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In the Comment by M. Mackie textit{et al.} [arXiv: physics/0212111 v.4], the authors suggest that the molecular conversion efficiency in atom-molecule STIRAP can be improved by lowering the initial atomic density, which in turn requires longer pulse durations to maintain adiabaticity. Apart from the fact that the mean-field approximation becomes questionable at low densities, we point out that a low-density strategy with longer pulses has several problems. It generally requires higher pulse energies, and increases radiative losses. We also show that even within the approximations used in the Comment, their example leads to no efficiency improvement compared to our high-density case. In a more careful analysis including radiative losses neglected in the Comment, the proposed strategy gives almost no conversion owing to the longer pulse durations required.
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The process of stimulated Raman adiabatic passage (STIRAP) provides a possible route for the generation of a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. We analyze this process in a three-dimensional mean-field theory, including atom-atom interactions and non-resonant intermediate levels. We find that the process is feasible, but at larger Rabi frequencies than anticipated from a crude single-mode lossless analysis, due to two-photon dephasing caused by the atomic interactions. We then identify optimal strategies in STIRAP allowing one to maintain high conversion efficiencies with smaller Rabi frequencies and under experimentally less demanding conditions.
We report the achievement of stimulated Raman adiabatic passage (STIRAP) in the microwave frequency range between internal states of a Bose-Einstein condensate (BEC) magnetically trapped in the vicinity of an atom chip. The STIRAP protocol used in this experiment is robust to external perturbations as it is an adiabatic transfer, and power-efficient as it involves only resonant (or quasi-resonant) processes. Taking into account the effect of losses and collisions in a non-linear Bloch equations model, we show that the maximum transfer efficiency is obtained for non-zero values of the one- and two-photon detunings, which is confirmed quantitatively by our experimental measurements.
We propose the use of stimulated Raman adiabatic passage (STIRAP) to offer a fast high fidelity method of performing SU(2) rotations on spinor Bose Einstein condensates (BEC). Past demonstrations of BEC optical control suffer from difficulties arising from collective enhancement of spontaneous emission and inefficient two-photon transitions originating from selection rules. We present here a novel scheme which allows for arbitrary coherent rotations of two-component BECs while overcoming these issues. Numerical tests of the method show that for BECs of ce{^{87}Rb} with up to $ 10^4 $ atoms and gate times of $ SI{1}{microsecond} $, decoherence due to spontaneous emission can be suppressed to negligible values.
We propose a technique which produces nearly complete ionization of the population of a discrete state coupled to a continuum by a two-photon transition via a lossy intermediate state whose lifetime is much shorter than the interaction duration. We show that using counterintuitively ordered pulses, as in stimulated Raman adiabatic passage (STIRAP), wherein the pulse coupling the intermediate state to the continuum precedes and partly overlaps the pulse coupling the initial and intermediate states, greatly increases the ionization signal and strongly reduces the population loss due to spontaneous emission through the lossy state. For strong spontaneous emission from that state, however, the ionization is never complete because the dark state required for STIRAP does not exist. We demonstrate that this drawback can be eliminated almost completely by creating a laser-induced continuum structure (LICS) by embedding a third discrete state into the continuum with a third control laser. This LICS introduces some coherence into the continuum, which enables a STIRAP-like population transfer into the continuum. A highly accurate analytic description is developed and numerical results are presented for Gaussian pulse shapes.
The coupling of electrons to matter is at the heart of our understanding of material properties such as electrical conductivity. One of the most intriguing effects is that electron-phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, the basis for BCS superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate (BEC) and show that it can excite phonons and eventually set the whole condensate into a collective oscillation. We find that the coupling is surprisingly strong as compared to ionic impurities due to the more favorable mass ratio. The electron is held in place by a single charged ionic core forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size comparable to the dimensions of the BEC, namely up to 8 micrometers. In such a state, corresponding to a principal quantum number of n=202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects due to the electron exploring the wings of the BEC. Based on our results we anticipate future experiments on electron wavefunction imaging, investigation of phonon mediated coupling of single electrons, and applications in quantum optics.
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