A method to discriminate between localized and chaotic quantum systems

We derive a criterion that distinguishes whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state, or chaotic. Our approach considers the time evolution in the Lanczos basis, which maps the system's dynamics onto that of a particle moving in a one-dimensional lattice where both the energy in the lattice sites and the tunneling from one lattice site to the next are inhomogeneous. We infer a criterion that allows distinguishing localized from chaotic systems. This criterion involves the coupling strengths between Lanczos states and their expectation energy fluctuations. We verify its validity by inspecting three cases, corresponding to Anderson localization as a function of dimension, the out-of-equilibrium dynamics of a many-body dipolar spin system, and integrable systems. We finally show that our approach provides a justification for the Wigner surmise and the eigenstate thermalization hypothesis, which have both been proposed to characterize quantum chaotic systems. Indeed, our criterion for a system to be chaotic implies the level repulsion (also known as spectral rigidity) of eigenenergies, which is characteristic of the Wigner-Dyson distribution; and we also demonstrate that in the chaotic regime, the expectation value of any local observable only weakly varies as a function of eigenstates. Our demonstration allows to define the class of operators to which the eigenstate thermalization applies, as the ones that connect states that are coupled at weak order by the Hamiltonian.Comment: 15 pages, 6 figure

Competition between Bose Einstein Condensation and spin dynamics

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation, by rapidly cooling a chromium multi-component Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin-degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin excited states. Small metastable spinor condensates are nevertheless produced, and manifest strong spin fluctuations.Comment: 5 pages, 4 figure

Cooling of a Bose-Einstein Condensate by spin distillation

We propose and experimentally demonstrate a new cooling mechanism leading to purification of a spinor Bose-Einstein Condensate (BEC). Our scheme starts with a BEC polarized in the lowest energy spin state. Spin excited states are thermally populated by lowering the single particle energy gap set by the magnetic field. Then these spin-excited thermal components are filtered out, which leads to an increase of the BEC fraction. We experimentally demonstrate such cooling for a spin 3 52Cr dipolar BEC. Our scheme should be applicable to Na or Rb, with perspective to reach temperatures below 1 nK.Comment: 4 figure

Spontaneous demagnetization of a dipolar spinor Bose gas at ultra-low magnetic field

Quantum degenerate Bose gases with an internal degree of freedom, known as spinor condensates, are natural candidates to study the interplay between magnetism and superfluidity. In the spinor condensates made of alkali atoms studied so far, the spinor properties are set by contact interactions, while magnetization is dynamically frozen, due to small magnetic dipole-dipole interactions. Here, we study the spinor properties of S=3 $^{52}$Cr atoms, in which relatively strong dipole-dipole interactions allow changes in magnetization. We observe a phase transition between a ferromagnetic phase and an unpolarized phase when the magnetic field is quenched to an extremely low value, below which interactions overwhelm the linear Zeeman effect. The BEC magnetization changes due to magnetic dipole-dipole interactions that set the dynamics. Our work opens up the experimental study of quantum magnetism with free magnetization using ultra-cold atoms.Comment: 6 pages, 4 figures, 2 appendice

Application of lasers to ultracold atoms and molecules

In this review, we discuss the impact of the development of lasers on ultracold atoms and molecules and their applications. After a brief historical review of laser cooling and Bose-Einstein condensation, we present important applications of ultra cold atoms, including time and frequency metrology, atom interferometry and inertial sensors, atom lasers, simulation of condensed matter systems, production and study of strongly correlated systems, and production of ultracold molecules.Comment: Review paper written in the name of IFRAF to celebrate 50 years of lasers and their applications to cold atom physics; 15 pages, 2 figures; to appear in Comptes Rendus de l'Academie des Sciences, Pari

Non-equilibrium quantum magnetism in a dipolar lattice gas

Research on quantum magnetism with ultra-cold gases in optical lattices is expected to open fascinating perspectives for the understanding of fundamental problems in condensed-matter physics. Here we report on the first realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. In contrast to their non-dipolar counterparts, dipolar lattice gases allow for inter-site spin-spin interactions without relying on super-exchange energies, which constitutes a great advantage for the study of spin lattice models. In this paper we show that a chromium gas in a 3D lattice realizes a lattice model resembling the celebrated t-J model, which is characterized by a non-equilibrium spinor dynamics resulting from inter-site Heisenberg-like spin-spin interactions provided by non-local dipole-dipole interactions. Moreover, due to its large spin, chromium lattice gases constitute an excellent environment for the study of quantum magnetism of high-spin systems, as illustrated by the complex spin dynamics observed for doubly-occupied sites.Comment: 10 pages, 5+5 figure

