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Physical Review A

Population transfer in the Nas-pRydberg ladder by a chirped microwave pulse

H. Maeda, J. H. Gurian, Thomas F. Gallagher

Published Dec 21, 2011• 6 citations
Publisher

Abstract

While quantum defects of $n\ensuremath{\ell}$ Rydberg states of Na with $\ensuremath{\ell}\ensuremath{\ge}2$ are nearly equal to zero, the quantum defects of $ns$ and $np$ states of Na are quite large due to the finite size of its ionic core. Since the Na $ns$ and $np$ states are energetically isolated from the higher angular momentum states of the same $n$, we can think of the Na $ns$ and $np$ Rydberg states as a specific example of a simple multilevel ladder system consisting of only alternating $s$ and $p$ angular momentum states. Here we report that population transfer in the Na s-p Rydberg ladder can be effectively achieved using a frequency-chirped microwave pulse, which couples only $s$ and $p$ states under suitable conditions.

DOI
10.1103/physreva.84.063421

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While quantum defects of n\ensuremathℓn\ensuremath{\ell}n\ensuremathℓ Rydberg states of Na with \ensuremathℓ\ensuremath≥2\ensuremath{\ell}\ensuremath{\ge}2\ensuremathℓ\ensuremath≥2 are nearly equal to zero, the quantum defects of nsnsns and npnpnp states of Na are quite large due to the finite size of its ionic core. Since the Na nsnsns and npnpnp states are energetically isolated from the higher angular momentum states of the same nnn, we can think of the Na nsnsns and npnpnp Rydberg states as a specific example of a simple multilevel ladder system consisting of only alternating sss and ppp angular momentum states. Here we report that population transfer in the Na s-p Rydberg ladder can be effectively achieved using a frequency-chirped microwave pulse, which couples only sss and ppp states under suitable conditions.
We demonstrate that Rydberg atoms can be transferred to states of lower principal quantum number by exposing them to a frequency chirped microwave pulse. Specifically, we have transferred n=75n=75n=75 atoms to n=66n=66n=66 with a 400-ns pulse chirped from 7.8 to 11.8 GHz. In spite of the large number of coupled levels, using a simplified model we can describe the process reasonably well as a sequence of adiabatic rapid passages.
We present a comprehensive and ab initio nonperturbative investigation of the coherent population transfer among the 3D high-lying Rydberg hydrogen and alkali atomic states via linearly polarized chirped microwave pulses. The time-dependent Schrödinger equation for the dynamical evolution of Rydberg atoms is accurately and efficiently solved by means of the time-dependent generalized pseudospectral method. For atomic H, the population transfer from n = 35 to 30 with nearly 100% efficiency is achieved by means of the sequential two-photon Deltan = -1 transitions. The calculation fully utilizes all of the available orbital angular momentum l states for a given n, and the interference pattern and population evolution dynamics of individual l states are analyzed in detail. It is shown that the coherent control of the population transfer from the high n to the low n states can be accomplished by the optimization of the chirping parameters and microwave field strength. Similar analysis is performed for the Na atom, where the alkali atomic structure is described by an accurate model potential. We found that while the global population transfer pattern is qualitatively similar, there are significant differences in the dynamical response of atomic H and Na to the chirped microwave fields. Due to the degeneracy of the l states (for a given n) in unperturbed atomic H, the population transfer involves significant coupling and interference among a number of low-lying l states. For the case of Na atoms, however, the population transfer from the n to (n - 1) state is dominated by a single channel, namely, from the |n,l = 0> to the |n - 1,l = 0> state.
Using the time-dependent multilevel approach, we have calculated the coherent population transfer between the quantum states of potassium atom by a single frequency-chirped laser pulse. The result shows that a pair of sequential 'broadband' frequency-chirped laser pulses can efficiently transfer population from the initial state of the ladder system to the target state. It is also found that the population can be efficiently transferred to a target state and trapped there by using an 'intuitive' or a 'counterintuitive' frequency sweep laser pulse in the case of 'narrowband' frequency-chirped laser pulse. Our research shows that the complete population transfer is related to the pulse duration, chirp rate, and amplitude of the laser pulse.
The time-dependent multilevel approach (TDMA) and B-spline expansion technique are used to study the coherent population transfer between the quantum states of a potassium atom by a single frequency-chirped microwave pulse. The Rydberg potassium atom energy levels of n = 6–15, l = 0–5 states in zero field are calculated and the results are in good agreement with other theoretical values. The time evolutions of the population transfer of the six states from n = 70 to n = 75 in different microwave fields are obtained. The results show that the coherent control of the population transfer from the lower states to the higher ones can be accomplished by optimizing the microwave pulse parameters.
Generally, high optical intensity is required for effective multiphoton excitation of quantum systems to highly excited states. In certain situations, however, lower-intensity, chirped pulses can provide more efficient transfer of population to the upper states by the process of adiabatic passage. We have studied the relative importance of these two mechanisms in the anharmonic $5s\ensuremath{-}5p\ensuremath{-}5d$ quantum ladder system of rubidium using frequency chirped laser pulses from an amplified Ti:sapphire laser (\ensuremath{\lambda}=780 and \ensuremath{\Delta}\ensuremath{\lambda}=10 nm). We measure simultaneously the three-photon ionization signal due to the Ti:sapphire and the population that remains in the 5d5d5d state with a postionizing 532-nm Nd:YAG pulse (where YAG denotes yttrium aluminum garnet). At low infrared fluences (80 \ensuremath{\mu}J/cm2{\mathrm{J}/\mathrm{c}\mathrm{m}}^{2}J/cm2), the transfer to the 5d5d5d state is significantly enhanced when the pulse frequency is swept from the red to the blue, such that it follows the frequency spacing of the rubidium ladder. Counterintuitively, population is also transferred efficiently for the blue-to-red chirp at high fluences (>5 mJ/cm2{\mathrm{m}\mathrm{J}/\mathrm{c}\mathrm{m}}^{2}mJ/cm2). We attribute both of these effects to adiabatic passage from the 5s5s5s state to the 5d5d5d state. Even at the highest fluences, more efficient transfer occurs for either direction of chirp than occurs at zero chirp, where the intensity is maximal. A comparison to theoretical predictions reveals striking agreement in both absolute magnitude and functional form. These results have important implications for the understanding of population transfer in complex ladder systems, such as molecular anharmonic vibrational ladders.