The nonlocal exchange of the conserved, gauge invariant quantity $e^{\frac{i}{\hslash }(p_k-\frac{e}{c}{A}_k)L^k}$, $L^k=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$, $k=1,2$ between the charged particle and the magnetic flux line (in the $k=3$ direction) is responsible for the Aharonov-Bohm effect. This exchange occurs at a definite time, before the wave packets are brought together to interfere, and can be verified experimentally.

We show that, contrary to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors—the customary paradigm of observable. Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that, when a nonorthogonal repeatable measurement is performed, the measured system retains some “memory” of the number of times that the measurement has been performed.

Physical and computer experiments involving systems describable by piecewise smooth continuous maps that are nondifferentiable on some surface in phase space exhibit novel types of bifurcations in which an attracting fixed point exists before and after the bifurcation. The striking feature of these bifurcations is that they typically lead to “unbounded behavior” of orbits as a system parameter is slowly varied through its bifurcation value. This new type of border-collision bifurcation is fundamental and robust. A method that prevents such “dangerous border-collision bifurcations” is given. These bifurcations may be found in a variety of experiments including circuits.

A rotated and harmonically trapped Bose gas with attractive interactions is expected to either remain stationary or escape from the trap. Here we report that, on the contrary, in an anharmonic trapping potential the Bose gas with attractive interactions responds to external rotation very differently, namely, through center-of-mass motion or by formation of vortices.

We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates and agree over a wide range of parameters with a recent numerical treatment of the sphere and plate with Dirichlet boundary conditions. Our approach improves upon the proximity force approximation. It can be generalized easily to other geometries, other boundary conditions, to the computation of Casimir energy densities, and to many other situations.

We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov–de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.

The combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson’s bound, $2\sqrt{2}$. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell’s inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.

We implemented the experiment proposed by Cabello in the preceding Letter to test the bounds of quantum correlation. As expected from the theory we found that, for certain choices of local observables, Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality ($2\sqrt{2}$) is not reached by any quantum states.

A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms’ velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10 000.

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [P. Engels et al., Phys. Rev. Lett. 90, 170405 (2003)]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.

It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept.

For physical systems described by smooth, finite-range, and confining microscopic interaction potentials $V$ with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space ${\Sigma }_v=\{(q_1,\dots ,q_N)\in {\mathbb{R}}^N|V(q_1,\dots ,q_N)=v\}$, $v\in \mathbb{R}$, change topology at some $v_c$ in a given interval $[v_0,v_1]$ of values $v$ of $V$, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature $\mathbf{(}\beta (v_0),\beta (v_1)\mathbf{)}$ also in the $N\to \infty$ limit. Thus, the occurrence of a phase transition at some ${\beta }_c=\beta (v_c)$ is necessarily the consequence of the loss of diffeomorphicity among the $\{{\Sigma }_v{\}}_{v<v_c}$ and the $\{{\Sigma }_v{\}}_{v>v_c}$, which is the consequence of the existence of critical points of $V$ on ${\Sigma }_{v=v_c}$, that is, points where $\nabla V=0$.

We investigate the stability of magnetically trapped atomic Bose-Einstein condensates and thermal clouds near the transition temperature at small distances $0.5\mu \mathrm{m}\le d\le 10\mu \mathrm{m}$ from a microfabricated silicon chip. For a $2\mu \mathrm{m}$ thick copper film, the trap lifetime is limited by Johnson noise induced currents and falls below 1 s at a distance of $4\mu \mathrm{m}$. A dielectric surface does not adversely affect the sample until the attractive Casimir-Polder potential significantly reduces the trap depth.

A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by $13\mu \mathrm{m}$ for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.

We experimentally analyze the behavior of a non-Markovian bistable system with noise, using a vertical cavity surface emitting laser with time-delayed optoelectronic feedback. The effects of the delayed feedback are observed in the probability distribution of the residence times of the two orthogonal polarization states, and in the polarization-resolved power spectrum. They agree well with recent theoretical predictions based on a two-state model with transition rates depending on an earlier state of the system. We also observe experimentally and explain theoretically that the residence time probability distribution deviates from exponential decay for residence times close to (and smaller than) the delay time.

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables $M$ describing the system are the (empirical) particle density $f=\{f(\underline{x},\underline{v})\}$ and the total energy $E$. We find that $S(f_t,E)$ is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of $S(M_t)=S(M_{X_t})$ should hold generally for “typical” (the overwhelming majority of) initial microstates (phase points) $X_0$ belonging to the initial macrostate $M_0$, satisfying $M_{X_0}=M_0$. This is a consequence of Liouville’s theorem when $M_t$ evolves according to an autonomous deterministic law.

We study the rotation of a ${}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensate confined in a quadratic plus quartic potential. This trap configuration allows one to increase the rotation frequency of the gas above the trap frequency. In such a fast rotation regime we observe a dramatic change in the appearance of the quantum gas. The vortices which were easily detectable for a slower rotation become much less visible, and their surface density is well below the value expected for this rotation frequency domain. We discuss some possible tracks to account for this effect.

A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.

Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a $d$-dimensional quantum system onto a $(d+1)$-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from the MF predictions.