Ultracold sodium molecules were produced from an atomic Bose-Einstein condensate by ramping an applied magnetic field across a Feshbach resonance. More than ${10}^5$ molecules were generated with a conversion efficiency of $\sim 4\%$. Using laser light resonant with an atomic transition, the remaining atoms could be selectively removed, preventing fast collisional relaxation of the molecules. Time-of-flight analysis of the pure molecular sample yielded an instantaneous phase-space density greater than 20.

Decoherence causes entropy increase that can be quantified using, e.g., the purity $\varsigma =\mathrm{T}\mathrm{r}{\rho }^2$. When the Hamiltonian of a quantum system is perturbed, its sensitivity to such perturbation can be measured by the Loschmidt echo $M(t)$. It is given by the squared overlap between the perturbed and unperturbed state. We describe the relation between the temporal behavior of $\varsigma (t)$ and the average $\overline{M}(t)$. In this way we show that the decay of the Loschmidt echo can be analyzed using tools developed in the study of decoherence. In particular, for systems with a classically chaotic Hamiltonian the decay of $\varsigma$ and $\overline{M}$ has a regime where it is dominated by the Lyapunov exponents.

We theoretically examine the creation of a Fermi-degenerate gas of molecules by considering a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of a degenerate gas atoms into a macroscopic number of diatomic molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and a rapid adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.

A widely accepted definition of “quantum chaos” is “the behavior of a quantum system whose classical limit is chaotic.” The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical counterparts. A fundamental reason for that is the linearity of Schrödinger equation. In this paper, we study the quantum dynamics of an ultracold quantum degenerate gas in a tilted optical lattice and show that it displays features very close to classical chaos. We show that its phase space is organized according to the Kolmogorov-Arnold-Moser theorem.

An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the correlation function (its coherent and incoherent parts), the signal-to-noise ratio (SNR), and the stochastic resonance (SR) gain are obtained. Within a suitably chosen range of parameter values this reduced description yields anomalous SR gains exceeding unity and, simultaneously, gives rise to a nonmonotonic behavior of the SNR vs the noise strength. The analytical results agree well with those obtained from numerical solutions of the Langevin equation.

We show that it is possible to have hysteretic behavior for magnets that does not form simple closed loops in steady state, but cycles multiple times before returning to its initial state. We show this by studying the low temperature dynamics of the 3D Edwards-Anderson spin glass. The specific multiple varies from system to system and is often quite large and increases with system size. The last result suggests that the magnetization could be aperiodic in the large system limit for some realizations of randomness. It should be possible to observe this phenomenon experimentally.

A new exact representation of the quantum propagator is derived in terms of semiclassical initial value representations. The resulting expression may be expanded in a series, of which the leading order term is the semiclassical one. Motion of a Gaussian wave packet on a symmetric double well potential is used to demonstrate numerical convergence of the series and the ability to compute each element in the series using Monte Carlo methods.

We show that in a dilute fermionic superfluid, when the fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in fermionic superfluids possible.

An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in ${}^7\mathrm{L}\mathrm{i}^{+}$ ions at $v=0.064c$ have been measured in the forward and backward direction to an accuracy of $\Delta \nu /\nu =1\times {10}^{-9}$ using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of $2.2\times {10}^{-7}$ for deviations from the time dilation factor ${\gamma }_{\mathrm{S}\mathrm{R}}=(1-v^2/c^2{)}^{-1/2}$.

We show that photoassociation of fermionic atoms into bosonic molecules inside an optical lattice can be described using a Jaynes-Cummings Hamiltonian with a nonlinear detuning. Using this equivalence to the Jaynes-Cummings dynamics, we show how one can construct a micromaser for the molecular field in each lattice site.

We show how the length scale hierarchy, resulting from different interaction strengths in an optically trapped spin-1 ${}^{23}\mathrm{N}\mathrm{a}$ Bose-Einstein condensate, can lead to intriguing core deformations in singular topological defects. In particular, a point defect can be unstable with respect to the formation of a stable half-quantum vortex ring (an “Alice ring”), providing a realistic scheme to use dissipation as a sophisticated state engineering tool. We compute the threshold for stability of the point monopole, which is beyond the current experimental regime.

A noise-induced phase transition to excitability is reported in oscillatory media with FitzHugh-Nagumo dynamics. This transition takes place via a noise-induced stabilization of a deterministically unstable fixed point of the local dynamics, while the overall phase-space structure of the system is maintained. Spatial coupling is required to prevent oscillations through suppression of fluctuations (via clustering in the case of local coupling). Thus, the joint action of coupling and noise leads to a different type of phase transition and results in a stabilization of the system. The resulting regime is shown to display characteristic traits of excitable media, such as stochastic resonance and wave propagation. This effect thus allows the transmission of signals through an otherwise globally oscillating medium.

In this work, we give a description of the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Rob’s frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in noninertial frames.

The Wigner-Araki-Yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity, and the notion of Wigner-Yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity. We demonstrate that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation. A quantum Cramér-Rao inequality and a new uncertainty relation in terms of the skew information are established, which shed considerable new light on the relationships between quantum measurement and statistical inference. The result is applied to estimating the evolution speed of quantum states.

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.

We show that weak measurements with postselection, proposed in the context of the quantum theory of measurement, naturally appear in the everyday physics of fiber optics telecom networks through polarization-mode dispersion (PMD) and polarization-dependent losses (PDL). Specifically, the PMD leads to a time-resolved discrimination of polarization; the postselection is done in the most natural way: one postselects those photons that have not been lost because of the PDL. The quantum formalism is shown to simplify the calculation of optical networks in the telecom limit of weak PMD.

We describe the generalization of Wilson’s numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, $J(\omega )\propto {\omega }^s$. We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents $0<s<1$; the line terminates in the well-known Kosterlitz-Thouless transition at $s=1$. Contact is made with results from perturbative renormalization group, and various other applications are outlined.

We have produced a quantum degenerate ${}^6\mathrm{L}\mathrm{i}$ Fermi gas with up to $7\times {10}^7$ atoms, an improvement by a factor of 50 over all previous experiments with degenerate Fermi gases. This was achieved by sympathetic cooling with bosonic ${}^{23}\mathrm{N}\mathrm{a}$ in the $F=2$, upper hyperfine ground state. We have also achieved Bose-Einstein condensation of $F=2$ sodium atoms by direct evaporation.

We apply the Yang-Lee theory of phase transitions to an urn model for the separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical calculations show that in the thermodynamic limit the zeros of the effective partition function are located on the unit circle in the complex $z$ plane. In the complex plane of the actual control parameter, certain roots converge to the transition point of the model. Thus, the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.

We derive the exact dynamics of a random walker with arbitrary non-Markovian transport and reaction rate distribution at a boundary, and present exact solutions in the continuum limit. We find that the ultimate escape probability of the particle is independent of the transport mechanism in contradiction to the long-standing belief based on the conventional approach. We also find a phase transition in the relaxation kinetics associated with the heterogeneity of the transport media.