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

Artificial gauge fields on neutral atoms – AGAFON

Artificial gauge fields for neutral atoms

The remarkable advances in the production of ultra-cold atomic gases have opened a new field of research at the interface of atomic physics and condensed matter physics. The goal of this project was to study theoretically and experimentally how two-dimensional gases of ultra-cold neutral atoms can be used to simulate orbital magnetism phenomena that occur for the electron fluids in conducting materials.

Orbital magnetism for neutral particles?

This project was devoted to the theoretical and experimental study of cold atomic gases submitted to external artificial magnetic fields and/or exhibiting permanent currents.<br /><br />From the theory point of view, we first wanted to explore the most promising situations to generate such situation and produce topologically non-trivial states. The lines that we explored dealt either with isolated systems, such as flux lattices, or with externally driven systems. We also wanted to take into account interactions between particles and characterize the correlated states that may appear, in analogy with integer and fractional quantum Hall effect for a planar fluid of electrons placed in a strong magnetic field.<br /><br />From the experimental point of view, we aimed at characterizing the properties of two-dimensional cold atom gases and setting in place tools that are well suited for the study of their (artificial) magnetic properties and the related permanent currents. We favoured flexible trapping geometries, such as “transport experiments” or “Aharonov-Bohm rings”, which will allow us in the future to transpose to cold atom setups the measurement procedures that have been developed in condensed matter physics.<br />

From a general point of view, we aimed at developing theoretical and experimental tools to (i) prepare in an optimal way the Hamiltonian governing the atomic motion, possibly using an explicit time dependence, (ii) detect the phases of matter that have been produced in this way (equation of state, correlation functions, topological defects).

On the theoretical side, the study of the correlated states in the bulk of the sample as well as localized states on the edge involved numerical calculation, implying important computational resources. Another essential part of the study dealt with a new engineering of optical lattices, both within the framework of flux lattices and the framework of short period lattices, for which the relevant energy scales are increased and thus become more accessible to experiments. We also explored another method for manipulating microscopic particles, which appeared recently in the cold atom context, and which uses a temporal modulation of the Hamiltonian of the gas.

On the experimental side, a particular effort was devoted to the realization of homogeneous samples, confined in flat bottom potentials. This allows one to avoid the masking of the desired signals by inhomogeneous broadening. The real-time control of these two-dimensional boxes has been explored, as well as the possibility to observe individual atoms.

From the experimental point of view, the first step was to realize uniform two-dimensional gases, similar to electron gases exhibiting the Quantum Hall effect. After having established the procedure for producing these gases, we succeeded - thanks to high-resolution imaging- to observe vortices similar to those appearing in superconducting materials. On the theory side, we put a particular effort in the exploration of the concept of a “flux lattice”; It consists in a standing light wave for which the energy bands characterizing the atomic motion have the same topology as the Landau levels for an electron in a magnetic field.

An important result deals with the theoretical characterization of the collective two-dimensional states that can appear in an optical flux lattice. Emblematic states have been identified for bosonic atoms, in analogy with Quantum Hall effect, either in the fractional regime (Laughlin state) or the integer one (calculation of the N-body Chern number). Another important result is the experimental realization of uniform 2D gases and the study of their dynamics in a quench cooling. In particular we were able to link our results to the generic Kibble-Zurek model, addressing universal aspects of the nucleation of topological quantum defects at the crossing of a phase transition point.

This project led to 16 publications in high-level, peer-reviewed journals: 5 Physical Review Letters, 1 PNAS, 1 Nature Communications, 1 Physical Review A, 7 Physical Review B, 1 Physical Review X. A significant fraction of these publications were co-signed with collaborators worldwide, notably B.A. Bernevig (Princeton, USA), N.R. Cooper (Cambridge, UK) and N. Goldman (ULB, Belgique). At least two other articles are in preparation, about results obtained during the last months of the project.

The study of atomic gases that can exhibit effects related to orbital magnetism and/or permanent currents is rapidly developing worldwide. Within the framework of this project, we concentrated on the understanding and the realization of two-dimensional atomic gases and of Quantum-Hall-type mechanisms that can occur inside them.

Thanks to the move of the experimental team from the ENS labs to the College de France labs, we could built an optimized setup, which will facilitate the future study of the states induced by this artificial magnetism. In particular this project allowed us to implement a new and flexible tool for the manipulation of cold gases, i.e., micro-mirror matrices. The principle of use is simple, since one just has to draw on the atom plane a given geometrical figure, which can then be modified in real time. We are convinced that this new device will play an important role in cold atom physics.

In parallel we have made important theoretical progress, concerning the existence and the characterization of new phases of matter related to these synthetic gauge fields. The experimental identification of these phases will be a major challenge during the coming years.

Articles
[1] N. R. Cooper and J. Dalibard, Phys. Rev. Lett. 110, 185301 (2013)
[2] N. Goldman, J. Dalibard, A. Dauphin, F. Gerbier, M. Lewenstein, P. Zoller, I. B. Spielman , PNAS 110(17) 6736-6741 (2013).
[3] N. Regnault and T. Senthil, Phys. Rev. B 88, 161106R (2013).
[4] S.C. Davenport, E. Ardonne, N. Regnault, and S.H. Simon, Phys. Rev. B 87, 045310 (2013).
[5] N. Goldman, J. Dalibard, Phys. Rev. X 4, 031027 (2014).
[6] R. Desbuquois, T. Yefsah, L. Chomaz, C. Weitenberg, L. Corman, S. Nascimbène, J. Dalibard, Phys. Rev. Lett. 113, 020404 (2014).
[7] L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weintenberg, S. Nascimbene, J. Dalibard, J. Beugnon, Physical Review Letters 113, 135302 (2014)
[8] C. Repellin, B. Andrei Bernevig, N. Regnault, Phys. Rev. B 90, 245401 (2014)
[9] C. Repellin, T. Neupert, Z. Papic, N. Regnault, Phys. Rev. B 90, 045114 (2014).
[10] A. Sterdyniak, B. Andrei Bernevig, N.R. Cooper, N. Regnault, Phys. Rev. B 91, 035115 (2015).
[11] Zhao Liu, R. N. Bhatt, N.Regnault, Phys. Rev. B. 91, 045126 (2015) .
[12] C. Repellin, T. Neupert, B. Andrei Bernevig, N. Regnault, Phys. Rev. B 92, 115128 (2015).
[13] N. Goldman, J. Dalibard, M. Aidelsburger, and N. R. Cooper, Phys. Rev. A 91, 033632 (2015)
[14] A. Sterdyniak, Nigel R. Cooper and N. Regnault, Phys. Rev. Lett. 115, 116802 (2015).
[15] L. Chomaz, L. Corman, T. Bienaimé, R. Desbuquois, C.Weitenberg, S. Nascimbene, J. Beugnon, J. Dalibard, Nature Communications 6, 6162 (2015)
[16] S. Nascimbene, N. Goldman, N. R. Cooper, J. Dalibard, Phys. Rev. Lett. 115, 140401 (2015)

Chapters
F. Chevy and J. Dalibard, in K.H. Bennemann & J.B. Ketterson (éd.), Novel Superfluids, Oxford University Press, 2013, 398-428.
Z. Hadzibabic and J. Dalibard, in Jorge V José (éd.), 40 Years of Berezinskii–Kosterlitz–Thouless Theory, World Scientific, 2013, 297-324.
J. Dalibard, in Quantum Matter at Ultralow Temperatures, edited by M. Inguscio, W. Ketterle, S. Stringari and G. Roati


The remarkable advances of the last decade in the manipulation of ultracold atomic systems have opened a novel field at the interface of quantum information, quantum optics and many-body physics. The unprecedented precision on the control of atomic gases allows one to shed a new light on fundamental problems originating from condensed matter physics, while benefiting from different observables to characterize the system. The goal of our project is to use two-dimensional gases of rubidium atoms to simulate the fractional quantum Hall effect that occurs when a planar electron fluid is placed in a strong transverse magnetic field.
Since the atoms are neutral, we must simulate the orbital magnetism at the origin of the quantum Hall effect by a mechanism that reproduces the action of the Lorentz force and the Aharonov-Bohm phase. We will use an artificial gauge field induced either by rotating the gas, or by using a `Berry-type' geometrical phase. We will address both the case of `mesoscopic' atomic samples (typically ten atoms) and of `macroscopic' ones (typically a few ten thousands atoms).
In the mesoscopic case, we will start from a microtrap that we will set in rotation, and we will subsequently detect the position of each particle with a good spatial resolution. We will perform in parallel an exact numerical analysis, which will take into account the geometry of the setup and finite-temperature effects. This will allow for a direct and accurate comparison between theory and experiment, and a non-ambiguous identification of the strongly correlated states that will be produced.
In the macroscopic case, we will use the new concept of flux lattice, i.e., a periodic distribution of light that provides a single-particle band spectrum with a structure and a topology analogous to the Landau levels of a charge in a magnetic field. We will explore the phase diagram of this new system in the presence of atomic interactions, and we will identify the region of parameters where correlated phases can emerge. We will develop several ways for detecting them experimentally, such as the search for edge states and the transposition to the real world of the gedanken experiment at the basis of the definition of entanglement entropy.
The completion of this project will provide us with a quantitative characterization of robust correlated states in the presence of a strong magnetic field, for example the Laughlin state, which is emblematic of fractional quantum Hall physics. The ability to measure individual atomic positions will give access to quantities that are complementary to those obtained with condensed matter samples, usually based on transport measurements. On the long term this project will open several fascinating perspectives, such as the study of anyonic statistics and gauge fields with a richer structure, e.g. non-Abelian.

Project coordination

Jean DALIBARD (CNRS Laboratoire Kastler Brossel) – jean.dalibard@lkb.ens.fr

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.

Partner

CNRS LKB CNRS Laboratoire Kastler Brossel
CNRS LPA CNRS Laboratoire Pierre Aigrain

Help of the ANR 250,000 euros
Beginning and duration of the scientific project: September 2012 - 36 Months

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