In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, propose the realization of characteristic model, introduced by Haldane, using optical lattices loaded with fermionic atoms two internal states. We demonstrate that time-of-flight measurements reveal system form momentum-space Skyrmions.

We explore the uses of ultracold molecules as a platform for future experiments in field quantum simulation, focusing on two molecular species, $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs. report development coherent state control using microwave fields both species; this is crucial ingredient many simulation applications. demonstrate proof-of-principle Ramsey interferometry measurements with fringe spacings $\sim 1~\rm kHz$ investigate dephasing time superposition $N=0$ $N=1$ rotational...

We discuss how the internal structure of ultracold molecules, trapped in motional ground state optical tweezers, can be used to implement qudits. explore rotational, fine and hyperfine $^{40}$Ca$^{19}$F $^{87}$Rb$^{133}$Cs, which are examples molecules with $^2\Sigma$ $^1\Sigma$ electronic states, respectively. In each case we identify a subset levels within single rotational manifold suitable 4-level qudit. Quantum gates implemented using two-photon microwave transitions via neighboring...

Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole--dipole interactions, which open new possibilities information processing and the simulation of strongly correlated systems. Here, we use magnetic microwave fields to design a fast entangling gate with $>0.999$ fidelity is robust respect fluctuations in trapping control small thermal excitations. These results establish feasibility build scalable processor broad range molecular species...

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in limit weak coupling. focus on dependence pairing gap and free energy variations number densities two species while total density system is held fixed. As asymmetry increased, exhibits transition from homogenous Bardeen-Cooper-Schrieffer (BCS) to phases spontaneously broken global space symmetries. One such realization deformed surface superfluidity (DFS) which exploits possibility...

We perform a comprehensive analysis of the spectral statistics molecular resonances in (166)Er and (168)Er observed recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with aim determining chaoticity this system. calculate different independent statistical properties to check their degree agreement random matrix theory (RMT), analyze if they are consistent possibility having missing resonances. The short-range fluctuations as function magnetic field points...

We propose a fast and non-destructive spectroscopic method for single molecular ions that implements quantum logic schemes between an atomic ion the of interest. Our proposal relies on hybrid coherent manipulation two-ion system, using optical or magnetic forces depending types levels to be addressed (Zeeman, rotational, vibrational electronic degrees freedom). The is especially suited precision spectroscopy ions, sets starting point new computation combine covering measurement entangling steps.

We present a distinct mechanism for the formation of bound states in continuum (BICs). In chiral quantum systems, there appear zero-energy which wave function has finite amplitude only one subsystems defined by symmetry. When system is coupled to leads with energy band, part these remain bound. derive some algebraic rules number depending on dimensionality and rank total Hamiltonian. examine transport properties such systems including appearance Fano resonances limiting cases. Finally, we...

We present a nondestructive method to probe complex quantum system using multiple-impurity atoms as probes. Our protocol provides access different equilibrium properties of the by changing its coupling In particular, we show that measurements with two probes reveal system's nonlocal two-point density correlations, for probe-system contact interactions. illustrate our findings analytic and numerical calculations Bose-Hubbard model in weakly strongly interacting regimes, under conditions...

We investigate the dynamics of a $F=1$ spinor Bose-Einstein condensate $^{87}\mathrm{Rb}$ atoms confined in quasi-one-dimensional trap both at zero and finite temperature. At temperature, we observe coherent oscillations between populations various spin components formation multiple domains condensate. study also temperature effects taking into account phase fluctuations Bogoliubov-de Gennes framework. $T$, despite complex multidomain condensate, population equipartition occurs. The length...

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial configurations. The rich dynamical evolution exhibited by these nonlinear systems is explained surprisingly simple principles: minimization energy temperature maximization entropy high temperature. Our analytical results homogeneous case are corroborated numerical simulations confined in a wide variety conditions. These predictions compare qualitatively well with...

We study quantum systems on a discrete bounded lattice (lattice billiards). The statistical properties of their spectra show universal features related to the regular or chaotic character classical continuum counterparts. However, decay dynamics open appear very different from case, being dominated by states in band center. identify class ('lattice scars') that survive for infinite times dissipative and are degenerate at center band. provide analytical arguments existence any bipartite...

