BEC on an optical hexagonal lattice

The technology with lasers has incredibly enriched our understanding of a huge width of systems. The ability to prepare honeycomb lattice offers chances to study graphene-type physics and beyond. In this PRL paper, the authors addressed the issues of what would befall a Bose-Einstein condensate moving on a honeycomb lattice. They employed Gross-Pitaviskii equation, which is a mean-field theory for describing superfluids, to compute the band structure and found that, arbitrary interaction would drastically alter the structure around the Dirac points. Is it possible to observe similar stuff using graphene instead of an artificial lattice ? One needs to have superfluid to flow on graphene. The candidate is cooper pairs condensate, which may be created by placing a superconductor in contact with a layer of graphene.

The ability to prepare ultracold atoms in graphenelike hexagonal optical lattices is expanding the types of systems in which Dirac dynamics can be observed. In such cold-atom systems, one could, in principle, study the interplay between superfluidity and Dirac physics. In a paper appearing in Physical Review Letters, Zhu Chen at the Chinese Academy of Sciences and Biao Wu of Peking University use mean-field theory to calculate the Bloch bands of a Bose-Einstein condensate confined to a hexagonal optical lattice.

The Dirac point is a point in the Brillouin zone around which the energy-momentum relation is linear. Its existence in graphene is at the heart of this material’s unusual properties, in which electrons behave as massless particles. Chen and Wu’s study predicts, surprisingly, that in the analog cold-atom system, the topological structure of the Dirac point is drastically modified: intersecting tubelike bands appear around the original Dirac point, giving rise to a set of new Dirac points that form a closed curve. More importantly, this transformation should occur even with an arbitrarily small interaction between the atoms, upending the idea that such topological effects can only occur in the presence of a finite interaction between atoms.

The modified band structure prevents an adiabatic evolution of a state across the Dirac point, violating the usual quantum rule that a system remains in its instantaneous eigenstate if an external perturbation is sufficiently slow. This effect could be tested experimentally in a so-called triple-well structure, which is a combination of rectangular and triangular optical lattices. – Hari Dahal [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.065301]

Solid He4

This solid is still very attractive for the likelihood of finding supersolidity in it. Supersolidity encompasses a thermodynamically large number of solid He atoms (or vacancies or dislocations or others) moving coherently. The route seems very ragged. A new report goes like this [Science, 332:821(2011)]:

Using a high-sensitivity torsional oscillator (TO) technique, we mapped the rotational and relaxational dynamics of solid helium-4 (⁴He) throughout the parameter range of the proposed supersolidity. We found evidence that the same microscopic excitations controlling the torsional oscillator motions are generated independently by thermal and mechanical stimulation. Moreover, a measure for the relaxation times of these excitations diverges smoothly without any indication for a critical temperature or critical velocity of a supersolid transition. Finally, we demonstrated that the combined temperature-velocity dependence of the TO response is indistinguishable from the combined temperature-strain dependence of the solid’s shear modulus. This implies that the rotational responses of solid ⁴He attributed to supersolidity are associated with generation of the same microscopic excitations as those produced by direct shear strain.

BEC is like laser, with perfect coherence: from an experimental point of view

In this work, BEC has been shown possessing the same kind of coherence properties of laser, as expected. The researchers measure directly the third order correlation functions regarding atom bunching (for bosons), g(0,t1,t2), which shows the likelihood of having three particles detected at moments 0, t1 and t2, respectively. For thermal bosons, this function features a broad peak, while for BEC it is rather uniform. This was just observed [Science, 331:3046(2011)] !

A major advance in understanding the behavior of light was to describe the coherence of a light source by using correlation functions that define the spatio-temporal relationship between pairs and larger groups of photons. Correlations are also a fundamental property of matter. We performed simultaneous measurement of the second- and third-order correlation functions for atoms. Atom bunching in the arrival time for pairs and triplets of thermal atoms just above the Bose-Einstein condensation (BEC) temperature was observed. At lower temperatures, we demonstrated conclusively the long-range coherence of the BEC for correlation functions to third order, which supports the prediction that like coherent light, a BEC possesses long-range coherence to all orders.

Molecular superfluidity ?

Bosons could become superfluid at low temperatures: it flows without feeling the friction. This is so due to the opening of an energy gap as bosons condense into a so-called macro-molecule in the presence of interactions. It is expected that such condensation happens at a number of bosons. Now it was demonstrated that, this number can be down to 9 pH2 molecules.

Clusters of para-hydrogen (pH2) have been predicted to exhibit superfluid behavior, but direct observation of this phenomenon has been elusive. Combining experiments and theoretical simulations, we have determined the size evolution of the superfluid response of pH2 clusters doped with carbon dioxide (CO2). Reduction of the effective inertia is observed when the dopant is surrounded by the pH2 solvent. This marks the onset of molecular superfluidity in pH2. The fractional occupation of solvation
rings around CO2 correlates with enhanced superfluid response for certain cluster sizes. [PRL 105, 133401 (2010)]