Due to the inevitability of nonlinear collisions between particles in ultracold atomic condensate experiments, it is of great significance to study the nonlinear effect for producing ultracold molecules from atomic condensates. In this work, we investigate theoretically the nonlinear effect induced by the two-body collision for producing ultracold Cs2 molecules from ultracold atoms by the stimulated Raman adiabatic passage in a tunneling four-level structure. Under the two-photon resonance condition and the coherent population trapping state, the conversion efficiency is influenced significantly by the nonlinear parameter. Meanwhile, the optimized parameter ranges of the resonance tunneling strength at the unstable excited molecular states, the effective Rabi frequencies of the two-laser fields, and the detuning of the pump field for different nonlinear parameters are suggested to obtain the high conversion efficiency of Cs2 molecules at the ground state. Finally, a maximum conversion efficiency of up to 88.56% can be realized in the optimized parameter ranges.
Due to the inevitability of nonlinear collisions between particles in ultracold atomic condensate experiments, it is of great significance to study the nonlinear effect for producing ultracold molecules from atomic condensates. In this work, we investigate theoretically the nonlinear effect induced by the two-body collision for producing ultracold Cs2 molecules from ultracold atoms by the stimulated Raman adiabatic passage in a tunneling four-level structure. Under the two-photon resonance condition and the coherent population trapping state, the conversion efficiency is influenced significantly by the nonlinear parameter. Meanwhile, the optimized parameter ranges of the resonance tunneling strength at the unstable excited molecular states, the effective Rabi frequencies of the two-laser fields, and the detuning of the pump field for different nonlinear parameters are suggested to obtain the high conversion efficiency of Cs2 molecules at the ground state. Finally, a maximum conversion efficiency of up to 88.56% can be realized in the optimized parameter ranges.
The optimum conditions for producing Cs2 molecular condensates from Cs atomic condensates with high transfer efficiency by stimulated Raman adiabatic passage are presented. Under the extended ``two-photon'' resonance condition, including the two-photon process, the mean-field correction, and the tunneling coupling between two upper excited molecular levels, a high and stable conversion efficiency is realized. The high conversion efficiency could be achieved by following two methods under experimentally less demanding conditions (relatively small effective Rabi frequency for pump laser pulse). One is adjusting the detuning difference between two laser pulses for same effective Rabi frequencies with up to 87.2% transfer efficiency. Another one is adjusting the effective Rabi frequency, the detuning of dump laser for given effective Rabi frequency, and the detuning of pump laser with up to 80.7% transfer efficiency.
On the basis of the stimulated Raman adiabatic passage technology, we study the conversion of ultracold atoms into diatomic molecules by using a square-shaped pulse field. By the method of adiabatic fidelity, we analyze the dynamical evolution process of the coherent population trapping state for the atom-molecule conversion system. We introduce two adiabatic fidelities to describe the efficiency of ultracold atom-molecule conversion, i.e.:1) the final adiabatic fidelity, which gives the value of the adiabatic fidelity at the end of the evolution:the closer to 1 it is, the higher the conversion efficiency is; 2) the final maximum adiabatic fidelity, which denotes the maximum value that can be achieved at the end of evolution, indicating the highest conversion efficiency. With these two quantities, we discuss how to achieve higher adiabatic fidelity for the coherent population trapping state through optimizing the pulse-delay time and the pulse-laser intensity of the stimulated Raman adiabatic passage. In addition, we also discuss the effects of the width of pulses on the ultracold atom-molecule conversion efficiency and the feasibility of continuous light. It is shown that the final adiabatic fidelity of the coherent population trapping state demonstrates a large periodic oscillation with the pulse-laser intensity. By calculating and analyzing the final adiabatic fidelity and the final maximum adiabatic fidelity, we obtain the conditions for higher efficiency conversion, which gives the best choice of the pulse-laser intensity, the pulse-delay time, and the width of pulses. The results show that the scheme of square-shaped pulses we discussed has obvious advantages compared with that of Gaussian-shaped pulses, which can achieve high adiabatic fidelity and realize higher ultracold atom-molecule conversion efficiency via employing the pulse-laser field with low intensity. Further detailed comparison between the square-shaped pulses and the Gaussian-shaped pulses is also given. Particularly, we find that the final adiabatic fidelity shows a periodic oscillation with the pulse width, which means that the high efficiency atom-molecule conversion can be achieved by using a pulse field with small width. Moreover, we find that the high efficiency conversion can also be achieved by using special continuous light under certain conditions.
