Optique atomique quantique
(last update: april 2012)
Metastable helium, in the 2 3S1 state (denoted hereafter as He*) is a fascinating subject for study in the context of degenerate quantum gases. It has a simple internal atomic structure, an easily accessible near-infrared transition for optical manipulation and, as was demonstrated in our group in 2001 it can undergo Bose-Einstein condensation at micro-K temperatures. He* BECs have also been obtained in the groups of M. Leduc at LKB Paris (France, 2001), W. Vassen at VU Amsterdam (Netherlands, 2005), A. Truscott at ANU Canberra (Australia, 2006) and J. Doyle at Harvard (USA, 2009).
Perhaps the most important feature of He* is its large internal energy which permits direct detection of the atoms using electron multipliers and micro-channel plates (MCP). This large internal energy also causes Penning ionizing collisions (He*+He*-> He + He+ +e) between metastable atoms, and the products from these collisions can also be electronically detected. Thus He* provides a new window on quantum degenerate gas phenomena which we have been exploiting in the past several years. Indeed, in almost all of the experiments we have performed to date, data was gathered by electronic detection (an MCP) rather than by optical means.
We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub–shot-noise interferometry and studies of Einstein-Podolsky-Rosen–type nonlocality tests.
We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.
We report the realization of a Bose-Einstein condensate of He∗ in an all-optical potential. Up to 105 spin-polarized He∗ atoms are condensed in an optical dipole trap formed from a single, focused, vertically propagating far-off-resonance laser beam. The vertical trap geometry is chosen to best match the resolution characteristics of a delay-line anode microchannel plate detector capable of registering single He∗ atoms. Dipole trap: λ=1547 nm, power of 1.5 W, oscillation frequencies of 15 Hz and 2.5 kHz.
We also confirm the instability of certain spin-state combinations of 4He∗ to two-body inelastic processes, which necessarily affects the scope of future experiments using optically trapped spin mixtures. To first order atomic clouds of m=-1 and of m=+1 are stable whereas those of m=0 are unstable (β00 ~ 6 10-10cm3/s). Mixtures of m=0/+1 and 0/-1 are stable to first order and mixtures of -1/+1 are unstable with β-1+1 ~ 6 10-10cm3/s.
A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect and C. I. Westbrook, Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates , Phys. Rev. Lett. 99, 150405 (2007) [HAL preprint] [PRL]
J. Chwedenczuk, P. Zin, M. Trippenbach, A. Perrin, V. Leung, D. Boiron, C. I. Westbrook, Pair correlations of scattered atoms from two colliding Bose-Einstein Condensates: Perturbative Approach, Phys. Rev. A 78, 5 (2008) 053605 [HAL preprint] [PRA]
In the center of mass frame of a binary collision, the scattered particles come out "back to back" because of momentum conservation. In the language of deBroglie waves, the same process is called spontaneous, four wave mixing and the oppositely directed wave vectors of the outgoing waves is fixed by a phase matching condition.
We have observed such a process by producing two colliding Bose-Einstein condensates using stimulated Raman transitions. A 3D reconstruction of the collision, obtained with our position sensitive detector, is shown in the figure (right). In the left, one sees a spherical shell represented by circles of varying diameter as the halo passes through the detector location. In the mid plane of the sphere one can see two unscattered pancake-shaped condensates I and II. One can also see a third condensate III, produced by imperfect polarization of the Raman beams, and a fourth condensate IV which results from stimulated four wave mixing of condensates I, II and III.
Using the atom positions, we can study correlation functions for back to back pairs. We have also observed pairs of atoms emitted in the same direction. This is another manifestation of the Hanbury Brown Twiss effect. Although the back to back correlation is easily understood in terms of classical particles, the HBT peak is necessarily an interference phenomenon, and therefore the process is quantum mechanical. The HBT effect here gives us a measure of the size of the pair production region and therefore allows us to confirm that the momentum spread of a back to back pair, is limited chiefly by the uncertainty principle.
T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect and C. I. Westbrook, Comparison of the Hanbury Brown-Twiss effect for bosons and fermions, Nature 445, 402 (2007) [HAL preprint] [Nature]
In the summer of 2006, we transported our detector to Amsterdam to collaborate with the VU Amesterdam metastable He group there. This group had recently produced a degenerate gas of the fermionic isotope 3He* using sympathetic cooling by 4He*. Much like in our experiment of 2005 in Orsay, we released the cloud of atoms onto the detector which was placed below the trap. The detector gives the arrival times and positions of individual atoms with a quantum efficiency estimated to be 10%. With this information we can plot a histogram of separations in 3D for all the pairs in a cloud. In Amsterdam, it was possible to use the same apparatus to make measurements on both fermions and bosons and clearly show their contrasting behavior. The figure below shows normalized pair separation histograms taken at the same temperature (about 500 nK), for fermions and bosons.
The fermions show "anti-bunching" (see "dégroupement" for a French version), i.e. a tendency to avoid each other, due purely to quantum statistical effects. Interactions between the atoms are entirely negligible. This antibunching effect is reminiscent of antibunching of photons, but it is different in that the Pauli exclusion principle (or the exchange anti-symmetry of wavefunctions) forbids more than one atom to occupy the same phase space cell, and thus antibunching is unavoidable.
We have also demonstrated that a diverging atomic lens in the form of a blue-detuned, focussed laser beam, can be used to change the size of the atom source as viewed from the detector. Decreasing the effective source size, the lens increases the correlation length at the detector. Since the antibunching contrast is limited by the detector resolution, which is not small compared to the correlation length, the defocussing technique allows us to increase the anti-bunching contrast.
