A rapidly expanding Bose-Einstein condensate: an expanding universe in the lab

We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have taken place at the end of inflation.Comment: 12 pages, 7 figure

Electronic states of PrCoO3_3: X-ray photoemission spectroscopy and LDA+U density of states studies

Electronic states of PrCoO$_3$ are studied using x-ray photoemission spectroscopy. Pr 3d$_{5/2}$ core level and valence band (VB) were recorded using Mg K$_\beta$ source. The core level spectrum shows that the 3d$_{5/2}$ level is split into two components of multiplicity 4 and 2, respectively due to coupling of the spin states of the hole in 3d$_{5/2}$ with Pr 4f holes spin state. The observed splitting is 4.5 eV. The VB spectrum is interpreted using density of states (DOS) calculations under LDA and LDA+U. It is noted that LDA is not sufficient to explain the observed VB spectrum. Inclusion of on-site Coulomb correlation for Co 3d electrons in LDA+U calculations gives DOS which is useful in qualitative explanation of the ground state. However, it is necessary to include interactions between Pr 4f electrons to get better agreement with experimental VB spectrum. It is seen that the VB consists of Pr 4f, Co 3d and O 2p states. Pr 4f, Co 3d and O 2p bands are highly mixed indicating strong hybridization of these three states. The band near the Fermi level has about equal contributions from Pr 4f and O 2p states with somewhat smaller contribution from Co 3d states. Thus in the Zaanen, Sawatzky, and Allen scheme PrCoO$_3$ can be considered as charge transfer insulator. The charge transfer energy $\Delta$ can be obtained using LDA DOS calculations and the Coulomb-exchange energy U' from LDA+U. The explicit values for PrCoO$_3$ are $\Delta$ = 3.9 eV and U' = 5.5 eV; the crystal field splitting and 3d bandwidth of Co ions are also found to be 2.8 and 1.8 eV, respectively.Comment: 12 pages, 7 figures; to appear J. Phys.: Condens. Matte

On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields

Recently, Gupta et.al. [GKKS2013] proved that over Q any $n^{O(1)}$-variate and $n$-degree polynomial in VP can also be computed by a depth three $\Sigma\Pi\Sigma$ circuit of size $2^{O(\sqrt{n}\log^{3/2}n)}$. Over fixed-size finite fields, Grigoriev and Karpinski proved that any $\Sigma\Pi\Sigma$ circuit that computes $Det_n$ (or $Perm_n$) must be of size $2^{\Omega(n)}$ [GK1998]. In this paper, we prove that over fixed-size finite fields, any $\Sigma\Pi\Sigma$ circuit for computing the iterated matrix multiplication polynomial of $n$ generic matrices of size $n\times n$, must be of size $2^{\Omega(n\log n)}$. The importance of this result is that over fixed-size fields there is no depth reduction technique that can be used to compute all the $n^{O(1)}$-variate and $n$-degree polynomials in VP by depth 3 circuits of size $2^{o(n\log n)}$. The result [GK1998] can only rule out such a possibility for depth 3 circuits of size $2^{o(n)}$. We also give an example of an explicit polynomial ($NW_{n,\epsilon}(X)$) in VNP (not known to be in VP), for which any $\Sigma\Pi\Sigma$ circuit computing it (over fixed-size fields) must be of size $2^{\Omega(n\log n)}$. The polynomial we consider is constructed from the combinatorial design. An interesting feature of this result is that we get the first examples of two polynomials (one in VP and one in VNP) such that they have provably stronger circuit size lower bounds than Permanent in a reasonably strong model of computation. Next, we prove that any depth 4 $\Sigma\Pi^{[O(\sqrt{n})]}\Sigma\Pi^{[\sqrt{n}]}$ circuit computing $NW_{n,\epsilon}(X)$ (over any field) must be of size $2^{\Omega(\sqrt{n}\log n)}$. To the best of our knowledge, the polynomial $NW_{n,\epsilon}(X)$ is the first example of an explicit polynomial in VNP such that it requires $2^{\Omega(\sqrt{n}\log n)}$ size depth four circuits, but no known matching upper bound

Opto-mechanical micro-macro entanglement

We propose to create and detect opto-mechanical entanglement by storing one component of an entangled state of light in a mechanical resonator and then retrieving it. Using micro-macro entanglement of light as recently demonstrated experimentally, one can then create opto-mechanical entangled states where the components of the superposition are macroscopically different. We apply this general approach to two-mode squeezed states where one mode has undergone a large displacement. Based on an analysis of the relevant experimental imperfections, the scheme appears feasible with current technology.Comment: 7 pages, 6 figures, to appear in PRL, submission coordinated with Sekatski et al. who reported on similar result

On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.Comment: 15 pages, 3 figure

Temperature independent band structure of WTe2 as observed from ARPES

Extremely large magnetoresistance (XMR), observed in transition metal dichalcogendies, WTe$_2$, has attracted recently a great deal of research interests as it shows no sign of saturation up to the magnetic field as high as 60 T, in addition to the presence of type-II Weyl fermions. Currently, there has been a lot of discussion on the role of band structure changes on the temperature dependent XMR in this compound. In this contribution, we study the band structure of WTe$_2$ using angle-resolved photoemission spectroscopy (ARPES) and first-principle calculations to demonstrate that the temperature dependent band structure has no substantial effect on the temperature dependent XMR as our measurements do not show band structure changes on increasing the sample temperature between 20 and 130 K. We further observe an electronlike surface state, dispersing in such a way that it connects the top of bulk holelike band to the bottom of bulk electronlike band. Interestingly, similar to bulk states, the surface state is also mostly intact with the sample temperature. Our results provide invaluable information in shaping the mechanism of temperature dependent XMR in WTe$_2$.Comment: 7 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.0721

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene

The electronic properties of graphene superlattices have attracted intense interest that was further stimulated by the recent observation of novel many-body states at "magic" angles in twisted bilayer graphene (BLG). For very small ("marginal") twist angles of 0.1 deg, BLG has been shown to exhibit a strain-accompanied reconstruction that results in submicron-size triangular domains with the Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, marginally-twisted BLG is predicted to remain conductive due to a triangular network of chiral one-dimensional (1D) states hosted by domain boundaries. Here we study electron transport through this network and report giant Aharonov-Bohm oscillations persisting to temperatures above 100 K. At liquid helium temperatures, the network resistivity exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the flat minibands formed by the 2D network of 1D states inside the gap. Our work shows that marginally twisted BLG is markedly distinct from other 2D electronic systems, including BLG at larger twist angles, and offers a fascinating venue for further research.Comment: 11 pages, 8 figure