Blanc SIMI 4 - Blanc - SIMI 4 - Physique des milieux condensés et dilués

Phase transitions with disorder and interactions – DisorderTransitions

Transitions de phase en présence d’interactions et de désordre

Transitions de phase en présence d’interactions et<br />de désordre

A better understanding of disordered quantum systems ?

The primary objectives of our project is to achieve a better understanding of disorder<br />systems in 2D and 3D. The physics in the presence of disorder is involved and there is no<br />exact theory even at the single particle level, i.e. this is the problem of Anderson localization.<br />In particular, we plan to study the impact of decoherence on Anderson localization. At the<br />many-body level, the interplay between disorder and inter-particle interactions leads to a<br />rich quantum phase diagram at very low temperatures, exemplify by the `exotic’ Bose glass<br />phase. This problem, referred to the “dirty boson problem”, is indeed so complex that the<br />theoretical description of even the simplest models poses severe difficulties and many issues<br />are still unsolved or even controversial. In this context, we believe that a lot can be learnt<br />from the study of quantum gases in controlled disorder potentials and microscopic<br />interactions. We will tackle to the problem in both 2D and 3D because we believe that the<br />observations of similarities and differences between the two dimensions will permit a better<br />understanding of the physics. In addition, we plan to study non-equilibrium physics in the<br />presence of disorder. Ultra-cold atoms with their accessible evolution time scales are<br />especially suited for such studies.

On the experimental side, in our project, we propose to go much further than the state of
the art in the observation of disorder effects in quantum gases. In particular, we plan to
develop and use several cutting edge techniques that have sometimes been demonstrated for
other purposes but never been used in the context of disordered quantum gases. These new
tools are in-situ high-resolution imaging in the disorder (even in 3D), all-optical cooling of
potassium atoms in order to be able to tune the interactions between atoms using Feshbach
resonance, and the use of Bragg spectroscopy in disordered systems. These three tools
require experimental efforts but will permit key advances for understanding the role of

A RF spectroscopy setup in order to populated quantum states of given energy in the disorder is installed. Results are especially interesting as they permit to access the spectral function. Tests are under way to evaluate the resolution and some work has to be done to interpret the results.

Regarding the physics of disorder, important advances have been realized. In particular, the timescales associated with scattering in the disorder have been precisely investigated and compared with the theory, as a function of the disorder strength and as a function of the particle velocity (publication is preparation). A collaboration is underway is under to really compare the latest theoretical prediction of the 3D Anderson transition with the experimental results.

The potassium experiment permits the control of the interaction and it is now used to produce matter-wave bright solitons, i.e. wavepackets which propagate without dispersion due to attractive interaction. The propagation of such wave packet in disorder have been studied theoretically. A dramatic effect of interaction is predicted as a soliton could propagate in the disorder whereas single particle at the same velocity would be localized. This striking dynamics is now under experimental study.

From the theoretical point of view, Monte-Carlo studies of the 2D disordered Bose gas has been performed (G. Carleo, et al, PRL 111, 050406 (2013)). In particular, these studies confirm the BKT nature of the phase transition in the presence of disorder. Some additional studies in the presence of a trapping potential have been done in order to allow for a direct comparison with experiments. Theory and experiments are found to fit. This has not been published.

The group of Vincent Josse has performed experiments on suppression and revival of weak localization through control of time-reversal symmetry. This work is related to the addition of controlled decoherence in disordered samples.

Great progresses have already been done in the control of in the understanding of ultra cold disordered atomic gases. The problem of interacting quantum disordered systems remains a great challenge.

G. Salomon, et al, PRA 90, 033405 (2014))
G. Salomon, et al., EPL 104, 63002 (2014)
K. Müller et. al. Phys. Rev. Lett. 114, 205301 (2015).
G. Carleo, et al, PRL 111, 050406 (2013)

In this project, we will launch a new research program on disorder-induced phase transitions in atomic gases, both in 2D and 3D, dimensions where no exact theory is available in the presence of disorder. We will study the competition between disorder, phase coherence, and interaction. The program can be divided into two parts: First we will go beyond the observation of Anderson localization at the single particle level aiming at a precise characterization of the effect, in particular in the critical regime in 3D or in the presence of decoherence or weak interactions. Second we will investigate the effect of disorder on quantum many-body physics where interplay between disorder and interactions leads to novel phenomena, such as phase transitions. Depending on the dimensionality, the physics of the disorder is expected to be different and the goal of our project is the better understanding of this complex physics. Finally, we plan to study non-equilibrium dynamics of disordered Bose gases.

For the realization of the project two experimental developments will be required: first a high numerical aperture objective for efficient atom detection with a high resolution. It will permit the detection of the density at the scale of the disorder and also of the density correlations, a fundamental investigating tool in the physics of strongly correlated systems. Second, we will develop the cooling of potassium atoms, for which practical Feshbach resonances permit to tune the interaction between atoms, one of the key parameters of the many-body physics.

Our project on disordered quantum systems is related to open problems in condensed-matter physics. It is relevant to several experimental condensed-matter systems, such as Si-MOSFETs, GaAs heterostructures, thin metallic films, where disorder related phase transitions are observed. Moreover, in high-Tc superconductors, doping intrinsically introduces inhomogeneities. In this regard, our proposed collaboration with M. Holzmann, who is specialized in the theoretical simulations of electronics systems, will not only help us to simulate and understand our disordered systems but also to really connect our studies to what is known and unknown in disordered condensed matter systems. In contrast to electronic systems, microscopic descriptions of disorder and interaction in ultracold gases are much simpler, and experiments can probe a broad parameter space. Therefore we expect important new insights from our studies with potentially large impact.

Project coordination

Thomas Bourdel (Laboratoire Charles Fabry (LCF)) –

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


LPMMC, UJF Laboratoire de physique et modélisation des milieux condensés, Université Joseph Fourier Grenoble 1
IOGS (Institut d'Optique théorique et appliquée) Laboratoire Charles Fabry (LCF)

Help of the ANR 169,516 euros
Beginning and duration of the scientific project: January 2013 - 36 Months

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