Abstract We study the null space degeneracy of open quantum systems with multiple non-abelian, strong symmetries. By decomposing Hilbert representation these symmetries into an irreducible involving direct sum multiple, commuting, invariant subspaces we derive a tight lower bound for stationary state degeneracy. apply results within context many-body systems, presenting three illustrative examples: fully-connected network, XXX Heisenberg model and Hubbard model. find that derived bound,...

In this work we compare the results of Gross-Pitaevskii and modified equations with ab initio variational Monte Carlo calculations for Bose-Einstein condensates atoms in axially symmetric traps. We examine both ground state excited states having a vortex line along $z$ axis at high values gas parameter demonstrate an excellent agreement between methods, states.

We study the dynamics of a trapped spin-1 condensate in magnetic field. First, we analyze homogeneous system, for which can be understood terms orbits phase space. analytically solve dynamical evolution populations various Zeeman components system. This result is then applied via local-density approximation to quasi-one-dimensional condensates. Our analysis system field shows that both mean-field and regimes are simultaneously realized, argue border between these two regions where spin...

Methods to manipulate the individual constituents of an ultracold quantum gas mixture are essential tools for a number applications, example direct simulation impurity physics. We investigate scheme in which species-selective control is achieved using magnetic potentials dressed with multiple radiofrequencies, exploiting different Land\'e g-factors constituent atomic species. describe two frequencies, where atoms confined harmonic controllable degree overlap between This then extended four...

We analyze the formation of ${\mathrm{Rb}}_{2}$ molecules with short photoassociation pulses applied to a cold $^{85}\mathrm{Rb}$ sample. A pump laser pulse couples continuum level ground electronic state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ bound levels in ${0}_{u}^{+}(5S+5{P}_{1∕2})$ and ${0}_{u}^{+}(5S+5{P}_{3∕2})$ vibrational series. The nonadiabatic coupling between two excited channels induces time-dependent beatings populations. propose take advantage these...

Abstract The non-equilibrium dynamics of quantum many-body systems is one the most fascinating problems in physics. Open questions range from how they relax to equilibrium extract useful work them. A critical point lies assessing whether a system has conserved quantities (or ‘charges’), as these can drastically influence its dynamics. Here we propose general protocol reveal existence charges based on set exact relations between out-of-equilibrium fluctuations and properties system. We apply...

The possibilities of pairing in two-dimensional boson-fermion mixtures are carefully analyzed. It is shown that the boson-induced attraction between two identical fermions dominates p-wave at low density. For a given fermion density, gap becomes maximal certain optimal boson concentration. conditions for observing current experiments discussed

We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine phase diagram of dipolar Bose-Hubbard model on a finite cylinder. consider several observables that are accessible typical optical lattice setups and assess how well these quantities perform as order parameters. find that, especially for small systems, occupation imbalance is less susceptible boundary effects than structure factor uncovering presence periodic modulation. By...

Spin-charge separation (SCS) is a striking manifestation of strong correlations in low-dimensional quantum systems, whereby fermion splits into separate spin and charge excitations that travel at different speeds. Here, we demonstrate periodic driving enables control over SCS Hubbard system near half filling. In one dimension, predict analytically an exotic regime where travels slower than can even become "frozen," agreement with numerical calculations. two dimensions, the slows both leads...

We study a two-level impurity coupled locally to quantum gas on an optical lattice. For state-dependent interactions between the and gas, we show that its evolution encodes information local excitation spectrum of at coupling site. Based this, design nondestructive method probe system's excitations in broad range energies by measuring state using standard atom optics methods. illustrate our findings with numerical simulations for lattice systems, including realistic dephasing noise probe,...

We show that finite lattices with arbitrary boundaries may support large degenerate subspaces, stemming from the underlying translational symmetry of lattice. When lattice is coupled to an environment, a potentially number these states remains weakly or perfectly uncoupled realizing new kind bound in continuum. These are strongly localized along particular directions lattice, which, limit strong coupling leads spatially subradiant states.