Molecules are created from a Bose-Einstein condensate of atomic ${}^{87}\mathrm{R}\mathrm{b}$ using a Feshbach resonance. A Stern-Gerlach field is applied, in order to spatially separate the molecules from the remaining atoms. For detection, the molecules are converted back into atoms, again using the Feshbach resonance. The measured position of the molecules yields their magnetic moment. This quantity strongly depends on the magnetic field, thus revealing an avoided crossing of two bound states at a field value slightly below the Feshbach resonance. This avoided crossing is exploited to trap the molecules in one dimension.

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality—local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multiparticle topological nonlocal effects which have no quantum analog.

We calculate the geometric phase of a spin-$1/2$ system driven by one and two mode quantum fields subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. We discuss the implications of our results from both fundamental as well as quantum computational perspectives.

We show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schrödinger equation for both $T=0$ and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For $T=0$, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essential.

The activation problem is investigated in two-dimensional nonequilibrium systems. A numerical approach based on dynamic importance sampling (DIMS) is introduced. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. The escape path is observed to be shifted compared to a heteroclinic trajectory calculated in the limit of zero-noise intensity. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology (“Loschmidt echo”), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time $t_r$ for maximum return probability is in general shorter. We find that $t_r$ depends on $\lambda ={\epsilon }_{\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{l}}/{\epsilon }_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{p}}$, being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin. It is tested for various models, in particular, the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.

We propose a new micromechanical approach to probe bending rigidity at molecular scale. Long flexible filaments made of magnetic colloids and linkers are shown to adopt under magnetic field a hairpin configuration. Measuring the hairpin curvature as a function of the field intensity and the linker length from diffracted light allows us to deduce the linker bending rigidity $\kappa$. The technique is presented for two types of linkers: a spontaneously adsorbing polymer and a grafted biomolecular.

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level, the system undergoes ordering transitions and demonstrates multistability. That is, for a strong enough positive feedback it exhibits a nonzero stationary mean-field ,and a variety of stable oscillatory mean-field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level; i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate.

We directly measured mechanical thermal fluctuations in mirrors over three decades of frequency range using a short-length Fabry-Perot interferometer. This is the first such measurement at wide off-resonant frequency band that is much lower than mechanical resonant frequencies. Theoretically, the mechanical fluctuation in mirrors had been thought to become the principal noise in precise interferometry, such as in gravitational wave detection. We identified the thermally induced noises in the interferometer, the so-called substrate Brownian noise, substrate thermoelastic noise, and coating Brownian noise.

Masses of the short-lived radionuclides ${}^{32}\mathrm{A}\mathrm{r}$ ($T_{1/2}=98\mathrm{m}\mathrm{s}$) and ${}^{33}\mathrm{A}\mathrm{r}$ ($T_{1/2}=173\mathrm{m}\mathrm{s}$) have been determined with the Penning trap mass spectrometer ISOLTRAP. Relative uncertainties of $6.0\times {10}^{-8}$ ($\delta m=1.8\mathrm{k}\mathrm{e}\mathrm{V}$) and $1.4\times {10}^{-8}$ ($\delta m=0.44\mathrm{k}\mathrm{e}\mathrm{V}$), respectively, have been achieved. At present, these new mass data serve as the most stringent test of the quadratic form of the isobaric-multiplet mass equation. Furthermore, the improved accuracy for the mass of ${}^{32}\mathrm{A}\mathrm{r}$ will allow for a better constraint on scalar contributions to the weak interaction. New mass values have also been measured for ${}^{44}\mathrm{A}\mathrm{r}$ and ${}^{45}\mathrm{A}\mathrm{r}$, and a $20\sigma$ deviation for ${}^{44}\mathrm{A}\mathrm{r}$ from the literature value was found and interpreted.

A general relation between the group delay and the dwell time is derived for quantum tunneling. It is shown that the group delay is equal to the dwell time plus a self-interference delay. The Hartman effect in quantum tunneling is explained on the basis of saturation of the integrated probability density (or number of particles) under the barrier.

We demonstrate that matter-wave solitary pulses formed from Bose condensed atoms moving inside optical lattices continuously radiate dispersive matter waves with prescribed momentum. Our analytical results for the radiation parameters and the soliton decay rate are found to be in excellent agreement with numerical modeling performed for experimentally relevant parameters.

We have experimentally demonstrated the absence of spectroscopic resonance shifts in a mixture of two interacting Fermi gases. This result is linked to observations in an ultracold gas of thermal bosons. There, the measured resonance shift due to interstate collisions is independent of the coherence in the system, and twice that expected from the equilibrium energy splitting between the two internal states in a fully decohered cloud. We give a simple theoretical explanation of these observations, which elucidates the effect of coherent radiation on an incoherent mixture of atoms.

The shot-noise detection limit in current high-precision magnetometry [I. Kominis, T. Kornack, J. Allred, and M. Romalis, Nature (London) 422, 596 (2003)] is a manifestation of quantum fluctuations that scale as $1/\sqrt{N}$ in an ensemble of $N$ atoms. Here, we develop a procedure that combines continuous measurement and quantum Kalman filtering [V. Belavkin, Rep. Math. Phys. 43, 405 (1999)] to surpass this conventional limit by exploiting conditional spin squeezing to achieve $1/N$ field sensitivity. Our analysis demonstrates the importance of optimal estimation for high bandwidth precision magnetometry at the Heisenberg limit and also identifies an approximate estimator based on linear regression.

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be $({\omega }_B/{\omega }_D{)}^2\simeq 3.1$, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure $({\omega }_B/{\omega }_D{)}^2\simeq 4$. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

We present numerical results from a second-order quantum field theory of Bose-Einstein condensates applied to the 1997 JILA experiment [D. S. Jin et al., Phys. Rev. Lett. 78, 764 (1997)]. Good agreement is found for the energies and decay rates for both the lowest-energy $m=2$ and $m=0$ modes. The anomalous behavior of the $m=0$ mode is due to experimental perturbation of the noncondensate. The theory is gapless and includes the coupled dynamics of the condensate and thermal cloud, the anomalous pair average, and all relevant finite size effects.

We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic ${}^6\mathrm{L}\mathrm{i}$ atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into ${}^6\mathrm{L}\mathrm{i}_2$ molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.

We demonstrate an atom laser using all-optical techniques. A Bose-Einstein condensate of rubidium atoms is created by direct evaporative cooling in a quasistatic dipole trap realized with a single, tightly focused ${\mathrm{C}\mathrm{O}}_2$-laser beam. An applied magnetic field gradient allows the formation of the condensate in a field-insensitive $m_F=0$ spin projection only, which suppresses fluctuations of the chemical potential from stray magnetic fields. A collimated and monoenergetic beam of atoms is extracted from the Bose-Einstein condensate by continuously lowering the dipole trapping potential in a controlled way to form a novel type of atom laser.

We study the role of dynamical constraints in the general problem of finding the best statistical strategy for random searching when the targets can be detected only in the limited vicinity of the searcher. We find that the optimal search strategy depends strongly on the delay time $\tau$ during which a previously visited site becomes unavailable. We also find that the optimal search strategy is always described for large step lengths $\ell$ by a power-law distribution $P(\ell )\sim {\ell }^{-\mu }$, with $1<\mu (\tau )\le 2$. Our findings appear to remain valid even if arbitrary energy costs of locomotion are considered.