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Physical Review A

Detuning-induced stimulated Raman adiabatic passage in atoms with hyperfine structure

Li Deng, Takashi Nakajima

Published Feb 7, 2014• 5 citations
Publisher

Abstract

We theoretically study the generation of coherence in generalized two-level atoms with hyperfine structure by utilizing the detuning-induced stimulated Raman adiabatic passage (D-STIRAP). As expected, the degree of attainable coherence between the ground and excited states cannot be as large as that for the ideal two-level atoms without hyperfine structure. However, we find that the substantial degree of coherence can still be produced with small modulations, and the modulation period is essentially determined by the hyperfine splittings in the ground and excited states. The D-STIRAP scheme in generalized two-level atoms is sufficiently robust against the various parameters such as intensities of lasers, initial detuning, time delay between the laser pulses, and Doppler broadening. As a specific example, we show realistic results for the ${D}_{1}$ transition of Na.

DOI
10.1103/physreva.89.023406

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We theoretically study the generation of coherence in generalized two-level atoms with hyperfine structure by utilizing the detuning-induced stimulated Raman adiabatic passage (D-STIRAP). As expected, the degree of attainable coherence between the ground and excited states cannot be as large as that for the ideal two-level atoms without hyperfine structure. However, we find that the substantial degree of coherence can still be produced with small modulations, and the modulation period is essentially determined by the hyperfine splittings in the ground and excited states. The D-STIRAP scheme in generalized two-level atoms is sufficiently robust against the various parameters such as intensities of lasers, initial detuning, time delay between the laser pulses, and Doppler broadening. As a specific example, we show realistic results for the D1{D}_{1}D1​ transition of Na.
We theoretically study the transparency in the generalized two-level system with hyperfine structure by utilizing double detuning-induced stimulated Raman adiabatic passage (double D-STIRAP). The double D-STIRAP is carried out by sequentially applying the three pulses, one near-resonant pump pulse and two far-off resonant Stark pulses before and after the pump pulse. From the study of single-atom response we can roughly learn the transparency conditions, since the full recovery of the system to the initial state is associated with the perfect transparency. After the numerical calculations we find that, for the perfect transparency, the pulse intensities of double D-STIRAP for the generalized two-level systems with hyperfine structure has to be stronger than that for the ideal two-level system. More precisely, we find that the ratio of amplitude to time for the Rabi frequency of the pump pulse and the detuning induced by the Stark pulse have to be close to each other to satisfy the adiabatic conditions. The above conditions, however, are necessary conditions we can learn from the single-atom response, and to ensure that they are indeed sufficient for perfect transparency, we perform the propagation calculations to obtain the temporal profile of the pump pulse at arbitrary propagation depths to find that double D-STIRAP, when applied to the generalized two-level system with hyperfine structure, is indeed robust for perfect transparency.
Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ^{23}Na^{40}K ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.
The detuning-induced stimulated Raman adiabatic passage (D-STIRAP) in two-level systems with permanent dipole moments (PDMs) is investigated. Based on a transformed Schr\"odinger equation, we discuss the coherence generation under the one- and two-photon excitations, respectively. In the one-photon excitation, our analysis shows that the envelope of the pump pulse gets modulated in presence of the PDMs. The modulation becomes stronger while the difference between the PDMs of the two levels becomes larger. Gradually, the adiabatic process of the D-STIRAP fails to complete and the robustness of the technique disappears. Therefore, parameters have to be chosen with care if maximum coherence is desired in systems with large or giant difference between the PDMs. Similar results can also be found in the two-photon excitation, although the influence of the PDMs on the D-STIRAP seems weaker compared with that in the one-photon excitation case. Finally, we point out that the negative role of the PDMs can be effectively avoided by simply choosing longer pulses instead and the D-STIRAP can be safely applied in two-level systems with PDMs.
In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are $N\ensuremath{-}1$ ground levels and one excited level. The ground levels are coupled with laser pulses through the excited level at multiphoton resonance. The ultimate aim of this scheme is to create coherent-superposition states on the ground levels. In a previous paper [J. Mod. Opt. (to be published), special issue on quantum interference] we have considered this problem from the optimal-control point of view. Here we apply a different approach: We reconsider the adiabatic approximation, which is commonly utilized to describing the STIRAP process. It is shown that in our case, in the adiabatic limit, the dark and bright subspaces of the Hamiltonian are decoupled; however, the nonadiabatic corrections influence significantly the dynamics in the dark subspace. An analytic solution is presented for the case of a five-level system. Moreover, we consider some special examples for the pulse sequences that effect prescribed final superposition states. The robustness of the scheme is studied, and the extension of our scheme is also considered.
We investigate the coherence generation in dense two-level systems under detuning-induced stimulated Raman adiabatic passage (D-STIRAP). In the dense two-level system, the near dipole–dipole (NDD) interaction should be taken into consideration. With the increase in the strength of the NDD interaction, it is found that a switchlike transition of the generated coherence from maximum value to zero appears. Meanwhile, the adiabatic condition of the D-STIRAP is destroyed in the presence of the NDD interaction. In order to avoid the sudden decrease in the generated coherence and maintain the maximum value, we can use stronger detuning pulse or pump pulse, between which increasing the intensity of the detuning pulse is of more efficiency. Except for taking advantage of such maximum coherence in the high density case into areas like enhancing the four-wave mixing process, we also point out that the phenomenon of the coherence transition can be applied as an optical switch.
We discuss the properties of a simple and robust scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states - fractional stimulated Raman adiabatic passage (fractional STIRAP) - first proposed by Marte et al (1991 Phys. Rev. A 44 R4118). As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, here the two pulses terminate simultaneously, while maintaining a constant ratio of amplitudes. We extend earlier research and suggest a realization of this scheme with two smoothly varying delayed laser pulses (which can be derived from a single laser), the parameters of the created superposition being controlled by the polarization of the delayed pulse. Furthermore, we provide simple analytic estimates of the robustness of this process against variations in the laser intensity, laser frequency and pulse delay. Finally, we discuss an extension to multistate systems which provides a possibility for creating coherent superpositions of more than two states.