Physical Review A

Nonadiabatic transitions in finite-time adiabatic rapid passage

Tianshi Lü, X. Miao, H. Metcalf

Published Jun 26, 2007• 20 citations

Abstract

To apply the adiabatic rapid passage process repetitively [T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 71, 061405(R) (2005)], the nonadiabatic transition probability of a two-level atom subject to chirped light pulses over a finite period of time needs to be calculated. Using a unitary first-order perturbation method in the rotating adiabatic frame, an approximate formula has been derived for such transition probabilities in the entire parameter space of the pulses.

DOI: 10.1103/physreva.75.063422

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Physical Review A

Nonadiabatic transitions in finite-time adiabatic rapid passage

Tianshi Lü, X. Miao, H. Metcalf

Published Jun 26, 2007• 20 citations

Publisher

Abstract

DOI: 10.1103/physreva.75.063422

Related papers

Population Inversion in Optical Adiabatic Rapid Passage with Phase Relaxation

Yōsuke Kayanuma

The transition probability $P$ in the optical adiabatic rapid passage is calculated for a two-level model with dephasing. In the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}0$, where ${T}_{2}$ is the dephasing time and ${\ensuremath{\tau}}_{p}$ is the time scale of passage through the resonance region, $P$ is given by $P=\frac{[1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})]}{2}$ in which $\ensuremath{\chi}$ is the Rabi flopping frequency at resonance and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ is the time derivative of the offset angular frequency. Generally, $P$ takes its maximum value at an intermediate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ for fixed $\ensuremath{\chi}$ and is bounded by the above formula and by $P=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{2|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})$, which gives the asymptotic value in the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}\ensuremath{\infty}$.The transition probability $P$ in the optical adiabatic rapid passage is calculated for a two-level model with dephasing. In the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}0$, where ${T}_{2}$ is the dephasing time and ${\ensuremath{\tau}}_{p}$ is the time scale of passage through the resonance region, $P$ is given by $P=\frac{[1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})]}{2}$ in which $\ensuremath{\chi}$ is the Rabi flopping frequency at resonance and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ is the time derivative of the offset angular frequency. Generally, $P$ takes its maximum value at an intermediate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ for fixed $\ensuremath{\chi}$ and is bounded by the above formula and by $P=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{2|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})$, which gives the asymptotic value in the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}\ensuremath{\infty}$.

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The transition probability

P

in the optical adiabatic rapid passage is calculated for a two-level model with dephasing. In the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}0$, where

{T}_{2}

is the dephasing time and ${\ensuremath{\tau}}_{p}$ is the time scale of passage through the resonance region,

P

is given by $P=\frac{[1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})]}{2}$ in which $\ensuremath{\chi}$ is the Rabi flopping frequency at resonance and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ is the time derivative of the offset angular frequency. Generally,

P

takes its maximum value at an intermediate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}$ for fixed $\ensuremath{\chi}$ and is bounded by the above formula and by $P=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\pi}{\ensuremath{\chi}}^{2}}{2|\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\omega}}|})$, which gives the asymptotic value in the limit $\frac{{T}_{2}}{{\ensuremath{\tau}}_{p}}\ensuremath{\rightarrow}\ensuremath{\infty}$.

^{40}\mathrm{Ca}

{}^{+}

ions by applying frequency-chirped optical pulses with time-dependent envelopes to perform rapid adiabatic passage on sideband transitions. One of the biggest advantages of adiabatic approaches is their robustness against variations in experimental parameters, which is verified by performing experiments for different pulse widths or peak Rabi frequencies. Fidelities exceeding 0.5, which is the threshold for inseparable states, are obtained over wide ranges of parameter values.