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Condensation and Coherence in Condensed Matter

Bose-Einstein Condensation of Metastable Helium

Claude N. Cohen-Tannoudji

Published Mar 1, 2003• 0 citations
Publisher

Abstract

Two groups, in Orsay and in Paris, have recently obtained experimental evidence for Bose-Einstein condensation on He4 atoms in the metastable state 23S1. The condensates which have been obtained are the first ones where atoms are condensed, not in their electronic ground state, but in an excited state, in this case a metastable state about 20 eV above the ground state. In principle, Penning collisions should very rapidly destroy the cloud of cold metastable atoms and it seems hopeless to observe Bose-Einstein condensation in such a system. But, as suggested by Shlyapnikov et al, the conservation of the total spin during the collision reduces the Penning collision cross-sections by several orders of magnitude and this explains why large enough densities of metastable atoms can be obtained to observe the condensation. We briefly describe the first experimental results which have been obtained in Paris. Atoms are optically detected by optical imaging at 1083 nm (wavelength of the transition connecting the metastable state 23S1 to the triplet state 23P2). The evolution of the anisotropy of the images during a ballistic expansion gives clear evidence for the condensation. Orders of magnitude are also obtained for the scattering length describing the collision between 2 metastable atoms. The large value of this scattering length (of the order of 10 nm) allows one to reach the so called hydrodynamic regime where the mean free path between 2 collisions in the thermal cloud becomes smaller than the size of the cloud. Preliminary results showing the transition between the collisionless regime and the hydrodynamic regime are presented and compared to theoretical predictions.

