The problem of achieving population inversion adiabatically in an $N$ -level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The $\mathrm{SU}(N)$ coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the (${N}^{2}\ensuremath{-}1$)-dimensional $\mathrm{SU}(N)$ space contains an ($N\ensuremath{-}1$)--dimensional steady-state subspace $\mathit{\ensuremath{\Gamma}}(t)$ whose orthonormal basis vectors ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{1},\dots{}, {\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{N\ensuremath{-}1}$ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ about $\mathit{\ensuremath{\Gamma}}$. Multilevel adiabatic following occurs when the angle $\ensuremath{\chi}(t)$ between the coherence vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ and its projection onto $\mathit{\ensuremath{\Gamma}}$ is very small. The multiple dimension of $\mathit{\ensuremath{\Gamma}}$ is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving $N\ensuremath{-}1$ simple equations for the directional cosines of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ on ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{i}$. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.The problem of achieving population inversion adiabatically in an $N$-level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The $\mathrm{SU}(N)$ coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the (${N}^{2}\ensuremath{-}1$)-dimensional $\mathrm{SU}(N)$ space contains an ($N\ensuremath{-}1$)--dimensional steady-state subspace $\mathit{\ensuremath{\Gamma}}(t)$ whose orthonormal basis vectors ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{1},\dots{}, {\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{N\ensuremath{-}1}$ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ about $\mathit{\ensuremath{\Gamma}}$. Multilevel adiabatic following occurs when the angle $\ensuremath{\chi}(t)$ between the coherence vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ and its projection onto $\mathit{\ensuremath{\Gamma}}$ is very small. The multiple dimension of $\mathit{\ensuremath{\Gamma}}$ is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving $N\ensuremath{-}1$ simple equations for the directional cosines of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ on ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{i}$. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.

Physical Review AFeb 1, 1984421 citations

Generalized adiabatic impulse approximation

Takayuki Suzuki, Hiromichi Nakazato

Nonadiabatic transitions in multilevel systems appear in various fields of physics, but it is not easy to analyze their dynamics in general. In this paper, we propose to extend the adiabatic impulse approximation to multilevel systems. This approximation method is shown to be equivalent to a series of unitary evolutions and facilitates to evaluate the dynamics numerically. In particular, we analyze the dynamics of the Landau-Zener grid model and the multilevel Landau-Zener-St\"uckelberg-Majorana interference model, and confirm that the results are in good agreement with the exact dynamics evaluated numerically. We also derive the conditions for destructive interference to occur in the multilevel system.Nonadiabatic transitions in multilevel systems appear in various fields of physics, but it is not easy to analyze their dynamics in general. In this paper, we propose to extend the adiabatic impulse approximation to multilevel systems. This approximation method is shown to be equivalent to a series of unitary evolutions and facilitates to evaluate the dynamics numerically. In particular, we analyze the dynamics of the Landau-Zener grid model and the multilevel Landau-Zener-St\"uckelberg-Majorana interference model, and confirm that the results are in good agreement with the exact dynamics evaluated numerically. We also derive the conditions for destructive interference to occur in the multilevel system.

arXiv:2112.04739Physical Review AFeb 17, 202214 citations

The problem of achieving population inversion adiabatically in an

N

-level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The

\mathrm{SU}(N)

coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the (${N}^{2}\ensuremath{-}1$)-dimensional

\mathrm{SU}(N)

space contains an ($N\ensuremath{-}1$)--dimensional steady-state subspace $\mathit{\ensuremath{\Gamma}}(t)$ whose orthonormal basis vectors ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{1},\dots{}, {\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{N\ensuremath{-}1}$ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ about $\mathit{\ensuremath{\Gamma}}$. Multilevel adiabatic following occurs when the angle $\ensuremath{\chi}(t)$ between the coherence vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ and its projection onto $\mathit{\ensuremath{\Gamma}}$ is very small. The multiple dimension of $\mathit{\ensuremath{\Gamma}}$ is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving $N\ensuremath{-}1$ simple equations for the directional cosines of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ on ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{i}$. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.