Evolution dynamics of a dense frozen Rydberg gas to plasma

Dense samples of cold Rydberg atoms have previously been observed to spontaneously evolve to a plasma, despite the fact that each atom may be bound by as much as 100 cm−1. Initially, ionization is caused by blackbody photoionization and Rydberg-Rydberg collisions. After the first electrons leave the interaction re- gion, the net positive charge traps subsequent electrons. As a result, rapid ionization starts to occur after 1 μs caused by electron-Rydberg collisions. The resulting cold plasma expands slowly and persists for tens of microseconds. While the initial report on this process identified the key issues described above, it failed to resolve one key aspect of the evolution process. Specifically, redistribution of population to Rydberg states other than the one initially populated was not observed, a necessary mechanism to maintain the energy balance in the system. Here we report new and expanded observations showing such redistribution and confirming theoretical predictions concerning the evolution to a plasma. These measurements also indicate that, for high n states of purely cold Rydberg samples, the initial ionization process which leads to electron trapping is one involving the interactions between Rydberg atoms

Evolution dynamics of a dense frozen Rydberg gas to plasma

Dense samples of cold Rydberg atoms have previously been observed to spontaneously evolve to a plasma, despite the fact that each atom may be bound by as much as 100 cm−1. Initially, ionization is caused by blackbody photoionization and Rydberg-Rydberg collisions. After the first electrons leave the interaction re- gion, the net positive charge traps subsequent electrons. As a result, rapid ionization starts to occur after 1 μs caused by electron-Rydberg collisions. The resulting cold plasma expands slowly and persists for tens of microseconds. While the initial report on this process identified the key issues described above, it failed to resolve one key aspect of the evolution process. Specifically, redistribution of population to Rydberg states other than the one initially populated was not observed, a necessary mechanism to maintain the energy balance in the system. Here we report new and expanded observations showing such redistribution and confirming theoretical predictions concerning the evolution to a plasma. These measurements also indicate that, for high n states of purely cold Rydberg samples, the initial ionization process which leads to electron trapping is one involving the interactions between Rydberg atoms

Atomes, molécules et plasmas ultra-froids :- Transition d'un gaz de Rydberg gelé vers un plasma ultra-froid.- Contrôle de collisions de photoassociation dans des schémas de résonance de Feshbach et de transition Raman stimulée

Ultra-cold atoms, molecules, and plasmas:-From a frozen Rydberg gas to an ultra-cold plasma-Manipulating photoassociation using Feshbach resonances and Raman transitionsAtomes, molécules et plasmas ultra-froids :- Transition d'un gaz de Rydberg gelé vers un plasma ultra-froid.- Contrôle de collisions de photoassociation dans des schémas de résonance de Feshbach et de transition Raman stimulé

A method to discriminate between localized and chaotic quantum systems

We derive a criterion that distinguishes whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state, or chaotic. Our approach considers the time evolution in the Lanczos basis, which maps the system's dynamics onto that of a particle moving in a one-dimensional lattice where both the energy in the lattice sites and the tunneling from one lattice site to the next are inhomogeneous. We infer a criterion that allows distinguishing localized from chaotic systems. This criterion involves the coupling strengths between Lanczos states and their expectation energy fluctuations. We verify its validity by inspecting three cases, corresponding to Anderson localization as a function of dimension, the out-of-equilibrium dynamics of a many-body dipolar spin system, and integrable systems. We finally show that our approach provides a justification for the Wigner surmise and the eigenstate thermalization hypothesis, which have both been proposed to characterize quantum chaotic systems. Indeed, our criterion for a system to be chaotic implies the level repulsion (also known as spectral rigidity) of eigenenergies, which is characteristic of the Wigner-Dyson distribution; and we also demonstrate that in the chaotic regime, the expectation value of any local observable only weakly varies as a function of eigenstates. Our demonstration allows to define the class of operators to which the eigenstate thermalization applies, as the ones that connect states that are coupled at weak order by the Hamiltonian