DOI
10.1142/9789812791269_0019

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Two groups, in Orsay and in Paris, have recently obtained experimental evidence for Bose-Einstein condensation on He4 atoms in the metastable state 23S1. The condensates which have been obtained are the first ones where atoms are condensed, not in their electronic ground state, but in an excited state, in this case a metastable state about 20 eV above the ground state. In principle, Penning collisions should very rapidly destroy the cloud of cold metastable atoms and it seems hopeless to observe Bose-Einstein condensation in such a system. But, as suggested by Shlyapnikov et al, the conservation of the total spin during the collision reduces the Penning collision cross-sections by several orders of magnitude and this explains why large enough densities of metastable atoms can be obtained to observe the condensation. We briefly describe the first experimental results which have been obtained in Paris. Atoms are optically detected by optical imaging at 1083 nm (wavelength of the transition connecting the metastable state 23S1 to the triplet state 23P2). The evolution of the anisotropy of the images during a ballistic expansion gives clear evidence for the condensation. Orders of magnitude are also obtained for the scattering length describing the collision between 2 metastable atoms. The large value of this scattering length (of the order of 10 nm) allows one to reach the so called hydrodynamic regime where the mean free path between 2 collisions in the thermal cloud becomes smaller than the size of the cloud. Preliminary results showing the transition between the collisionless regime and the hydrodynamic regime are presented and compared to theoretical predictions.
We have observed a Bose-Einstein condensate in a dilute gas of 4He{}^{4}\mathrm{He}4He in the 32S1^{3}2S_{1}32S1​ metastable state. We find a critical temperature of $(4.7\ifmmode\pm\else\textpm\fi{}0.5)\ensuremath{\mu}\mathrm{K}$ and a typical number of atoms at the threshold of $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$. The maximum number of atoms in our condensate is about $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$. An approximate value for the scattering length $a\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(16\ifmmode\pm\else\textpm\fi{}8)\mathrm{nm}$ is measured. The mean elastic collision rate at threshold is then estimated to be about $2\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{s}}^{\ensuremath{-}1}$, indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is 2s2\mathrm{s}2s, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.
This thesis presents an experimental study of an atomic cloud in the vicinity of Bose-Einstein condensation. The atoms used in our experiment are special in the sense that they are metastable -- we use metastable helium. The metastability opens the door for using new and original detection methods. Due to their internal energy, the atoms can be detected electronically by means of a micro-channel plate. The use of metastable helium is also interesting due of the presence of ionizing collisions in the sample. The He+ ions produced in collisions between the metastable atoms can be detected in real-time, and the ion signal constitutes an alternative and useful diagnostic. In particular, this signal allows one to identify very precisely the Bose-Einstein condensation threshold. One of the advantages of using this signal to probe the cloud, is its ''non-invasive nature: observing the ions does not at all alter the natural evolution of the cloud, in contrast to the ordinary detection technique which consists of releasing the atoms from the trap and then imaging the cloud. In this thesis, by using the new diagnostics based on the ion signal, we have measured some important parameters governing the collisions, and thereby the behavior of the cloud: the ionizing rate constants and the scattering length.
We report the realization of a Bose-Einstein condensate of metastable atoms (helium in the lowest triplet state). The excitation energy of each atom with respect to the ground state is 20 electron volts, but inelastic processes that would destroy the sample are suppressed strongly enough in a spin-polarized sample to allow condensation. Our detection scheme takes advantage of the metastability to achieve detection of individual atoms as well as of the decay products of inelastic processes. This detection opens the way toward new studies in mesoscopic quantum statistical physics, as well as in atomic quantum optics.
This article first provides guide lines for the understanding of laser cooling and Bose Einstein Condensation, with a general bibliography of the domain. Some details are given about the case of an ultracold gas of helium atoms in the 23S1 metastable state. Obtention of BEC will be recalled, with discussion of the inhibition of Penning ionization collisions. Recent studies at ENS with photoassociation methods will be summarized, including the formation of giant dimers providing another example of ionization inhibition.
The field of Bose-Einstein condensation (BEC) in dilute atomic gases provides a fruitful playground to test well-developed theories of quantum fluids. Research using BECs can address open questions relating to the many-body aspects of two-component quantum liquids, namely the interaction between the hydrodynamic normal and the superfluid component at finite temperatures. After the first realization of BEC some pilot experiments have been carried out, but detailed experiments are missing. This has to be compared to the case of liquid helium II, where many experiments since the 1950s have added to our understanding of novel phenomena in quantum liquids, like collective excitations, first and second sound, and others. One of the drawbacks of liquid helium is that the interactions are so strong that a clear distinction between the two components is difficult and the interpretation of the phenomena remains ambiguous. Most experimental studies of dilute Bose-Einstein condensed gases use clouds, which are in the collisionless regime. The reason for the lack of detailed experiments in BECs to study quantum liquids and in particular the hydrodynamical aspects of it, is the limited number of atoms (typically 1--10 million) in the experiments leaving the thermal atoms virtually collisionless. Efforts to decrease the mean free path by increasing the confinement limits the lifetime of the sample, since the density is limited by three-body decay. Experiments on dilute clouds of cold atoms are generally conducted in highly asymmetric traps. In these elongated, cigar-shaped geometries the mean free path of the atoms can become much shorter than the size of the cloud in the long, axial direction, but at the same time exceeds the size in the other, radial directions. In this so-called hydrodynamic-collisionless regime the system can be considered radially collisionless and axially hydrodynamic. In our setup we have created BECs containing up to 300 million sodium atoms by evaporation of atoms in an axially strongly decompressed trap with an aspect ratio of 1:65. Hot atoms created in three-body collisions are able to leave the sample in this highly asymmetric trap, before they can heat other atoms in an avalanche. The sample is axially hydrodynamic, but due to the large aspect ratio collisionless in the radial direction. Such samples are ideal for the observation of the interaction between the superfluid and normal fluid component of the cloud. In this thesis we describe the setup which is used to reach the hydrodynamic regime and we describe a novel implementation of the well-known phase contrast imaging technique. Next, we study collective excitations in the crossover from the collisionless toward the hydrodynamic regime, we determine the heat conduction in a cold, hydrodynamic thermal cloud and observe the propagation of a thermal wave in the two-fluid regime. Furthermore, we study the friction between the superfluid and normal fluid component of the cloud. In the final chapters of this thesis we study the propagation of second sound, as well as the formation and propagation of shock waves.
The thematics treated in this manuscript illustrate two specificities of ultracold metastable Helium gases: the ability to compare experimental measurement with precise theoretical evaluations (simplicity of the atomic structure) and to easily detect products of Penning ionisations. We present the building and the characterisation of a novel magnetic trap with large optical access, allowing to combine the production of a Bose-Einstein condensate with its in situ loading into a 3D optical lattice. The theoretical fundaments of the experiments planned in those optical potentials are then detailed. In a crossed dipole trap, the influence of the magnetic field, now a free parameter, on the Penning collision rates can be measured and compared to a new theoretical evaluation. Concerning Helium in optical lattices, two subjects are developped: the effect of the confinement on the inelastic Penning collisions (1D optical lattice) and the modelisation of the Penning losses via a dissipative Bose-Hubbard model (3D lattice). Finally we present the first direct measurement of the dipolar magnetic transition 23S1 to 23P2, linking the singlet and triplet families in Helium 4. This spectroscopy experiment, realised in collaboration with the group of W. Vassen (LaserLab - Amsterdam), combines cold atoms knowledge with the frequency comb technique, in order to reach an accuracy of 5 kHz.