This project aims at exploring the properties of spinor Bose-Einstein condensates, i.e. condensates formed in several internal states. We work with Sodium atoms, with a spin 1 in their electronic ground state. The atomes are cooled down to the Bose-Einstein transition temperature and held in a tightly focused optical trap. Our goal is to use this system to produce and study collective or correlated spin states. Examples of collective states could be Schrödinger cat -like states, which are predicted to occur during the temporal evolution of such spinor condensates if decoherence is negligible, or novel antiferromagnetic phases, for instance in a spin chain realized in a one-dimensional optical lattice.
Towards strongly correlated states
An all solid-state laser source for Sodium cooling
Preparing a microcondensate
Phase diagram of antiferromagnetic spin 1 Bose-Einstein condensates
- Permanent members :
- Fabrice Gerbier (CNRS)
- Jean Dalibard (Collège de France)
- Luigi de Sarlo (2008-2011)
- Tilman Zibold (2012- )
- PhD students:
- Emmanuel Mimoun (2006-2010)
- David Jacob (2008-2012)
- Lingxuan Shao (2010- )
- Vincent Corre (2011- )
- Visitors and internships:
- Pierre Hunger (stagiaire ENS Lyon, sping 2006)
- Xing-Xing Zhou (stagiaire ENS Paris, summer 2006)
- Benjamin Charnay (stagiaire ENS Paris, summer 2006)
- Aviv Keshet (visiteur MIT, june 2008)
- Tilman Zibold (visiteur Heidelberg, winter 2009)
- Wilbert Kruithof (visiteur Groningen, spring 2009)
- Sophie Weber (MIT, summer 2012)
This project is supported by
- ANR: Gascor project (2005-2008)
- IFRAF: microbec project, in collaboration with Institut d’Optique
- DARPA: OLE project, in collaboration with MIT, coordinator W. Ketterle
- European Union: MIDAS network, coordinator G. Kurizki (2008-2010)
Publications de l’équipe:
- D. Jacob, L. Shao, V. Corre, T. Zibold, E. Mimoun, L. DeSarlo, J. Dalibard, F. Gerbier, Phase diagram of antiferromagnetic spin 1 Bose-Einstein condensates, arXiv:1209.2533 (2012).
- D. Jacob, E. Mimoun, L. DeSarlo, M. Weitz, J. Dalibard, F. Gerbier, Production of sodium Bose–Einstein condensates in an optical dimple trap, New J. Phys. 13, 065022 (2011); arXiv:1104.1009.
- E. Mimoun, L. de Sarlo, D. Jacob, J. Dalibard, F. Gerbier, Fast production of ultracold sodium gases using light-induced desorption and optical trapping,Phys. Rev A 81, 023631 (2010);arXiv:0911.5656
- E. Mimoun, L. de Sarlo, J.-J. Zondy, J. Dalibard, and F. Gerbier, All solid-state laser system for laser cooling of sodium, Applied Physics B 99, 31 (2010); arXiv:0908.0279. arXiv:0908.0279.
- E. Mimoun, L. de Sarlo, J.-J. Zondy, J. Dalibard, and F. Gerbier, Sum-frequency generation of 589 nm light with near-unit efficiency, Optics Express 16, 18684-18691 (2008); arXiv:0807.2965.
Towards strongly correlated states
The observation in 1995 of the Bose-Einstein condensation phenomenon in atomic vapours has been a major breakthrough in the field of ultracold atoms. A Bose-Einstein condensate (BEC) is a state of matter where a macroscopic population builds up in a particular quantum state to form a "coherent matter wave". The tremendous success of this domain of research is first due to the diversity of problems that can be addressed experimentally, from basic quantum mechanics to quantum condensed matter. This success also originates from the refinement of experimental techniques developed in atomic physics and quantum optics over the years. Ultracold quantum gases can now be "engineered" to mimic more complex systems, and can be considered as "atomic analog simulators" which will eventually provide a solution of open problems in other related fields of research.
One of the most promising directions is to use quantum gases as resources to produce strongly correlated atomic states, which exhibit interparticle correlations that cannot be accounted for by classical arguments. In quantum optics, various protocols have been proposed to produce such states using the interaction between coherent light and non-linear media . However such experiments have not been performed to date, due to the weakness of the optical non-linearities. Interestingly these proposals can be transposed to atomic BECs, where the condensate can be viewed as a coherent "atom laser" beam and where the non-linearity is provided by interatomic interactions. In this context it seems feasible to experimentally produce such entangled states, to demonstrate the non-classical correlations built in these many-particle systems, and to study their robustness under decoherence.
Because quantum correlations become more and more fragile when the number of particles increases, many experimental difficulties are softened when working with small samples containing at most a hundred particles. We aim to create such quantum objects with a reproducibility and a detection sensitivity at the single-atom level. Experimentally, we plan to achieve this in a tightly focused dipole trap, whose depth can be tuned finely enough that only the trap ground state remains bound. This requires to focus the laser beam down to the size of the trap ground state, around 1 micron.
We envision a number of qualitatively new experiments that would become possible in this setting. For instance, a major goal would be to create an entangled superposition of two condensates in two distinct internal states a and b [2-4], or the controlled generation of twin condensates with exactly as many atoms in state a as in state b . Such a microcondensate naturally has a very small entropy, as well as a self-regulating mechanism for the atom number. If the atom number is too large, the bound state will be expelled out of the trap due to the interaction energy between the atoms, causing evaporation. This evaporation stops when the atom number is lower than the threshold at which the ground state becomes bound again. We hope to achieve fine control over the atom number, temperature and interatomic interactions in such a trapping geometry, and to characterize more precisely this new mechanism for quantum evaporation. In addition to the bound level, the spectrum also supports a continuum of free states eventually coupled to the bound atoms by interactions or fluctuations of the trap potential. This system is therefore interesting in its own right as a well-defined open quantum system, and we plan to study its stability and its robustness with respect to external perturbations.
