Benno S. Rem

Experimental reconstruction of the Berry curvature in a Floquet Bloch band

Cold atoms do geometry Electrons in solids populate energy bands, which can be simulated in cold atom systems using optical lattices. The geometry of the corresponding wave functions determines the topological properties of the system, but getting a direct look is tricky. Fläschner et al. and Li et al. measured the detailed structure of the band wave functions in hexagonal optical lattices, one resembling a boron-nitride and the other a graphene lattice. These techniques will make it possible to explore more complex situations that include the effects of interactions. Science, this issue pp. 1091 and 1094 Berry curvature is engineered and measured in a simulated boron-nitride optical lattice filled with fermionic K atoms. Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved measurement of the ensuing Berry curvature. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures.

Lifetime of the Bose gas with resonant interactions.

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient L(3). Our data follow a L(3)=λ(3)/T(2) law with λ(3)=2.5(3)(stat)(6)(syst)×10(-20) (μK)(2) cm(6) s(-1) and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length a at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where |a| is smaller than the thermal wavelength. We find that L(3) is continuous across the resonance, and over the whole a<0 range our data quantitatively agree with our calculation.

Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas.

We measure the zero-temperature equation of state of a homogeneous Bose gas of (7)Li atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.

Observation of dynamical vortices after quenches in a system with topology

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters1. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number2. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention3–6. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices7. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude8, which signal a so-called dynamical phase transition9,10. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.Non-equilibrium signatures of topology—the appearance, movement and annihilation of vortices in a cold-atom system—are identified, showing that topological phase can emerge dynamically from a non-topological state.Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental concepts for systems far from equilibrium are just being explored, such as the recently introduced dynamical phase transition (DPT). Here we report on the first observation of a DPT in the dynamics of a fermionic many-body state after a quench between two lattice Hamiltonians. With time-resolved state tomography in a system of ultracold atoms in optical lattices, we obtain full access to the evolution of the wave function. We observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at the critical times of the DPT. Our observation of a DPT is an important step towards a more comprehensive understanding of non-equilibrium dynamics in general.

A mixture of Bose and Fermi superfluids

Making a superfluid lithium mixture At some of the coldest temperatures achieved in the laboratory, researchers can coax dilute gases of atoms into becoming a superfluid, with the whole gas behaving as one entity. Bosonic atoms, which like to congregate in one state, achieve this willingly. Fermions, which effectively repel each other, require more persuasion. Ferrier-Barbut et al. made a superfluid mixture of two gases, one made up of bosons and one of fermions. They used two isotopes of lithium, fermionic 6Li and bosonic 7Li. When they made the mixture oscillate, the two components took turns feeding energy into each other. Science, this issue p. 1035 An ultracold gas mixture of two lithium isotopes, one bosonic and the other fermionic, manifests superfluidity. Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two lithium isotopes, lithium-6 and lithium-7. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high-precision spectroscopy of these modes, we observe coherent energy exchange and measure the coupling between the two superfluids. Our observations can be captured theoretically using a sum-rule approach that we interpret in terms of two coupled oscillators.

Λ-enhanced sub-Doppler cooling of lithium atoms inD1gray molasses

Following the bichromatic sub-Doppler cooling scheme on the D1-line of 40K recently demonstrated in (Fernandes et al. 2012), we introduce a similar technique for 7Li atoms and obtain temperatures of 60 uK while capturing all of the 5x10^8 atoms present from the previous stage. We investigate the influence of the detuning between the the two cooling frequencies and observe a threefold decrease of the temperature when the Raman condition is fulfilled. We interpret this effect as arising from extra cooling due to long-lived coherences between hyperfine states. Solving the optical Bloch equations for a simplified, \Lambda-type three-level system we identify the presence of an efficient cooling force near the Raman condition. After transfer into a quadrupole magnetic trap, we measure a phase space density of ~10^-5. This laser cooling offers a promising route for fast evaporation of lithium atoms to quantum degeneracy in optical or magnetic traps.

Universal Loss Dynamics in a Unitary Bose Gas

The low temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here we first present a theoretical model that describes the dynamic competition between two-body evaporation and three-body re-combination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal magic trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the 2D evaporation case. Experiments performed with unitary 133 Cs and 7 Li atoms fully support our predictions and enable quantitative measurements of the 3-body recombination rate in the low temperature domain. In particular, we measure for the first time the Efimov inelasticity parameter

Observation of Topological Bloch-State Defects and Their Merging Transition

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Characterizing topology by dynamics: Chern number from linking number

* = 0.098(7) for the 47.8-G d-wave Feshbach resonance in 133 Cs. Combined 133 Cs and 7 Li experimental data allow investigations of loss dynamics over two orders of magnitude in temperature and four orders of magnitude in three-body loss. We confirm the 1/T 2 temperature universality law up to the constant

The road to the unitary bose gas

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