We theoretically investigated the properties of the effective four-level stimulated Raman adiabatic passage scheme in a cold gas of Cs atoms and molecules, where exists the tunnelling coupling between two excited molecular states due to the 0(g)- (6S,6P(3/2)) double well structure. The double dark resonance is predicted in the absorption spectrum when the tunnelling coupling strength is large enough. The double dark resonance not only reveals the formation of the ultra-cold molecules, but also provides further evidence for the tunnelling as one effective coupling mechanism between the two excited molecular states. The effect of the various experimental conditions on this phenomena has been discussed.
We study two-photon Raman photoassociation for creating a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. By exploring the dynamics of the coupled system, we show that the atom-to-molecule conversion efficiency can be controlled by changing the atom-molecule coupling strength and the effective two-photon Raman detuning. Atom-molecule coupling strength and the effective two-photon Raman detuning can be controlled by changing the laser intensity. We analyze the dynamics of the coupled atom-molecular condensate system by changing the laser intensity over a broad range, keeping the effective two-photon Raman detuning fixed. The effective two-photon Raman detuning depends on the two-photon detuning, Rabi frequencies, and the light shifting (AC Stark shift) of the levels. To keep the effective two-photon Raman detuning fixed, the two-photon detuning is varied to compensate for the light shifting of levels with laser intensity. The corresponding changes in the effective decay rates and the scattering length due to the change in the Rabi frequencies have been taken into account. Dependence of the conversion efficiency on the effective two-photon Raman detuning has also been studied by varying the laser intensity over a narrow range, keeping the two-photon detuning unchanged. The dynamics of the coupled system has been studied in Gross-Pitaevskii and modified Gross-Pitaevskii approaches to demonstrate the effect of the higher order nonlinearity (Lee-Huang-Yang term) with the increase in the laser intensity.
One possibility for the creation of ultracold, high phase space density quantum gases of molecules in the rovibronic ground state relies on first associating weakly-bound molecules from quantum-degenerate atomic gases on a Feshbach resonance and then transferring the molecules via several steps of coherent two-photon stimulated Raman adiabatic passage (STIRAP) into the rovibronic ground state. Here, in ultracold samples of Cs2 Feshbach molecules produced out of ultracold samples of Cs atoms, we observe several optical transitions to deeply-bound rovibrational levels of the excited 0(u)+ molecular potentials with high resolution. At least one of these transitions, although rather weak, allows efficient STIRAP transfer into the deeply-bound vibrational level (see text for symbols)v = 73 > of the singlet X1 sigma(g)+ ground state potential, as recently demonstrated (J. G. Danzl, E. Haller, M. Gustavsson, M. J. Mark, R. Hart, N. Bouloufa, O. Dulieu, H. Ritsch, and H.-C. Nägerl, Science, 2008, 321, 1062). From this level, the rovibrational ground state (see text for symbols)v = 0, J = 0 > can be reached with one more transfer step. In total, our results show that coherent ground state transfer for Cs2 is possible using a maximum of two successive two-photon STIRAP processes or one single four-photon STIRAP process.
A quantum gas of ultracold molecules, with long-range and anisotropic interactions, will enable a series of fundamental studies in physics and chemistry. In particular, samples of ground-state molecules at ultralow temperatures and high number densities will facilitate the explorations of a large number of many-body physical phenomena and applications in quantum information processing. However, due to the lack of efficiently cooling techniques such as laser cooling for atomic gases, high number densities for ultracold molecular samples are not readily attainable. Associating ultracold atoms to weakly bound dimer molecules via Feshbach resonance and subsequently transferring them to a wanted molecular ro-vibronic ground state by a stimulated Raman adiabatic passages (STIRAP) have proved to be an effective way in producing ideal ultracold molecular samples. As a typical illustration, in a recent study (2010 Nat. Phys. 6 265) Danzl et al. experimentally realized the preparation of Cs2 molecule into its ro-vibronic ground state via two different multi-level STIRAPs:one is based on a single conversion route and the others are based on a cascade-connected route (labeled by 4p-STIRAP and s-STIRAP, respectively). In this work, we present a theoretical study for these two STIRAP schemes, focusing on the differences in physical principle and realistic performance between them. On the one hand, according to the theoretical approach of quasi-dark eigenstates, we conclude that a highly efficient population transfer is achievable in both schemes. On the other hand, by systematically studying the influences of the relevant parameters, including the spontaneous decays and the detunings from the intermediate states, and the temporal sequence and the amplitude of the laser pulses, we disclose their respective advantages and weaknesses in the realistic implementation. We theoretically predict that for both schemes their maximal conversion efficiencies each can attain 0.97 as long as the spontaneous decays from the intermediate excited states are sufficiently suppressed. Yet considering the fact that the already implemented efficiency is only around 0.6 for both schemes, there is still room for optimization, e.g. using stable Rydberg energy levels in future experiment. Furthermore, the success of these two schemes can provide a new route to the controllable entanglement preparation, opening more applications in the fields of quantum logic gate and so on.