An all solid-state laser source for Sodium cooling
Collaboration : Jean-Jacques Zondy (LNE-INM)
In comparison with most laser cooling experiments relying on diode laser technology, experiments with Sodium atoms are more involved. They typically require using dye laser systems to reach the cooling transition at 589 nm. Dye lasers are expensive, notoriously difficult to use and require heavy maintenance. We have developped an alternative all-solid state laser source emitting at 589 nm suitable for laser cooling of Sodium that is free of the disadvantages of dye laser, very reproducible while achieving similar power levels at 589 nm. In our setup we perform sum-frequency mixing of two infrared lasers (1319 nm and 1064 nm) in a non-linear crystal placed inside a doubly-resonant build-up cavity. Both infrared lasers are monolithic YAG lasers, emitting around 500 mW at 1320 nm and 1.2 W at 1064 nm. The yellow output is locked on the Sodium D2 transition. Our setup currently delivers more than 700 mW in a single longitudinal and spatial mode (M2<1.02). This power level corresponds to a nearly optimal conversion efficiency, where 90 % of the photons from the 1319 nm wource entering the cavity are converted into yellow photons. We have been able to reach such an unusual efficiency by developping a patented novel laser system [*] that corrects for instabilities arising in this regime of strong conversion. Our source is a serious alternative to the use of dye lasers in this wavelength range, for a significantly lower cost and a better comfort of utilization.
[*] Brevet INPI 0803153 (6 juin 2008): Dispositif optique de conversion de longueur d’onde et source de lumière utilisant un tel dispositif.
Preparing a microcondensate
We designed our experimental apparatus for minimal size and maximale simplicity. The vacuum chamber was custom made from Titanium (amagnetic material) and closed by optical-quality viewports also built from Titanium flanges. The chamber includes two large reentrant viewportsallowing one to place a microscope objective (numerical aperture 0.35) close to the atoms. Sodium atoms are introduced using dispensers, and deposit on the chamber walls and viewports surfaces; we are able to desorb those atoms using strong near-ultraviolet light. This allows us to modulate the Sodium partial pressure in the chamber by a factor 50, going from a situation where a magneto-optical trap (MOT) can be efficiently loaded to a situation with much better vacuum level for evaporation in the optical trap. We trap typically a few tens millions atoms in the MOT after several seconds loading. Once atoms are laser-cooled in the PMO, we turn on a crossed optical trap formed by a 1070 nm laser focused down to 40 microns and folded onto itself. After loading, MOT lasers are switched off and atoms, which are now "in the dark", can relax via elastic collisions to a kinetic equilbrium state. During this phase, the depth of the dipole trap is fixed, and atoms can accumulate in the crossing region. A dense sample builds up there, allowing one to perform evaporative cooling.
We use in fact a secondary crossed dipole trap to improve the efficiency of evaporative cooling. This second trap, more focused than the first one, (8 microns 1/e2 waist) is use as a relay to boost spatial density (and thus collisions rate) during evaporation. At the end of the evaporation sequence, the first crossed dipole trap is turned off and microcondensates are produced in the smaller "dimple" trap.
Sodium Bose-Einstein condensates
Left : condensed fraction as a function of temperature T (related to the ideal gas condensation temperature Tc). The dashed line shows the expected relationship for an ideal gas, the solid one for an interacting gas described in the Hartree-Fock approximation. The data shown correspond to two different time of flights, indicated as "TdV" on the figure. Right : Density profile measured for three different temperatures. The measured profiles are compared to an adjustment by a bimodal function describing condensed and non-condensed atoms separately.
Phase diagram of an antiferromagnetic spin 1 Bose-Einstein condensate
We have measured the equilibrium phase diagram of the spin 1 condensates produced in the microtrap. It results from the competition between spin-spin interactions and the quadratic Zeeman effect due to an applied magnetic field. Spin-spin interactions on the one hand favor the so-called "polar" condensates, corresponding without any applied field or magnetization to a spinor in the m=0 state along any axis. Atoms in the Zeeman states m=+1 or m=-1 are miscible with each other, while atoms in m=0 are not. As a consequence, for a positive magnetization (which imposed the presence of atoms in m=+1), it is energetically favoured to populated m=-1 and suppress the population of m=0. Another crucial element of this system is the conservation of the magnetization mz, due to the spin rotational invariance of the microscopic interaction potential. One important consequence is that the linear Zeeman effect only introduces a constant energy offset, and plays no role in the dynamics or the determination of the equilibrium state: The dominant term in the atom-field interaction is the quadratic Zeeman shift instead, which favors occupying the m=0 state. The competion between the interactions and the quadratic Zeeman energy gives rise to a quantum phase transition from an "antiferromagnetic" state, where m=0 is absent, to a "mixed" state where the population in m=0 does not vanish and increases with applied magnetic field. We have performed systematic measurents of the transition, as a function of magnetization and applied field. We obtain a phase diagram (shown below) in excellent agreement with the mean-field theoretical prediction.
Phase diagram of antiferromagnetic spin 1 condensates
(a) Measured phase diagram. The color scale quantifies the population in the Zeeman state m=0. (b) Phase diagram predicted in the mean-field approximation.
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