A simple solution is given to the tunneling time problem from the viewpoint of interfering alternatives. Using Gell-Mann and Hartle's decoherence functional for real time Feynman histories, it is shown that (i) the probability distribution of tunneling times cannot be defined for “resident time” type but (ii) the range of values of the time is definable. The range turns out to be so broad for opaque barriers that a unique tunneling time cannot be considered even in a loose sense.

A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only features known before an experiment is performed are the probabilities for various events to occur. The sum of the individual measures of information for mutually complementary observations is invariant under the choice of the particular set of complementary observations and conserved if there is no information exchange with an environment. That operational quantum information invariant results in $k$ bits of information for a system consisting of $k$ qubits.

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$.

Using a spontaneous-down-conversion photon source, we produce true nonmaximally entangled states, i.e., without the need for postselection. The degree and phase of entanglement are readily tunable, and are characterized both by a standard analysis using coincidence minima, and by quantum state tomography of the two-photon state. Using the latter, we experimentally reconstruct the reduced density matrix for the polarization. Finally, we use these states to measure the Hardy fraction, obtaining a result that is $122\sigma$ from any local-realistic result.

We calculate the QED effect of the renormalization of the bare potential for the tunneling of a charged particle due to the interaction with its own radiation field (an analog of the Lamb shift for tunneling). It is demonstrated that radiative corrections increase the tunneling probability.

We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\Delta t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\Delta t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute $0$ to the path integral, while all other configurations contribute $1$. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

A Comment on the Letter by Mohideen, U. Anushree, Roy, Phys. Rev. Lett. 81, 4549 (1998).

A Reply to the Comment by S. K. Lamoreaux.

We report on a novel, practical method of determining the nonrelativistic wave function of a decaying quantum system at all positions and times. The system consists of a particle which is initially confined around the origin and leaks out tunneling through a potential barrier. We show that the wave function $\psi (r,t)$ of the particle can be expressed as a linear combination of Moshinsky functions, each of which is associated with a pole of the scattering $\mathbf{S}$ matrix of the system. The $\psi (r,t)$ so obtained is normalizable. In the light of this approach we reexamine the Gamow wave function, which is not normalizable. We elucidate the source of this difficulty.

The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a “Bell test of local realism.” However, it has been suggested that this is incorrect due to the $50\%$ postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.

Stimulated small-angle light scattering was used to measure the structure factor of a Bose-Einstein condensate in the phonon regime. The excitation strength for phonons was found to be significantly reduced from that of free particles, revealing the presence of correlated pair excitations and quantum depletion in the condensate. The Bragg resonance line strength and line shift agreed with predictions for the homogeneous Bose gas using a local density approximation.

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions $x_n$ that obeys the spacing law $x_n\sim Q(1+p{)}^n$. The dependence of the parameters $p$ and $Q$ on the initial concentration of the reagents is determined and we find that the functional form of $p$ is in agreement with the experimentally observed Matalon-Packter law.

We present a Monte Carlo calculation for up to $N\sim 20000$ bosons in 3D to determine the shift of the transition temperature due to small interactions $a$. We generate independent configurations of the ideal gas. At finite $N$, the superfluid density changes by a certain correlation function in the limit $a\to 0$; the $N\to \infty$ limit is taken afterwards. We argue that our result is independent of the order of limits. Detailed knowledge of the noninteracting system for finite $N$ allows us to avoid finite-size scaling assumptions.

In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density.

The low energy quantal spectrum is considered as a function of the total angular momentum for a system of weakly interacting bosonic atoms held together by an external isotropic harmonic potential. It is found that besides the usual condensation into the lowest state of the oscillator the system exhibits two additional kinds of condensate and associated thermodynamic phase transitions. These new phenomena are derived from the degrees of freedom of “partition space” which describe the multitude of different ways in which the angular momentum can be distributed among the atoms while remaining all the time in the lowest state of the oscillator.

In the context of the decoherent histories approach to quantum theory, it is shown that a class of macroscopic configurations consisting of histories of local densities (number, momentum, energy) exhibits negligible interference. This follows from the close connection of the local densities with the corresponding exactly conserved (and so exactly decoherent) quantities, and also from the observation that the eigenstates of local densities (averaged over a sufficiently large volume) remain approximate eigenstates under time evolution. The result is relevant to the derivation of hydrodynamic equations using the decoherent histories approach.

We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allow a unified description of all three phenomena. We also elucidate Lorentz transformations which allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose two experimental schemes for measuring the He-McKellar-Wilkens phase.

We present an experiment for testing quantum state reduction. The state reduction rule is tested using optical homodyne tomography by directly measuring the fidelity between the theoretically expected reduced state and the experimental state.

Quantum delay time tomography data obtained from the intensity of a Gaussian wave packet are used to approximately construct the 3D scattering potential of the time dependent Schrödinger's equation by a least action tomography algorithm which decouples into multiple 2D x-ray tomography algorithms when the mean energy of the wave packet is sufficiently high. We obtain two “miracle” identities for the characterization of admissible quantum delay time tomography data. The first is related to Newton's miracle identity. The second is a new curved miracle identity.