We observe violation of a Bell inequality between the quantum states of two remote ${\mathrm{Yb}}^{+}$ ions separated by a distance of about 1 m with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint detection of two emitted photons, whose polarization is entangled with each ion. The entanglement of remote qubits is also characterized by full quantum state tomography.

We present a scheme for the extraction of singlet states of two remote particles of arbitrary quantum spin number. The goal is achieved through post-selection of the state of interaction mediators sent in succession. A small number of iterations is sufficient to make the scheme effective. We propose two suitable experimental setups where the protocol can be implemented.

We report a limit on the fractional temporal variation of the proton-to-electron mass ratio as $\frac{1}{(m_P/m_e)}\frac{\partial }{\partial t}(m_P/m_e)=(-3.8\pm 5.6)\times {10}^{-14}{\mathrm{yr}}^{-1}$, obtained by comparing the frequency of a rovibrational transition in ${\mathrm{SF}}_6$ with the fundamental hyperfine transition in Cs. The ${\mathrm{SF}}_6$ transition was accessed using a ${\mathrm{CO}}_2$ laser to interrogate spatial 2-photon Ramsey fringes. The atomic transition was accessed using a primary standard controlled with a Cs fountain. This result is direct and model-free.

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy $E_F$, with a preferred value of ($0.45\pm 0.05$) $E_F$. The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.

We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.

We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable phase. Based on a microscopic description of interacting boson-fermion mixtures we derive an effective action for the critical droplet and obtain an asymptotic expression for the nucleation rate in the vicinity of the phase transition and near the spinodal instability of the mixed phase. We also discuss effects of dissipation which play a dominant role close to the transition point, and identify the regimes where quantum nucleation can be experimentally observed in cold-atom systems.

We load cold atoms into an optical lattice dramatically reshaped by radio-frequency coupling of state-dependent lattice potentials. This radio-frequency dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice potential. Radio-frequency dressing has previously been performed at length scales from mm to tens of $\mu \mathrm{m}$, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we measure as a function of lattice depth and dressing amplitude. We also investigate the dressing by measuring changes in the momentum distribution of the dressed states.

Mixtures of bosonic and fermionic atoms in optical lattices provide a promising arena to study strongly correlated systems. In experiments realizing such mixtures in the quantum-degenerate regime the temperature is a key parameter. We investigate the intrinsic heating and cooling effects due to an entropy-preserving raising of the optical lattice, identify the generic behavior valid for a wide range of parameters, and discuss it quantitatively for the recent experiments with ${}^{87}\mathrm{Rb}$ and ${}^{40}\mathrm{K}$ atoms. In the absence of a lattice, we treat the bosons in the Hartree-Fock-Bogoliubov-Popov approximation, including the fermions in a self-consistent mean-field interaction. In the presence of the full three-dimensional lattice, we use a strong coupling expansion. We find the temperature of the mixture in the lattice to be always higher than for the pure bosonic case, shedding light onto a key point in the analysis of recent experiments.

A novel measure, quantumness of correlations ${\mathcal{Q}}_{AB}$ is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in special cases and it vanishes for separable states—a feature not captured by the measures proposed earlier. It is found that an optimal generalized measurement on one of the parts leaves the overall state in its closest separable form, which shares the same marginal for the other part, implying that ${\mathcal{Q}}_{AB}$ is nonzero for all entangled bipartite states and it serves as an upper bound to the relative entropy of entanglement.

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)].

A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and $N$-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.

We present novel Fourier Monte Carlo simulations of a compressible ${\varphi }^4$-model on a simple-cubic lattice with linear-quadratic coupling of order parameter and strain, focusing on the detection of fluctuation-induced first-order transitions and deviations from standard critical behavior. The former is indeed observed in the constant stress ensemble and for auxetic systems at constant strain, while for regular isotropic systems at constant strain, we find strong evidence for Fisher-renormalized critical behavior and are led to predict the existence of a tricritical point.

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modeling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to $N={10}^5$ particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter $n{a}^3\lesssim {10}^{-4}$. This value is different from the estimate $n{a}^3\lesssim {10}^{-6}$ for the validity of the asymptotic expansion in the limit of vanishing $n{a}^3$. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice $|\psi {|}^4$ model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

We experimentally demonstrate multiple rounds of heat-bath algorithmic cooling in a 3 qubit solid-state nuclear magnetic resonance quantum information processor. By pumping entropy into a heat bath, we are able to surpass the closed system limit of the Shannon bound and purify a single qubit to 1.69 times the heat-bath polarization. The algorithm combines both high fidelity coherent control and a deliberate interaction with the environment. Given this level of quantum control in systems with larger reset polarizations, nearly pure qubits should be achievable.

Even in nonequilibrium systems, the mechanism of rare reactive events caused by small random noise is predictable because they occur with high probability via their maximum likelihood path (MLP). Here a geometric characterization of the MLP is given as the curve minimizing a certain functional under suitable constraints. A general purpose algorithm is also proposed to compute the MLP. This algorithm is applied to predict the pathway of transition in a bistable stochastic reaction-diffusion equation in the presence of a shear flow, and to analyze how the shear intensity influences the mechanism and rate of the transition.

The ${}^{1}S_0$-${}^{3}P_0$ clock transition frequency ${\nu }_{\mathrm{Sr}}$ in neutral ${}^{87}\mathrm{Sr}$ has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the $1\times {10}^{-15}$ level makes ${\nu }_{\mathrm{Sr}}$ the best agreed-upon optical atomic frequency. We combine periodic variations in the ${}^{87}\mathrm{Sr}$ clock frequency with ${}^{199}\mathrm{Hg}^{+}$ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant $\alpha$, electron-proton mass ratio $\mu$, and light quark mass. Furthermore, after ${}^{199}\mathrm{Hg}^{+}$, ${}^{171}\mathrm{Yb}^{+}$, and H, we add ${}^{87}\mathrm{Sr}$ as the fourth optical atomic clock species to enhance constraints on yearly drifts of $\alpha$ and $\mu$.

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.

We study one-dimensional Bose liquids of interacting ultracold atoms in the $Y$-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single $Y$ junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring-interferometer-type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast with the Aharonov-Bohm effect of a single particle in the same geometry.