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arXiv:1503.07395 · Journal of Physics B Atomic Molecular and Optical Physics

Two-photon adiabatic passage in ultracold Rb interacting with a single nanosecond, chirped pulse

Gengyuan Liu, Svetlana Malinovskaya

Published Aug 13, 2015• 4 citations
arXivHTMLPDF

Abstract

Abstract A semiclassical, four-level model of a nanosecond, chirped pulse interacting with all optically accessible hyperfine states in an ultracold alkali atom, e.g., the 85 Rb, is analyzed aiming at population inversion within 5S 1/2 electronic state. The nature of two-photon adiabatic passage performed by a single pulse having the bandwidth prior to chirping significantly narrower than the hyperfine splitting of 5S 1/2 state is investigated in the framework of the dressed state picture. It is shown that two dressed states are involved in the adiabatic dynamics of population inversion. The excited state manifold appeared to play an important mediating role in the mechanism of population transfer.

DOI
10.1088/0953-4075/48/19/194001

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arXiv:physics/0404028•Physical Review A•Sep 27, 2004•107 citations
Abstract A semiclassical, four-level model of a nanosecond, chirped pulse interacting with all optically accessible hyperfine states in an ultracold alkali atom, e.g., the 85 Rb, is analyzed aiming at population inversion within 5S 1/2 electronic state. The nature of two-photon adiabatic passage performed by a single pulse having the bandwidth prior to chirping significantly narrower than the hyperfine splitting of 5S 1/2 state is investigated in the framework of the dressed state picture. It is shown that two dressed states are involved in the adiabatic dynamics of population inversion. The excited state manifold appeared to play an important mediating role in the mechanism of population transfer.
We implement a four-level semiclassical model of a single pulse interacting with the hyperfine structure in ultracold rubidium aimed at control of population dynamics and quantum state preparation. We discuss a method based on pulse chirping to achieve population inversion between hyperfine states of the 5S5S5S shell. The results may prove useful for quantum operations with ultracold atoms.
At ultracold temperatures, atoms are free from thermal motion, which makes them ideal objects of investigations aiming to advance high-precision spectroscopy, metrology, quantum computation, producing Bose condensates, etc. The quantum state of ultracold atoms may be created and manipulated by making use of quantum control methods employing low-intensity pulses. We theoretically investigate population dynamics of ultracold Rb vapor induced by nanosecond linearly chirped pulses having kW/cm2 beam intensity and show a possibility of controllable population transfer between hyperfine (HpF) levels of 5(2)/S(1/2) state through Raman transitions. Satisfying the one-photon resonance condition with the lowest of the HpF states of 5(2)/P(1/2) or 5(2)/P(3/2) state allows us to enter the adiabatic region of population transfer at very low field intensities, such that corresponding Rabi frequencies are less than or equal to the HpF splitting. This methodology provides a robust way to create a specifically designed superposition state in Rb in the basis of HpF levels and perform state manipulation controllable on the picosecond-to-nanosecond time scale.
We theoretically investigate the population dynamics of the valence electron of elements of the alkali series induced by nanosecond linearly chirped (LC) pulses having kW cm−2 beam intensity and examine two different shapes of the pulse envelope. We demonstrate the possibility of controllable population transfer between hyperfine (HpF) levels of the S orbital through Raman transitions. We assume that the atoms are in the state of an ultracold vapor and Doppler free. Detuning slightly below the one-photon resonance condition with the lowest of the HpF states of the corresponding P orbital avoids interaction of the pulse with the other HpF levels of the P orbital and allows us to enter the adiabatic region of population transfer at very low field intensities, such that the corresponding Rabi frequencies are on the order of the hyperfine splitting of the S orbital. This methodology provides a robust way to create a specially designed superposition state in such atoms in the basis of the HpF levels and perform state manipulation controllable on the picosecond-to-nanosecond timescale.
We investigate the behavior of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in the field of a sequence of frequency-chirped short laser pulses. The analysis is based on a numerical solution of equations for the probability amplitudes of the hyperfine levels of the ${5S}_{1/2}{\ensuremath{-}5P}_{3/2}$ transition in the 85Rb{}^{85}\mathrm{Rb}85Rb atom and the dressed-states analysis. We analyze different regimes of interaction, including relatively short laser pulses (when the width of the pulse envelope spectrum is of the order of or exceeds the frequency interval between the hyperfine levels resulting in effective mixing of them) and relatively long ones (when the ground hyperfine levels are resolved but the excited ones are not resolved). In the latter case dependence of the population transfer efficiency on the initial coherence of the ground states is analyzed. The case of long laser pulses when all working hyperfine levels are resolved is also discussed using numerical simulations and a dressed-states analysis. We show that in all regimes considered, the interaction of a frequency-chirped laser pulse with the multilevel 85Rb{}^{85}\mathrm{Rb}85Rb system is similar to the interaction with an effective two-level atom at sufficiently large peak intensities of the pulses. It allows us to perform efficient excitation of the multilevel atom by transferring populations of two hyperfine ground states to the excited ones and back to the ground states using a pair of frequency-chirped laser pulses. We propose to utilize this scheme of population transfer for the coherent manipulation of a beam of 85Rb{}^{85}\mathrm{Rb}85Rb atoms using sequences of counterpropagating frequency-chirped short laser pulses.
Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s->5p->5d of the rubidium atom by frequency swept ultra short laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s->5p transition, and later with the 5p->5d transition. With this intuitive scheme it is possible to achieve complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a {open_quote}counterintuitive{close_quote} direction of the frequency-sweep, in which case population of the intermediate level during the pulse is strongly reduced. The atomic system can be seen as a model system for multistep vibrational excitation in an anharmonic molecular potential.
This theoretical paper presents numerical calculations for the photoassociation of ultracold cesium atoms with a chirped laser pulse and a detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wave function. In the chosen example, it is shown that an important population transfer is achieved to $\ensuremath{\approx}15$ vibrational levels in the vicinity of the v=98v=98v=98 bound level in the external well of the ${0}_{g}^{\ensuremath{-}}(6s+6{p}_{3∕2})$ potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a ``photoassociation window.'' Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\sum}_{u}^{+}(6\mathrm{s}+6\mathrm{s})$ state is significant, making stable molecules. The results are interpreted in the framework of a two-state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating in the excited state a vibrational wave packet that is focusing at the barrier of the double-well potential.