With radio-frequency fields one can control ultracold atoms in magnetic traps. These fields couple the atomic spin states, and are used in evaporative cooling that can lead to Bose-Einstein condensation in the atom cloud. Also, they can be used in controlled release of the condensate from the trap, thus providing output couplers for atom lasers. In this paper we show that the time-dependent multistate models for these processes have exact solutions that are polynomials of the solutions of the corresponding two-state models. This allows simple, in many cases analytic, descriptions for the time-dependent control of the magnetically trapped ultracold atoms.

We have measured the emission spectrum of two-level-like Ba atoms driven by a continuous-wave bichromatic field containing a strong resonant component and a weaker component detuned from atomic resonance by the strong-field Rabi frequency. With the specified detuning, the weak field resonantly drives a transition of the atom–strong-field dressed states. Observed spectra show that each peak of the normal (single-driving-field) resonance fluorescence triplet is split into three subpeaks separated by one-half the weak-field Rabi frequency. Also seen is another triplet of peaks displaced from the atomic resonance by twice the strong-field Rabi frequency. Splitting of the normal triplet peaks can be explained through weak-field dressing of the strong-field dressed states. The origin of the additional triplet is less transparent. Comparison with theory is made.

We report a measurement of the ion recoil energy in photoionization of laser-cooled atoms. ${}^{87}\mathrm{Rb},$ cooled in a magneto-optical trap, is two-photon ionized by a pulsed laser. The recoil energy is determined by time-of-flight in a weak electric field. A resolution in the range of 1 μeV is demonstrated. Refinement of the technique promises resolution in the range of several neV to be feasible.

Using information from a recent ${}^{85}$Rb two-color photoassociation experiment, we evaluate the merits of fountain clocks based on ${}^{87}$Rb and ${}^{85}$Rb isotopes as alternatives to ${}^{133}$Cs and find that they offer significant advantages. In the case of ${}^{87}$Rb the collisionally induced fractional frequency shift is 15 times smaller than for ${}^{133}$Cs. This small shift is associated with a small difference in the triplet and singlet scattering lengths for ${}^{87}$Rb. For ${}^{85}$Rb, the shift produced by the two $m_f=0\mathrm{}$ clock states may have opposite signs allowing the shift to be eliminated by controlling the relative populations of these states. We also present collision quantities relevant to atomic fountain clocks containing multiply launched groups of atoms, and for evaporative cooling of ${}^{85}$Rb atoms.

An explanation of discrepancies between predictions of the Kroll-Watson theory and cross sections measured in the Wallbank-Holmes experiments on electron-atom scattering in the presence of a powerful low-frequency laser field is presented. Our model calculations for helium and argon as target atoms come out to be in good agreement with experimental results; i.e., obtained cross sections are by many orders of magnitude larger than those predicted by the Kroll-Watson theory. A mechanism responsible for such a substantial increase of the calculated cross sections is found to be due to the diffraction scattering of electrons by atomic obstacles.

In terms of analytical results, we demonstrate that, within most parts in parameter space for a two-level magnetic system, suppression of quantum coherence can be induced by the circularly polarized fields. Low-frequency driving yields a dynamical localization opposite to the case of intermediate-to-high-frequency driving. The intrinsic relation between coherent suppression and the dressed-state level-crossing resonance is revealed.

In a nonlinear optical system with single-mirror feedback, several experiments displayed stationary hexagonal patterns. A linear stability analysis, however, predicts drifting patterns even for an arbitrarily small misalignment of the mirror. Studying the situation of small tilt angles we observe that the patterns remain stationary up to a critical value ${\alpha }_{\mathrm{c}}$ of the angle (locking). Above this threshold they discontinuously start to drift with a velocity that depends linearly on the tilt angle. Both features are reproduced by numerical simulations with a Gaussian input beam. The existence of the locking region is traced back to the boundary conditions imposed by the spatially limited input beam.

A Maxwell’s demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell’s demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally realizable models of quantum Maxwell’s demons, explicates their thermodynamics, and shows how the information produced by quantum measurement and by decoherence acts as a source of thermodynamic inefficiency.

The decoherence effect, which may be held responsible for the vanishing of macroscopic quantum interferences, has only been exhibited in special models though it is presumed to be universal (at least when there is a possibility of dissipation). A more general model encompassing the already known ones is proposed in the present work. A master equation for the reduced density operator is established by means of two different methods. A direct method, which is given first, is simple but too specific. A second method relies on the projection method in the theory of irreversible processes. It is in principle very general and not confined to a special model. It shows that decoherence is a typical irreversible process from a theoretical standpoint. The master equation is worked out in detail when there exist convenient, so-called microstable collective observables (for which a criterion is given), selecting a preferred basis in which diagonalization occurs. For macroscopic mechanics, this basis is given by the position coordinates in three-dimensional space of relatively small parts in an object. Previously proposed models, including the quantum diffusion model, are found to be special cases of the present theory.

