Multifrequency evaporative cooling to Bose-Einstein condensation in a high magnetic field

Abstract

We demonstrate a way to circumvent the interruption of evaporative cooling observed at high bias field for 87 Rb atoms trapped in the (F = 2, m = +2) ground state. Our scheme uses a 3-frequencies-RF-knife achieved by mixing two RF frequencies. This compensates part of the non linearity of the Zeeman effect, allowing us to achieve BEC where standard 1-frequency-RF-knife evaporation method did not work. We are able to get efficient evaporative cooling, provided that the residual detuning between the transition and the RF frequencies is smaller than the power broadening of the RF transitions at the end of the evaporation ramp.Forced evaporative cooling of atoms [1,2] in a magnetic trap is at the moment the only known way to achieve Bose-Einstein condensation [3][4][5]. Particles with energy significantly larger than the average thermal energy are removed from the trap and the remaining ones thermalize to a lower temperature by elastic collisions. For that, a radiofrequency (RF) magnetic field is used to induce a multi-photon transition from a trapping state to a non-trapping state via all intermediate Zeeman sublevels. Atoms moving in the trap with sufficient energy can reach the resonance point (RF knife) and exit the trap. If the RF-frequency is decreased slowly enough, and no other process is hampering the forced-evaporation, the increase of the phase space density obtained by this method eventually leads to Bose-Einstein condensation.In a previous publication [6], we reported that RF forced evaporative cooling of 87 Rb atoms in the (F = 2, m = +2) ground state in a magnetic trap with a high bias field is hindered and eventually interrupted. Our interpretation of this phenomenon is based on the non-linear terms of the Zeeman effect that lift the degeneracy of transition frequencies between adjacent Zeeman sublevels. This interpretation is supported by numerical calculations [7]. Interrupted evaporative cooling in a large magnetic field is a serious problem in several situations, interesting for practical reasons -like the use of permanent magnets [8] or of an iron core electromagnet as the one described in [9]. High magnetic field evaporation is also important in connection with Feshbach resonances [10][11][12][13]. In this paper, we demonstrate that it is possible to achieve efficient evaporative cooling in a high magnetic field, by use of a multi-frequency RF knife allowing a multi-photon transition to take place across non equidistant levels. We show that, for our range of magnetic fields, it is possible to use a simple experimental scheme where the three required frequencies are obtained by RF frequency mixing yielding a carrier and two sidebands. 1We focus in this paper on 87 Rb in the F = 2 manifold of the electronic ground state. Atoms are initially trapped in the m = +2 state. Our high bias field magnetic trap follows the Ioffe-Pritchard scheme. To the second order in position (see eq. 1 in [6]), the magnetic field modulus B has a 3D quadratic dependence allowing trapping, plus a bias field B 0 b...

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“…Indeed, the atoms in F = 2 see a trapping potential twice as steep as for F = 1, and as in [5], very few target atoms are evaporated at the beginning of the evaporation sequence. Moreover, at our high bias field, the non linear Zeeman effect prevents rf coupling of the |F = 2, m F = 2 trapping state to any non trapping state at the end of the evaporation [6,8]. When starting with a very small (≤ 3 × 10 4 ) number of atoms in F = 2, we get a F = 1 condensate with typically 10 6 atoms.…”

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“…Typically, our BECs comprise 3.5 ×10 5 atoms and are characterized by a chemical potential µ TF /2π ∼ 4.6 kHz and Thomas-Fermi half length L TF = 150 µm and radius R TF = 1.5 µm. Further details of our experimental apparatus are presented in [33].…”

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“…Typically, our BECs comprise 3.5 × 10 5 atoms and are characterized by a chemical potential µ TF /2πh ∼ 4.6 kHz and Thomas-Fermi half length L TF = 150 µm and radius R TF = 1.5 µm. Further details of our experimental apparatus are presented in [33]. The large aspect ratio of the trap is of primary importance for the experiments described in this paper.…”