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Optics Letters

Manipulation of ultracold Rb atoms using a single linearly chirped laser pulse

Tom Collins, Svetlana Malinovskaya

Published Jun 7, 2012• 24 citations
Publisher

Abstract

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.

DOI
10.1364/ol.37.002298

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•Mar 1, 2009•4 citations
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.
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.
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.
We develop a pulse-driven jump protocol to achieve all-optical Raman control of ultracold atomic hyperfine states. By establishing general conditions for adiabatic evolution between quantum states in parameter space, we derive the essential pulse area and phase conditions necessary for quantum state transfer in a resonant single-ΛΛΛ three-level system. We extend this approach to a double-ΛΛΛ four-level system by incorporating a neighboring intermediate state, which leads to a single-photon detuned ΛΛΛ three-level system. Through numerical simulations of the ultracold 87^{87}87Rb atomic system, we demonstrate that high-fidelity and robust control of quantum state transfer can be achieved in the single-ΛΛΛ three-level system using stimulated Raman adiabatic passage (STIRAP) and the pulsed jump protocol. Furthermore, we show that the destructive quantum interference effects between resonant and detuned Raman pathways in the double-ΛΛΛ four-level system can be mitigated by optimizing the pulse area and two-photon detuning parameters within the pulsed jump protocol. This work presents a promising approach for achieving all-optical Raman control of quantum state transfer in ultracold atomic hyperfine states.
The range of atoms which can be cooled by lasers is limited to those which have a closed two level structure. Several schemes have been proposed which aim to extend this range by using coherent control of the particle momenta, but none have yet been demonstrated. We hope to implement these and other coherent manipulation schemes, and we begin with a system which is well understood and over which we can exert precise control. This thesis covers the design and construction of an experiment to demonstrate coherent manipulation of cold rubidium atoms collected in a magneto-optical trap. The lower hyperfine levels of these cold atoms very closely mimic the ideal two-level atom, and we use carefully crafted laser pulses to prepare, manipulate, and read their quantum state. The hyperfine levels are coupled using two fields whose frequency difference is equal to the hyperfine splitting. The way in which these Raman coupled levels can be used to emulate a two-level atom is explored, and the experimental apparatus used to create and control the driving fields is described in detail. The amplitude, frequency and phase of these fields is programmable, and complex manipulation schemes can be implemented merely by programming a computer. We have observed Raman transitions in the cold rubidium atoms, and the experimental methods used to detect these features amidst large experimental noise are discussed. Although we have not yet seen Rabi oscillations, we are confident that we can now have sufficient control to begin to implement simple interferometric sequences. However, there remain significant challenges if we are to coherently manipulate the momentum, and the prospects for such manipulation are discussed.