Measuring topology of BECs in a synthetic dimensions lattice

We describe several experiments performed on a two species apparatus capable of producing Bose-Einstein condensates (BECs) of rubidium 87 and degenerate Fermi gases (DFGs) of potassium 40. We first describe computational results for observed optical depths with absorption imaging, in a regime where imaging times are long enough that recoil-induced detuning introduces significant corrections. We report that the obseved optical depth depends negligibly on the cloud shape. We also find that the signal-to-noise(SNR) ratio for low atom numbers can be significantly improved by entering this regime and applying the appropriate corrections. We take advantage of this SNR improvement in our subsequent experiment colliding two clouds of potassium 40 for different values of background magnetic field in the vicinity of a Feshbach resonance. We directly imaged the fraction of scattered atoms, which was low and difficult to detect. We used this method to measure the resonance location to be B_0 = 202.06(15) Gauss with a width of 10.(5) Gauss, in good agreement with accepted values. Next, we describe experiments creating an elongated effectively 2D lattice for a BEC of rubidium 87 with non-trivial topological structure using the technique of synthetic dimensions. We set up the lattice by applying a 1D optical lattice to the atoms along one direction, and treating the internal spin states of the atoms as lattice sites in the other direction. This synthetic direction is therefore very short, creating a strip geometry. We then induce tunneling along the synthetic direction via Raman coupling, adding a phase term to the tunneling coefficient. This creates an effective magnetic flux through each lattice plaquette, in the Hofstadter regime, where the flux is of order the flux quantum $h/e$. We detect the resulting eigenstate structure, and observe chiral currents when atom are loaded into the central synthetic site. We further launch analogues of edge magnetoplasmons and image the resulting skipping orbits along each edge of the strip. We then applied a force along the real dimension of the 2D lattice and directly imaged the resulting motion in the transverse, synthetic, direction. We performed these measurements with 3 and 5-site width lattices along the synthetic direction. We used these measurements to identify the value of the Chern number, the topological invariant in 2D, by leveraging the Diophantine equation derived by Thouless, Kohomoto, Nightingale, and den Nijs. We measure Chern numbers with typical uncertainty of 5%, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in extremely narrow systems

Brownian motion of solitons in a Bose-Einstein Condensate

For the first time, we observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated $^{87}\rm{Rb}$ BECs and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one-dimension (1-D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1-D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.Comment: 4 figure

Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past

We introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past. The maximum probability of simulation is determined by causality and depends on the amount and type (classical or quantum) of information that the channel can transmit. We illustrate this dependence in several examples, including ideal classical and quantum channels, measure-and-prepare channels, partial trace channels, and universal cloning channels. For the simulation of partial trace channels, we consider generalized teleportation protocols that take N input copies of a pure state in the future and produce M < N output copies of the same state in the past. In this case, we show that the maximum probability of successful teleportation increases with the number of input copies, a feature that was impossible in classical physics. In the limit of asymptotically large N, the probability converges to the probability of simulation for an ideal classical channel. Similar results are found for universal cloning channels from N copies to M > N approximate copies, exploiting a time-reversal duality between universal cloning and partial trace.Comment: 16 pages, 6 figures, published versio

NASICON-type Na3V2(PO4)3

Single crystals of the title compound, tris­odium divanadium(III) tris­(orthophosphate), were grown from a self-flux in the system Na4P2O7–NaVP2O7. Na3V2(PO4)3 belongs to the family of NASICON-related structures and is built up from isolated [VO6] octa­hedra (3. symmetry) and [PO4] tetra­hedra (.2 symmetry) inter­linked via corners to establish the framework anion [V2(PO4)3]3−. The two independent Na+ cations are partially occupied [site-occupancy factors = 0.805 (18) and 0.731 (7)] and are located in channels with two different oxygen environments, viz sixfold coordination for the first (. symmetry) and eightfold for the second (.2 symmetry) Na+ cation

Brownian motion of solitons in a Bose-Einstein Condensate

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated 87 Rb Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one-dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton\u27s diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment