$ degenerate states is constructed. The full control field exploits an $(M+N\ensuremath{-}1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multilevel quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via $N$ nondegenerate intermediate states, to one arbitrary member of $M\phantom{\rule{0.3em}{0ex}}(M\ensuremath{\leqslant}N)$ degenerate states is constructed. The full control field exploits an $(M+N\ensuremath{-}1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multilevel quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.

arXiv:quant-ph/0402150Physical Review AJun 15, 200423 citations

Methods for efficient population transfer and quantum logic

Asoka Biswas

Nov 16, 20040 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 $n=3$ .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/0308015Aug 2, 20030 citations

A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via

N

nondegenerate intermediate states, to one arbitrary member of $M\phantom{\rule{0.3em}{0ex}}(M\ensuremath{\leqslant}N)$ degenerate states is constructed. The full control field exploits an $(M+N\ensuremath{-}1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multilevel quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.

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