We report a model-independent measurement of the entropy, energy, and critical temperature of a degenerate, strongly interacting Fermi gas of atoms. The total energy is determined from the mean square cloud size in the strongly interacting regime, where the gas exhibits universal behavior. The entropy is measured by sweeping a bias magnetic field to adiabatically tune the gas from the strongly interacting regime to a weakly interacting regime, where the entropy is known from the cloud size after the sweep. The dependence of the entropy on the total energy quantitatively tests predictions of the finite-temperature thermodynamics.

We show that a molecular Bose-Einstein condensate in a trap is stabilized against stimulated dissociation if the trap size is smaller than the resonance healing length $({\hslash }^2/2mg\sqrt{n}{)}^{1/2}$. The condensate shape determines the critical atom-molecule coupling frequency. We discuss an experiment for triggering dissociation by a sudden change of coupling or trap parameters. This effect demonstrates one of the unique collective features of “superchemistry” in that the yield of a chemical reaction depends critically on the size and shape of the reaction vessel.

We quantify the resolution with which any probability distribution may be distinguished from a displaced copy of itself in terms of a characteristic width. This width, which we call the $ϵ$ resolution, is well defined for any normalizable probability distribution. We use this concept to study the broadcasting of classical probability distributions. Ideal classical broadcasting creates two (or more) output random variables each of which has the same distribution as the input random variable. We show that the universal broadcasting of probability distributions may be achieved with arbitrarily high fidelities for any finite $ϵ$ resolution. By restricting probability distributions to any finite $ϵ$ resolution we have therefore shown that the classical limit of quantum broadcasting is consistent with the actual classical case.

We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a five-dimensional quartic oscillator that exhibits a quantum phase transition between vibrational and rotational phases. For certain parameters, $10\times 10$ matrices give better results than obtained by diagonalizing $1000\times 1000$ matrices.

We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm ${}^{199}\mathrm{Hg}^{+}$ optical clock transition to the ground state hyperfine splitting in ${}^{133}\mathrm{Cs}$. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of $<5.8\times {10}^{-6}$ per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of $|\frac{\dot{\alpha }}{\alpha }|<1.3\times {10}^{-16}{\mathrm{yr}}^{-1}$, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and ${}^{171}\mathrm{Yb}^{+}$ vs other ${}^{133}\mathrm{Cs}$ standards yield a coupled constraint of $-1.5\times {10}^{-15}<\dot{\alpha }/\alpha <0.4\times {10}^{-15}{\mathrm{yr}}^{-1}$ and $-2.7\times {10}^{-15}<\frac{d}{dt}\ln \frac{{\mu }_{\mathrm{Cs}}}{{\mu }_B}<8.6\times {10}^{-15}{\mathrm{yr}}^{-1}$.

We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks—one at NIST and three in Europe—as the Sun’s gravitational potential at Earth’s surface varies due to Earth’s orbital eccentricity.

We establish a connection between the level density of a gas of noninteracting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution function for the number of excited particles follows the three universal distribution laws of extreme value statistics, namely, the Gumbel, Weibull, and Fréchet distributions. Implications of this result, as well as general properties of the level density at different energies, are discussed.

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution $W(t)$. Below $T_m$, $W(t)$ is associated with the continuum of scattering states of the repulsive Coulomb potential. At $T_m$, the Coulomb potential vanishes and $W(t)$ assumes a power-law tail with nontrivial dynamic exponents: the critical exponent of the entropy loss factor may cause a finite mean lifetime. Above $T_m$ (attractive potential), the long-time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Systems of coupled rate equations are ubiquitous in many areas of science, for example, in the description of electronic transport through quantum dots and molecules. They can be understood as a continuity equation expressing the conservation of probability. It is shown that this conservation law can be implemented by constructing a gauge theory akin to classical electrodynamics on the network of possible states described by the rate equations. The properties of this gauge theory are analyzed. It turns out that the network is maximally connected with respect to the electromagnetic fields even if the allowed transitions form a sparse network. It is found that the numbers of degrees of freedom of the electric and magnetic fields are equal. The results shed light on the structure of classical Abelian gauge theory beyond the particular motivation in terms of rate equations.

We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one-dimensional configurations. The ground state properties are determined with the local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the Fulde-Ferrell-Larkin-Ovchinnikov type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell are calculated as a function of the coupling strength.

Based on the integrable Gaudin model and local density approximation, we discuss the ground state of a one-dimensional trapped Fermi gas with imbalanced spin population, for an arbitrary attractive interaction. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an Fulde-Ferrell-Larkin-Ovchinnikov structure, and predict the resulting mode frequency as a function of the spin polarization.

A nuclear spin can act as a quantum switch that turns on or off ultracold collisions between atoms even when there is neither interaction between nuclear spins nor between the nuclear and electron spins. This “exchange blockade” is a new mechanism for implementing quantum logic gates that arises from the symmetry of composite identical particles, rather than direct coupling between qubits. We study the implementation of the entangling $\sqrt{\mathrm{SWAP}}$ gate based on this mechanism for a model system of two atoms, each with ground electronic configuration ${}^{1}S_0$, spin $1/2$ nuclei, and trapped in optical tweezers. We evaluate a proof-of-principle protocol based on adiabatic evolution of a one-dimensional double Gaussian well, calculating fidelities of operation as a function of interaction strength, gate time, and temperature.

The cluster states and Greenberger-Horne-Zeilinger (GHZ) states are two different types of multipartite quantum entangled states. We present the first experimental results generating continuous variable quadripartite cluster and GHZ entangled states of electromagnetic fields. Utilizing two amplitude-quadrature and two phase-quadrature squeezed states of light and linearly optical transformations, the two types of entangled states for amplitude and phase quadratures of light are experimentally produced. The combinations of the measured quadrature variances prove the full inseparability of the generated four subsystems. The presented experimental schemes show that the multipartite entanglement of continuous variables can be deterministically generated with the relatively simple implementation.

We study how the Hurst exponent $\alpha$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker’s position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer’s disease and other dementias.

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model—the toric code—which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of “magnetic” vortices, leading to confinement of the elementary “charge” excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and relate our results to error rates for topological quantum computations.

Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target’s topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges $a$ and $a^{\prime }$ in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with $a$ to give $a^{\prime }$.

We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of bosonic polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low-dimensional trapping geometries. As an illustration, we discuss the 2D superfluid-crystal quantum phase transition for polar molecules interacting via an electric-field-induced dipole-dipole potential.

The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of a quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from a gas to a solid phase when the density increases. In the gas phase, the condensate fraction is calculated as a function of the density. Using the Feynman approximation, the collective excitation branch is studied and the appearance of a roton minimum is observed. The results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindemann ratio at the transition point becomes $\gamma =0.230(6)$. The condensate fraction in the gas phase is estimated as a function of the density.

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.