A critical analysis of the problem of causality in the energy transfer between a pair of atoms is carried out. One of the pair, the source, is initially excited and the other, the detector, is in its ground state. The probabilities are calculated for the detector to be excited at a later time $t$ under different experimental conditions. In the first, a precise specification is made of the state of the source and that of the radiation field at the observation time $t.\mathrm{}$ In the second, the final state of the field is unspecified, whereas in the third, the state of neither the field nor the source is specified at time $t.\mathrm{}$ These three cases correspond to predicting the outcomes of different experimental measurements. It is shown that of the three cases, only the third exhibits exact causal behavior. The other two are noncausal. The noncausal contributions to the probability arise from the correlation of vacuum fluctuations at the two atoms at different times in the interval 0 to $t.\mathrm{}$ The probabilities for these cases can be significant for times slightly less than $R/c,$ where $R$ is the interatomic separation. Explicit expressions, correct to fourth order in the transition moments, for the probabilities in the three cases are given. A proof of strict causality to all orders is presented for the third case where the final measurement is solely made on the detector. In Appendix A the related problem of the time dependence of the electric energy density associated with the source is analyzed and shown to be causal.

It is shown by use of Milne’s nonlinear transform of a one-dimensional Schrödinger eigenproblem that the wave function bears the classical statistical information of the density of time spent by the system at any point of the configuration space, as already suggested by White [Phys. Rev. 37, 1416 (1931)].

Kinematical and dynamical aspects of the noncyclic geometric phase for coherent states are analyzed. It is shown for Glauber and SU(2) coherent states that the geometric phase obeys a geodesic closure rule associated with the coset space of the respective Lie group. In the former case the geodesic is a straight line in phase space, while in the latter the geodesic is a great circle on the Bloch sphere $\left({\mathcal{S}}^2\right).\mathrm{}$ An alternative expression for the geometric phase is derived from the time-dependent variational principle by making a specific choice of gauge. The noncyclic geometric phase is numerically calculated in a time-dependent variational treatment of the $E\otimes \varepsilon$ Jahn-Teller model first introduced by Longuet-Higgins and co-workers. The electronic and nuclear degrees of freedom are parametrized by SU(2) and Glauber coherent states respectively. In particular, the adiabatic limit is studied and shown to yield the anticipated Berry geometric phase.

A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a spatial point.

A field-dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing. It is pointed out that weak and strong potential curve crossing interactions are interchanged under this transformation, thus realizing a naive strong and weak duality. A reliable perturbation theory should thus be formulated in limits of both weak and strong interactions. In fact, the main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well described by simple (time-independent) perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double-well potential is generally suppressed by the effect of a potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.

We present a network consisting of quantum gates that produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network.

Results of a search for parity nonconservation (PNC) in a pair of nearly degenerate opposite-parity states in atomic dysprosium are reported. The sensitivity to PNC mixing is enhanced in this system by the small energy separation between these levels, which can be crossed by applying an external magnetic field. The metastable odd-parity sublevel of the nearly crossed pair is first populated. A rapidly oscillating electric field is applied to mix this level with its even-parity partner. By observing time-resolved quantum beats between these sublevels, we look for interference between the Stark-induced mixing and the much smaller PNC mixing. To guard against possible systematic effects, reversals of the signs of the electric field, the magnetic field, and the decrossing of the sublevels are employed. We report a value of $|H_w|=|2.3\pm 2.9$ (statistical)±0.7(systematic)| Hz for the magnitude of the weak-interaction matrix element. A detailed discussion is given of the apparatus, data analysis, and systematic effects.

A special kind of unitary transformation capable of changing the degrees of freedom of a quantum system, a super quantum coordinate transformation, is introduced. Two such transformations in the Hilbert space of a two-mode boson are investigated in detail. Under one transformation, this two-mode bosonic Hilbert space is transformed to a Hilbert space of a two-mode boson plus a single-mode fermion; under the other transformation, it is transformed to a Hilbert space of a single-mode boson. Their applications to phase operators and the phase difference operator are discussed.

We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the “Kholevo capacity”) when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.

We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell’s analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.

A local realistic theory of single neutral kaons and of correlated neutral kaon pairs is formulated by deducing the most general consequences of three assumptions: (i) the Einstein-Podolsky-Rosen (EPR) reality criterion, (ii) locality, and (iii) no retroactive causality. Variables must be introduced for every kaon determining the stable $\mathrm{CP}$ value and the variable value of strangeness $S.\mathrm{}$ Instantaneous $S$ jumps are shown to take place. If kaon pairs are produced in Φ meson decays, the local realistic probability of observing ${\overline{K}}^0{\overline{K}}^0$ pairs at certain different proper times necessarily differs by 30% from the quantum-mechanical predictions. The size of this difference justifies our systematic neglect of $\mathrm{CP}$ violation. A Φ factory is thus shown to provide a unique tool for the study of the EPR problem