M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, C. I. Westbrook and A. Aspect, Hanbury Brown Twiss effect for ultracold quantum gases, Science 310, 648 (2005) [HAL preprint] [Science]
In 1956, two Astronomers, Hanbury Brown and Twiss, showed that photons emitted by a thermal light source, such as a sodium lamp or a star, behaved in a surprising way. They showed that those photons tended to arrive in groups despite the chaotic nature of the source. This bunching (see "dégroupement" for a French version) effect was especially surprising since there is no physical interaction between the photons. Later on, this effect was shown to be related to the quantum mechanical nature of those photons. Quantum mechanics separates all particles in two populations: bosons and fermions. These two classes,obey different statistics compared to classical particles. Bose statistics tend to favor configurations in which individual particles end up in a same quantum state (a Bose-Einstein Condensate is one dramatic example), whereas Fermi statistics exclude those configurations.
The combination of our metastable Helium BEC with a position sensitive micro-channel plate detector allowed us to observe this bunching behavior in 3 dimensions. To perform the experiment, we simply released a cloud of ultra-cold atoms from a magnetic trap onto the detector. After their 308ms time of flight, the arrival times and positions of each atom were recorded and the separation of all pairs was computed and histogrammed.
The atom bunching signal corresponds to the bump in the 1st figure at separations less than 1mm in the run at 0.55 microK. The 2nd two dimensional figure shows the correlation function in the plane of the detector. The asymmetry is due to the asymmetry of the spatial distribution of the source.
In order to explore atom correlations with the metastable Helium BEC apparatus, the group acquired in 2005 a position sensitive micro-channel plate detector with a delay line anode (from Roentdek). Though very common in particle and nuclear physics, this is the first use in a cold-atom physics experiment. The detector can hand high mean particle rates (up to 10MHz for the delay-line) while measuring position and arrival times of individual particles with good resolutions (230 μm and 1 ns respectively for the moment). This makes the detector particularly suitable for our experimental conditions especially because of our MHz particle rates (for a duration of 20 ms). The detector allows us to reconstruct the atomic cloud on an atom by atom basis.
Here is an example of 3D reconstruction:
See O. Sirjean, S. Seidelin, J. Gomes, D. Boiron, C. Westbrook, A. Aspect, and G. Shlyapnikov, Ionization rates in a Bose-Einstein condensate of metastable Helium, Phys. Rev. Lett. 89, 220406 (2002) [arXiv preprint: cond-mat/0208108] [PRL].
See S. Seidelin, O. Sirjean, J. Viana Gomes, D. Boiron, C. Westbrook, and A. Aspect, Using ion production to monitor the birth and death of a metastable helium Bose-Einstein condensate, J. Opt. B: Quantum Semiclass. Opt. 5, S112 (2003) [arXiv preprint: cond-mat/0211112] [JOptB].
See S. Seidelin, J. Viana Gomes, R. Hoppeler, O. Sirjean, D. Boiron, A. Aspect, and C. Westbrook, Getting the elastic scattering length by observing inelastic collisions in ultracold metastable helium atom, Phys. Rev. Lett. 93, 090409 (2004) [arXiv preprint: cond-mat/0401217] [PRL].
The observation of BEC of He* hinged, among other things, on the elastic and inelastic collision properties of the atom at micro-K temperatures. Encouraging theoretical predictions existed, but no experimental information was available. The crucial question was whether elastic collisions, characterized by their scattering length a, were sufficiently rapid compared to inelastic processes in a spin polarized sample, involving presumably both two-body and three-body collisions. Conventionally, the two-body collision rate constant is denoted by β, and the three-body rate constant by L. Because of the large internal energy of He*, a significant fraction if not all of the inelastic collisions result in ions which can be detected by a microchannel plate. Thus monitoring of the ion products in a BEC permits a qualitatively new observation of BEC. The figure below shows the detected ion rate during evaporation through BEC. The sudden increase in the ion production rate is due to the increase in density associated with the BEC transition. This type of data also allows one to reproducibly place a cloud near the BEC transition point Tc.
Using clouds at Tc, it is possible to extract values for the inelastic rate constants. Surprisingly, it is also possible to get an accurate estimate of the elastic scattering length from the ionization measurements. The key idea in these measurements is to use the fact that at Tc the density of the sample is well known using the theory for a weakly interacting Bose gas. A second important ingredient is that in a BEC, the chemical potential μ is simply related to the density and the scattering length. Accurate measurements of Tc and μ are possible by observing the expansion of clouds of atoms, either at Tc or in a BEC. The known density estimated at Tc allows one to use the ion rate to get the ionization rate constants and knowing the ionization rate constants, we can get infer the density in a BEC from the ion rate. The BEC density together with the a measurement of the chemical potential finally gives a value for the scattering length, which is independent of the absolute calibration of the MCP.
Our final results are]:
A. Robert, O. Sirjean, A. Browaeys, J. Poupard, S. Nowak, D. Boiron, C. I. Westbrook, A. Aspect, A Bose-Einstein condensate of metastable atoms, Science 292, 461 (2001) [Science]
We observed a BEC of He* (in the 2 3S1 state) during the evening of 12 February 2001. Our apparatus used a cloverleaf-type magnetic trap with coils placed in re-entrant vacuum flanges. This design allows us to use a microchannel plate 5 cm below the trap to detect the atoms after releasing them from the trap. An example of a single-shot time-of-flight spectrum is shown in the figure. The horizontal axis is the arrival time of the atoms, but the distribution closely corresponds to the spatial profile of the atoms along one of the strong axes of the trap. The red curve shows a fit to the wings of the distribution giving a temperature of 0.7 μK. The condensate peak shown contains about 50 000 atoms. The trap is initially loaded from a MOT with 3 108 atoms and the rf evaporation ramp lasts about 60s.