LKB - Bose-Einstein condensates

Ytterbium in optical lattices

Research

Artificial gauge potentials for neutral atoms in an optical lattice

The interplay between the motion of a charged particle and an applied magnetic field plays an important part in many areas of physics. In classical mechanics, this gives rise to the Lorentz force whereas in quantum mechanics, this leads to the Aharonov-Bohm effect. The latter means that the wavefunction of a charged particle moving through space in presence of a vector or gauge potential accumulates a phase, even if the classical Lorentz force has a negligible effect. The role of gauge potentials is central to modern physics, from high to low energies. In condensed matter physics, for instance, the coupling between the motion of conducting electrons and a strong applied magnetic field gives rise to a wealth of physical phenomena, from the emergence of vortex lattices in certain superconducting materials to the integer and fractional quantum Hall effects in quasi-two-dimensional semiconductors.

Even though Ytterbium atoms used in our experiment are electrically neutral, the phase of their wavefunction can be manipulated using coherent atom-light interaction in order to couple different internal states of the atom. Our specific experimental scheme [1] uses an ultra-narrow optical transition (the so-called “clock” transition) linking the ground state to a metastable excited state in bosonic Ytterbium. In the “Hofstadter optical lattice” [2], where the trapping sites depend spatially on the internal state of the atom, the clock laser induces tunnelling between the lattice sites and also imprints a spatially-dependent phase on the wavefunction. Under suitable conditions, this geometrical phase emulates the Aharonov-Bohm phase experienced by charged particles moving in a magnetic field. Combining this artificial orbital magnetism and a many-body interacting phase, typical in optical lattices, one expects to observe strongly correlated states.

References:

[1] Gauge fields for ultracold atoms in optical superlattices,

F. Gerbier, J. Dalibard , New J. Phys. 12, 033007 (2010); arXiv:0910.4606

[2] Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,

D. Hofstadter, Phys. Rev. B 14, 2239–2249 (1976)

Rabi oscillations on the clock transition of ytterbium

Here we present a set of experiments performed on trapped atoms after loading the Bose-Einstein condensate in a vertical optical lattice at the magic wavelength (759 nm). We use a horizontally propagating laser to promote atoms to the excited clock state. We detect metastable excited atoms through a decrease of the measured atom number in the ground state. A vertical magnetic field of magnitude 150 G is also applied, enabling a non-zero transition matrix element between ground and excited states.

We observe Rabi-like oscillations between the ground and metastable states, as shown in the figure. This demonstrates the coherent nature of the excitation by the clock laser, and allows us to prepare a Bose-Einstein condensate in a coherent superposition of the ground state and of an optically excited state. The oscillation period is consistent with the expected Rabi frequency of about 2 kHz.

Doppler spectroscopy of a Bose-Einstein condensate

We have performed spectroscopy of an ytterbium Bose-Einstein condensate on the one-photon “clock” transition between the ground state and a metastable optically excited state. In one such experiment, we released the condensate in a “waveguide” formed by a single-beam dipole trap before the spectroscopy pulse. The atoms then undergo a quasi-one dimensional expansion inside the waveguide, after which the atoms are  released for a time of flight expansion and finally imaged using absorption from a weak resonant probe beam. The absorption images (which only record the ground state density) in the figure (top) show visually the position of the “missing” atoms transferred to the excited state as the laser frequency is scanned.

Time of flight maps initial velocities to final positions, so that the “slice” of missing atoms corresponds directly to the resonant velocity class of atoms. We fitted the profiles of the cloud to a Thomas-Fermi profile multiplied by an heuristic “hole” function to account for the missing atoms. The lower panels (a,b) show two profiles (integrated along the horizontal direction) together with the fit used to extract the cloud and hole centres and widths. From this experiment one can directly measure the bare resonance frequency of the atoms, when both centres coincide (atoms with zero velocity are excited). For future experiments, this result suggests the possibility to measure the absolute laser frequency in one shot by locating the slice position in a given image.

Clock spectroscopy of interacting ytterbium atoms in deep optical lattices

Bose-Einstein condensation of ytterbium atoms

We produce Bose-Einstein condensates of ytterbium 174 atoms. To reach the ultralow temperatures required to observe this state of matter, we start from a collimated atomic beam of ytterbium near 400 °C obtained at the output of an oven (picture, right). The atoms are slowed down to a few m/s in a Zeeman slower operating on a strong optical transition near 400 nm, and are then collected in a magneto-optical trap (MOT) (picture, left) operating on a weaker transition at a wavelength of 556 nm (intercombination line). We trap around two-hundred millions atoms in the MOT, at a fairly low temperature around 10 microKelvin thanks to the narrow linewidth (around 180 kHz).

Atoms are then transferred into a dipole trap at 1070 nm and transported over 20 cm to a science chamber with good optical access. Atoms are progressively transferred to a crossed dipole trap formed at the intersection of the 1070 nm laser and of a 532 nm laser beam crossing at right angle. Condensation happens after a few seconds of forced evaporative cooling in the crossed dipole trap.