Thin-film GaAs photovoltaic solar energy cells Final report

Thin film gallium arsenide photovoltaic solar cell

Synthetic gauge fields in synthetic dimensions

We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the "dimension" provided by the internal atomic degrees of freedom, yielding a synthetic 2D lattice. Suitable laser-coupling between these internal states leads to a uniform magnetic flux within the 2D lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter butterfly spectrum and the chiral edge states of the associated Chern insulating phases.Comment: 5+4 pages, 5+3 figures, two-column revtex; v2: discussion of role of interactions added, Fig. 1 reshaped, minor changes, references adde

Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.Comment: 11 pages, 6 figure

Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm

The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is considered the best algorithm in practice and performs best in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$.Comment: Extended abstract to appear in the proceedings of COCOON 201

Onset of Interlayer Phase Coherence in a Bilayer Two-Dimensional Electron System: Effect of Layer Density Imbalance

Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $\nu_T = 1$. We find that the phase boundary between the interlayer phase coherent state and the weakly-coupled compressible phase moves to larger layer separations as the electron density distribution in the bilayer is imbalanced. The critical layer separation increases quadratically with layer density difference.Comment: 4 pages, 3 figure

Feedback cooled Bose-Einstein condensation: near and far from equilibrium

Continuously measured interacting quantum systems almost invariably heat, causing loss of quantum coherence. Here, we study Bose-Einstein condensates (BECs) subject to repeated weak measurement of the atomic density and describe several protocols for generating a feedback signal designed to remove excitations created by measurement backaction. We use a stochastic Gross-Pitaevskii equation to model the system dynamics and find that a feedback protocol utilizing momentum dependant gain and filtering can effectively cool both 1D and 2D systems. The performance of these protocols is quantified in terms of the steady state energy, entropy, and condensed fraction. These are the first feedback cooling protocols demonstrated in 2D, and in 1D our optimal protocol reduces the equilibrium energy by more than a factor of 100 as compared with a previous cooling protocol developed using the same methodology. We also use this protocol to quench-cool 1D BECs from non-condensed highly excited states and find that they rapidly condense into a far from equilibrium state with energy orders of magnitude higher than the equilibrium ground state energy for that condensate fraction. We explain this in terms of the near-integrability of our 1D system, whereby efficiently cooled low momentum modes are effectively decoupled from the energetic `reservoir' of the higher momentum modes. We observe that the quench-cooled condensed states can have non-zero integer winding numbers described by quantized supercurrents.Comment: 14 pages, 7 figure

Strong enhancement of drag and dissipation at the weak- to strong- coupling phase transition in a bi-layer system at a total Landau level filling nu=1

We consider a bi-layer electronic system at a total Landau level filling factor nu =1, and focus on the transition from the regime of weak inter-layer coupling to that of the strongly coupled (1,1,1) phase (or ''quantum Hall ferromagnet''). Making the assumption that in the transition region the system is made of puddles of the (1,1,1) phase embedded in a bulk of the weakly coupled state, we show that the transition is accompanied by a strong increase in longitudinal Coulomb drag, that reaches a maximum of approximately $h/2e^{2}$. In that regime the longitudinal drag is increased with decreasing temperature.Comment: four pages, one included figur

Observation of Quantized Hall Drag in a Strongly Correlated Bilayer Electron System

The frictional drag between parallel two-dimensional electron systems has been measured in a regime of strong interlayer correlations. When the bilayer system enters the excitonic quantized Hall state at total Landau level filling factor \nu_T=1 the longitudinal component of the drag vanishes but a strong Hall component develops. The Hall drag resistance is observed to be accurately quantized at h/e^2.Comment: 4 pages, 3 figures. Version accepted for publication in Physical Review Letters. Improved discussion of experimental and theoretical issues, added references, correction to figure

Spin Transition in Strongly Correlated Bilayer Two Dimensional Electron Systems

Using a combination of heat pulse and nuclear magnetic resonance techniques we demonstrate that the phase boundary separating the interlayer phase coherent quantum Hall effect at $\nu_T = 1$ in bilayer electron gases from the weakly coupled compressible phase depends upon the spin polarization of the nuclei in the host semiconductor crystal. Our results strongly suggest that, contrary to the usual assumption, the transition is attended by a change in the electronic spin polarization.Comment: 4 pages, 3 postscript figur