# Ytterbium in optical lattices

Research**Anomalous decay of coherence in a dissipative many-body system**

We study the loss of spatial coherence of a bosonic superfluid loaded into an optical lattice and subjected to a controlled amount of spontaneous emission. Whereas we expect an exponential decay of this coherence versus time for a non-interacting system, we show in this work that the presence of strong interactions between particles leads to a slowing down of the decoherence process. We characterized this decay and found good agreement with theoretical predictions describing anomalous diffusion in Fock space.

**Publication:**Anomalous decay of coherence in a dissipative many-body system

**,**R. Bouganne, M. Bosch Aguilera, R. , A. Ghermaoui, J. Beugnon, F.Gerbier, , (2019); arXiv:1905.04808.

See also article on phys.org

**Non-linear relaxation of interacting bosons coherently driven on a narrow optical transition**

In this work we present the coherent driving of Rabi oscillations on Yb’s optical clock transition for a BEC loaded in an optical dipole trap. Spontaneous emission being negligible, the dynamics of the relaxation of these oscillations is strongly influenced by the following effects: asymmetric elastic interactions (due to different values in intra- and inter-state scattering lengths), inelastic losses and Doppler broadening due to the finite momentum width imposed by the confinement. In particular, we observe the transition between two regimes: a first one, when the driving strength prevails with respect to the relaxation processes, in which Rabi oscillations are observed, to an irreversible decay when the relaxation takes over. This crossover is reminiscent of the textbook problem of a discrete level coupled to a continuum: in the case of a broad continuum the evolution leads to an irreversible Weisskopf-Wigner decay, whereas if the continuum is so narrow that it can be approximated by a discrete state, Rabi oscillations are observed.

We compare our observations to a two-component Gross-Pitaevskii (GP) model and we conclude that for moderate values of interactions, the main damping source is the finite momentum width of the BEC, while inelastic losses lead to a non-exponential decay of the populations. The GP model shows excellent agreement for the regime of small interactions. However, we find that for larger values of interactions it fails to reproduce the observed damping of the oscillations, pointing to the existence of beyond mean-field phenomena.

**Publication:**Non-linear relaxation of interacting bosons coherently driven on a narrow optical transition,

M. Bosch Aguilera et al., EPL (Europhysics Letters) 123, 40004 (2018); arXiv:1806.07210.

**Clock spectroscopy of interacting bosons in deep optical lattices**

We report on high-resolution optical spectroscopy of interacting bosonic ^{174}Yb atoms in deep optical lattices with negligible tunneling. We prepare Mott insulator phases with singly- and doubly-occupied isolated sites and probe the atoms using an ultra-narrow ‘clock’ transition. Atoms in singly-occupied sites undergo long-lived Rabi oscillations.

Atoms in doubly-occupied sites are strongly affected by interatomic interactions, and we measure their inelastic decay rates and energy shifts. We deduce from these measurements all relevant collisional parameters involving both clock states, in particular the intra- and inter-state scattering lengths.

**Publication:**Clock spectroscopy of interacting bosons in deep optical lattices,

R. Bouganne et al.,

*New J. Phys.*

**19**113006 (2017), arXiv:1707.04307.

**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.

**Publication:**Doppler spectroscopy of an ytterbium Bose-Einstein condensate on the clock transition,

A. Dareau et al., Phys. Rev. A 91, 023626 (2015), arXiv:1412.5751.

**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 tunneling 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).