Organisers

• Lode Pollet (Harvard University)
• Tilman Esslinger (Swiss Federal Institute of Technology Zurich (ETHZ))
• Antoine Georges (CNRS-CPHT and Polytechnic School Palaiseau)
• Alejandro Muramatsu (University of Stuttgart)

Supports

QSIT

   CECAM

CTS

Description

We will first outline the state of the art of experiments on cold atoms in an optical lattice. We will then show how numerics are useful for these systems, and finally discuss how successful numerical studies have been, which is the keystone of this proposal.

Since the seminal paper by Greiner et al. [1], showing the transition from the superfluid to the Mott-insulating phase in the Bose-Hubbard model, physicists have realized that modeling strongly-interacting systems in the atomic physics lab is feasible.
The field had started with the theoretical prediction by Jaksch et al., showing theoretically that this model could indeed be analyzed realistically in experiments [2]. The key observation was that the atom-photon interactions could be used and controlled in such a way that the Bose-Hubbard model can be realized for a sufficiently long time and at sufficiently low temperature.

Systems consisting of atoms in an optical lattice have the advantage over strongly-interacting systems of (1) being ultra-clean, (2) the interaction couplings are controllable, and (3) the type, mass and density of the atoms are controllable. Having the possibility to change the parameters of the Hamiltonian at will makes these systems prime candidates for building a quantum analog computer. On the negative side, the detection of (neutral) atoms is more difficult than detection in condensed matter physics, the temperature is relatively high (e.g., in units of the Fermi temperature for fermionic systems present experiments operate on the scale of 0.1 ), there are no phonons since the lattice is built by laser light, and there is an external harmonic trapping potential.

Experimental progress has been rapid. The most recent advances include the observation of the Mott-instulating phase in the Fermi-Hubbard model [2] and the observation of the superexchange mechanism in a two-well system [3].

These experiments have mostly been explained qualitatively so far. Further progress is only possible when lower temperatures are reached and better detection schemes developed, but also when current experiments are better understood quantitatively, and this is where numerics become useful.

In particular for the bosons, the theory is well understood and the numerical algorithms (Quantum Monte Carlo) very powerful. The so-called 'worm algorithm' is at present able to address the Bose-Hubbard model from first principles and for realistic system sizes [4]. Previous studies addressed individual aspects of the experiments, such as the role of the trapping potential, the role of entropy in fixing the temperature and the influence of the time-of-flight duration [5]. Fully ab-initio studies took off approximately a year ago and are still going on, with promising first results. The overall agreement is close to excellent, but it turns out that there are deviations which are not completely negligible though controllable. They hint at experimental imperfections, such as density variations, lattice laser calibration uncertainties, heating, and losses of atoms. Estimating the importance of such effects accurately has now become available thanks to the large-scale simulations.

For the fermions, such numerical methods as DMFT [6] and high-temperature series expansions [7] addressed the recent observation of the Mott-insulating state. Fermions are intrinsically harder to handle experimentally than bosons. The Mott-insulating state has only been observed experimentally over the last few months [2]. Numerical studies using Dynamical Mean Field Theory (DMFT) and high-temperature series expansions have already appeared [8, 2], but finding a quantity that clearly indicated the transition is hard to find. Temperature and out-of-equilibrium effects are more serious concerns here than for the bosons. It is clear that much more numerical and experimental work is needed before consensus can be reached in the community. Numerical studies have also looked at lower temperatures, trying to see where anti-ferromagnetism sets in [8]. At these temperatures the numerical methods are no longer exact, but the approximations need further assessment.

Experimental studies have also been undertaken to measure critical exponents. The critical exponent of the correlation length of the U(1) transition between a normal and a condensed three-dimensional Bose gas was measured [9]. The Berezinskii-Kosterlitz-Thouless for a two-dimensional Bose gas was also successfully studied experimentally [10]. A full numerical study taking the trapping potential, temperature, heating, and detection schemes into account is numerically challenging and largely open.

Scientific Objectives

The aim of the workshop is to bring together the leading experimentalists and computational physicists in order to discuss the status of ab initio modeling and the remaining difficulties in a variety of contexts :
- bosons in an optical lattice
- fermions in an optical lattice
- extracting critical exponents from experiment
- one dimensional systems
- rotating systems
- disordered systems
- cold molecules
The numerical methods include :
- Quantum Monte Carlo (QMC)
- Density Matrix Renormalization group (DMRG)
- Dynamical Mean Field Theory (DMFT)
- high temperature series expansions
It will be shown how each of the methods can be applied to a different system in atomic physics, and comparison with experiments will be made. The workshop will be successful when new ideas emerge on how to model the systems in atomic physics as accurately as possible. Importantly, an assessment of how closely the prototypical models of condensed matter physics can be realized in the cold-atoms lab is warranted, since heating rates, state preparation, life time and other effects due to atom-photon interactions might play an important role.

References

[1] M. Greiner, O. Mandel, T. Esslinger, T. W. Haensch, and I. Bloch, Nature 415, 39 (2002).
[2] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
[3] R. Joerdens, N. Strohmaier, K. Guenter, H. Moritz, and T. Esslinger, Nature 455, 204 (2008) ; U. Schneider et al, cond-mat/0809.1464 (2008).
[4] S. Foelling et al, Nature 448, 1029 (2007), S. Trotzky et al., Science 319, no. 5861, 295 (2008).
[5] N. V. Prokofev,B. V. Svistunov, and I. S. Tupitsyn, Sov. Phys. JETP 87, 310 (1998); Phys. Lett. A 238, 253 (1998).
[6] L. Pollet, K. Collath, K. Van Houcke, and M. Troyer, New Journal of Physics 10, 065001 (2008); F. Gerbier et al., accepted for publication in Phys. Rev. Lett., cond-mat/0808.2212 (2008).
[7] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
[8] J. Oitmaa et al., Series Expansion Methods for Strongly Interacting Lattice Models, Cambridge University Press, Cambridge, 2006.
[9] L. De Leo, C. Kollath, A. Georges, M. Ferrero, and O. Parcollet, cond-mat/0807.0790 (2008); V. W. Scarola, L. Pollet, J. Oitmaa, and M. Troyer, cond-mat/0809.3239 (2008).
[10] T. Donner, S. Ritter, T. Bourdel, A. Oettl, M. Koehl, and T. Esslinger, Science 315, 1556 (2007)
[11] Z. Hadzibabic, P. Krueger, M. Cheneau, B. Battelier, and J. B. Dalibard, Nature 441, 1118 (2006); New Journal of Physics 10, 045006 (200).