Eric Sembrat's Test Bonanza

Conventional methods of quantum simulation rely on kinectic energy determined by free particle dispersions or simple sinusoidal optical lattices. Solid state systems, by contrast, exhibit a plethora of band structures which differ quantitatively, qualitatively, and even topologically. To what extent does this variety explain the many electronic phenomena observed in these materials? Here we address this question by subjecting an otherwise simple Bose superfluid to a customized band structure engineered by dynamically phase modulating (shaking) an optical lattice. The engineered dispersion contains two minima which we associate to a pseudospin degree of freedom. Surprisingly, in such a system the Bose superfluid exhibits many new behaviors. The psuedospin develops a ferromagnetic order, which can lead to polarization of the entire sample or to sub-division into polarized domains. The excitations of the system also exhibit the roton-maxon structure associated with strong interactions in superfluid helium.

A trial wave function \f (1,2,...,N) of an N electron system can always be written as the product of an antisymmetric Fermion factor F {Zij }= Tii<jZij , and a symmetric correlation factor G {Zij }. F results from Pauli principle, and G is caused by Coulomb interactions. One can represent G diagrammatically ( I J by distributing N points on the circumference of a circle, and drawing appropriate lines representing correlation factors (cfs) Zij between pairs. Here, of course, Zij = Zi­ Zj, and Zi is the complex coordinate of the i111 electron. Laughlin correlation for the v=l/3 filled incompressible quantum liquid (IQL) state contain two cfs  connecting each pair i,j. For the Moore-Read state of the half-filled excited Landau level (LL), with v=2 + 1/ 2, the even value of N for the half-filled LL is partitioned into two subsets A and B, each containing N/2 electrons[21.

For any one partition(A,B)the contribution to G is given by GAB = Tiiz\Tik<Ii;sZ2kt · The full G is equal to the symmetric sum of contributions GAB over all possible partitions of N into two equal subsets. For Jain states at filling factor v=p/ q < 1/ 2 , the  value  of  the  single  particle angular momentum e satisfies the equation  20=v- 1N-Cv, with Cv = q + 1 - p. The values of (2 N) define the function space of G {Zij}, which must satisfy a number of conditions.

For example, the highest power of any Zi cannot exceed 2e+ 1-N. In addition, the value of the total angular momentum L of the lowest correlated state must satisfy the equation L=(N / 2) (2e+ 1-N)-Ka, where Ka is the degree of the homogeneous polynomial generated by G. Knowing the values of L for IQL states (and for states containing a few quasielectrons or a few quasiholes) from Jain's mean field CF picture allows one to determine Ka. The dependence of the pair pseudopotential V(L2) on pair angular momentum L2 , suggests a small number of correlation diagrams  for a given value of the total angular momentum L. Correlation diagrams and correlation functions for the Jain state at v=2 /S and for the Moore-Read stated will be presented as example.

[1] J.J. Quinn, Waves in random and complex media (2014) 898867

[2] S.B. Mulay, J.J . Quinn, and M.A. Shattuck, submitted to J. Math. Phys. (2014) 

Our method of nanoscale magnetic sensing and imaging makes use of nitrogen-vacancy (NV) color centers a few nanometers below the surface of a diamond crystal. Using individual NV centers, we perform NMR experiments on single protein molecules, labeled with ^{13}C and ^2H isotopes. In order to achieve single nuclear-spin sensitivity, we use isolated electronic-spin quantum bits (qubits), that are present of the diamond surface, as magnetic resonance "reporters". Their quantum state is coherently manipulated and measured optically via a proximal NV center. This system is used for sensing, coherent coupling, and imaging of individual proton spins on the diamond surface with angstrom resolution. Our approach may enable direct structural imaging of complex molecules that cannot be accessed from bulk studies, and realizes a new platform for probing novel materials, and manipulation of complex spin systems on surfaces.

mso-fareast-font-family:"Times New Roman"">Since the 2001 Nobel Physics Prize was awarded for the creation of Bose-Einstein condensates, dilute atomic gases at ultralow temperatures have been a driving force behind the quantum simulation of manybody physics. However, studying highly correlated quantum states with small energy gaps can still pose severe challenges to contemporary experiments with even the coldest atomic samples. The power of cold-atom experiments will be greatly enhanced by precision measurements, allowing, for example, physics that is normally probed at nK temperatures to be studied at μK temperatures. This is precisely what we have achieved. Thanks to the development of ultrastable lasers with 1×10^-16 instability, the JILA strontium (Sr) optical clock now realizes a powerful laboratory to study a many-body spin system with strongly interacting, open, and driven dynamics [1]. For the first time, s- and p-wave inter-atomic interactions in the clock are characterized to high precision, which enables a spectroscopic observation of SU(N mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-char-type:symbol;mso-symbol-font-family:Mathematica1">£ mso-fareast-font-family:"Times New Roman""> 10) symmetry in ⁸⁷Sr gases at μK temperatures [2]. This study lays the groundwork for pushing the frontier of emergent many-body quantum physics beyond experimental limitations, as well as realizing exotic quantum states that have no counterparts in nature.  

mso-fareast-font-family:"Times New Roman"">To go beyond current experimental capabilities, one will need to combine the power of precision measurements with state-of-the-art cold-atom techniques to cool, probe, and manipulate atomic quantum gases. High-spatial-resolution imaging is one such technique, which has been utilized in the observation of quantum criticality with two-dimensional Bose gases in optical lattices [3]. In this experiment, high-resolution imaging allows one not only to access the equation of state and dynamics of a quantum gas, but also to engineer arbitrary trapping potentials for studying novel quantum transport phenomena. Based on my experiences with both ultracold atoms and precision measurements, I will discuss my future research plans and explain how ultracold strontium atoms with optical flux lattices will provide a unique opportunity to explore some of the most interesting strongly correlated quantum systems.

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mso-fareast-font-family:"Times New Roman"">[1] A quantum many-body spin system in an optical lattice clock.

mso-fareast-font-family:"Times New Roman"">M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).

[2] Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism.

X. Zhang, M. Bishof, S. L. Bromley, C.V. Kraus, M. Safronova, P. Zoller, A. M. Rey, and J. Ye, mso-fareast-language:ZH-CN">Science 345, 1467 (2014).

 [3] ZH-CN">Observation of quantum criticality with ultracold atoms in optical lattices mso-fareast-font-family:"Times New Roman"">.

X. Zhang, C.-L. Hung, S.-K. Tung, and C. Chin, Science 335, 1070 (2012).

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We introduce an inverse design approach based on minimal theoretical modeling, direct numerical simulations and artificial intelligence techniques for the investigation of biolocomotion in fluids. Its application to the characterization of inertial aquatic phenomena and to the identification of optimal swimming gaits and morphologies is presented.

The collective motion of a large group of individuals has two different scales. Individuals move and interact on a local scale, while the motion of the group as a whole occurs on a global scale. All the movement of the group on the global scale is produced by the many movements of its members, and so a good model for the global behaviour should arise from local models for the individuals. We investigate the link between the two scales, and create formulae for producing a global model for any particular lattice-based local model using mean-field approximations.