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Physical Review A

Transparency under double detuning-induced stimulated Raman adiabatic passage in atoms with hyperfine structure

Li Deng, Takashi Nakajima, Shangqing Gong

Published Jun 20, 2017• 4 citations

Abstract

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.

DOI: 10.1103/physreva.95.063828

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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.

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.

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-

Λ

three-level system. We extend this approach to a double-

Λ

four-level system by incorporating a neighboring intermediate state, which leads to a single-photon detuned

Λ

three-level system. Through numerical simulations of the ultracold

^{87}

Rb atomic system, we demonstrate that high-fidelity and robust control of quantum state transfer can be achieved in the single-

Λ

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-

Λ

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.

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.

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.

Coherent manipulation of quantum states is of crucial importance in accurate control of a quantum system. A fundamental goal is coherently transferring the population of a desired state with near-unit fidelity. For this purpose, we theoretically demonstrate a novel coherent double-stimulated Raman adiabatic passage (STIRAP) in a three-level Λ-type system for realizing the switch of unequal initial preparations on two ground states. This operation uses a single optical pulse sequence accomplishing both bright-STIRAP and dark-STIRAP processes, in which the intermediate-level detuning and the pulse delay must be given an optimal adjustment. Besides, owing to the imperfection of double-STIRAP transition, the sensitivity of the switch fidelity with respect to the spontaneous loss from the intermediate state, to the pulse amplitude and to the population difference, is also discussed. This work suggests a simple and experimentally feasible all-optical approach to switch a superposition quantum state, serving as one-step closer to the goal of coherent manipulation of quantum systems.