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Journal of Modern Optics

Robust control in ultracold alkali metals using a single linearly chirped pulse

Tom Collins, Svetlana Malinovskaya

Published Aug 17, 2012• 4 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2012.712726

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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.
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.
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 present a scheme of population transfer between two metastable (ground) states of the $\ensuremath{\Lambda}$ atom without considerable excitation of the atom using single frequency-chirped laser pulses. The physics of the process is generation of the ``trapped'' superposition of the ground states by the laser pulse at sufficiently high laser peak intensity. The main conditions for realization of this regime are the following: The width of the transform-limited laser pulse envelope frequency spectrum (without chirp) must be smaller and the peak Rabi frequency of the pulse must be larger than the frequency interval between the two ground states of the $\ensuremath{\Lambda}$ atom. During the frequency chirp, the laser pulse must first come into resonance with the transition from the initially occupied ground state to the excited state and after that with the transition between the excited and second initially empty ground states. In the case when the envelope frequency spectrum width (without chirp) of the pulse exceeds the frequency interval between the two ground states, we show a possibility of controllable generation of superposition of the ground states with a controllable excitation of the $\ensuremath{\Lambda}$ atom.
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.
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.