We describe a model for s-wave collisions between ground-state atoms in optical lattices, considering especially the limits of quasi-one- and two-dimensional axisymmetric harmonic confinement. When the atomic interactions are modeled by an s-wave Fermi pseudopotential, the relative motion energy eigenvalues can easily be obtained. The results show that except for a bound state, the trap eigenvalues are consistent with one- and two-dimensional scattering with renormalized scattering amplitudes. For absolute scattering lengths large compared with the tightest trap width, our model predicts a bound state of low energy and nearly-isotropic wave function extending on the order of the tightest trap width.

It is shown that the vector collision-sequence interference dip in the fundamental band of ${\mathrm{H}}_2$ fills in at densities, such that the mean free path becomes large compared with the wavelength. The same effect contributes an additional but unobservable narrowing to the interference dip in the pure translational spectra. The scalar interference lines observed in $\mathrm{HD}-X$ will undergo the same Doppler broadening and motional narrowing as their allowed counterparts, but this occurs at densities sufficiently low such that the interference contributions are small relative to the allowed lines.

We propose a scheme for producing entangled spin-squeezed states of an atomic ensemble inside an optical cavity by backaction of a detuned quantum-nondemolition (QND) measurement. By illuminating the atoms with bichromatic light, an interaction Hamiltonian of the cross-Kerr effect between the cavity and atoms is generated to implement QND measurements. The feedback effect is obtained through mixing the phase and amplitude quadratures of the cavity field, due to the detuning of the optical cavity. Therefore the continuous nondemolition measurements are fed back to correct the quantum state of the atomic sample such that unconditional spin squeezing is produced without requiring the use of any external electronics.

We determine the zero-temperature density profile of a cloud of fermionic atoms in a trap subject to a mutual attractive interaction, as the strength of the interaction is progressively increased. We find a significant decrease of the size of the atomic cloud as it evolves from the weak-coupling regime of overlapping Cooper pairs to the strong-coupling (Bose-Einstein) regime of nonoverlapping bound-fermion pairs. Most significantly, we find a pronounced increase of the value of the density at the center of the trap (even by an order of magnitude) when evolving between the two regimes. Our results are based on a generalized Thomas-Fermi approximation for the superfluid state, which covers continuously all coupling regimes.

The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.

We obtain the solution of a relativistic wave equation and compare it with the solution of the Schrödinger equation for a source with a sharp onset and excitation frequencies below cutoff. A scaling of position and time reduces to a single case all the (below cutoff) nonrelativistic solutions, but no such simplification holds for the relativistic equation, so that qualitatively different “shallow” and “deep” tunneling regimes may be identified relativistically. The nonrelativistic forerunner at a position beyond the penetration length of the asymptotic stationary wave does not tunnel; nevertheless, it arrives at the traversal (semiclassical or Büttiker-Landauer) time $\tau .$ The corresponding relativistic forerunner is more complex: it oscillates due to the interference between two saddle-point contributions and may be characterized by two times for the arrival of the maxima of lower and upper envelopes. There is in addition an earlier relativistic forerunner, right after the causal front, which does tunnel. Within the penetration length, tunneling is more robust for the precursors of the relativistic equation.

A requirement for many quantum computation schemes is the ability to measure single spins. This paper examines one proposed scheme: magnetic resonance force microscopy (MRFM), including the effects of thermal noise and back action from monitoring. We derive a simplified equation using the adiabatic approximation and produce a stochastic pure state unraveling which is useful for numerical simulations. We also calculate the signal-to-noise ratio for single-spin measurement by MRFM, using a quantum Langevin equation approach.

Using high-resolution photoelectron spectroscopy and 120-fs, 800-nm Ti:sapphire laser pulses, we observe and analyze intensity-dependent resonant population of specific intermediate excited states of neutral magnesium atoms and their subsequent photoionization in the laser field. Various participating states are identified using angular-momentum selection rules, partial yields, and angular distributions. Several unexpected results are observed and discussed, including peaks that do not correspond to expected resonant processes, and order-to-order variations in the photoelectron spectra.

We present a closed-form expression for the finite temperature first-order density matrix of an isotropic harmonically trapped ideal Fermi gas in any dimension. This constitutes a much sought after generalization of the recent results in the literature, where analytical expressions have been limited to quantities derived from the diagonal first-order density matrix. We compare our results with the Thomas-Fermi approximation (TFA) and demonstrate numerically that the TFA provides an excellent description of the first-order density matrix in the large-$N$ limit. As an interesting application, we derive a closed-form expression for the finite temperature Hartree-Fock exchange energy of a two-dimensional (2D) parabolically confined quantum dot. We numerically test this result against the 2D TF exchange functional, and comment on the applicability of the local-density approximation to the exchange energy of an inhomogeneous 2D Fermi gas.

The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of $\alpha ,$ the strength of the ohmic coupling to the environment, and $\varepsilon ,$ the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For $\varepsilon =0,$ the entanglement increases monotonically with $\alpha ,$ until it becomes maximal for $\overrightarrow{\alpha }{1}^{-}.$ For fixed $\varepsilon >0,$ the entanglement is a maximum as a function of $\alpha$ for a value, $\alpha ={\alpha }_M<1.\mathrm{}$

We propose a scheme for generating entangled states for two or more multilevel atoms in a thermal cavity. The photon-number-dependent parts in the effective Hamiltonian are canceled with the assistance of a strong classical field. Thus the scheme is insensitive to both the cavity decay and the thermal field. The scheme does not require individual addressing of the atoms in the cavity. The scheme can also be used to generate entangled states for many hot multilevel ions.

We have computed cross sections and asymmetry parameters for the C $1s$ photoionization of $\mathrm{C}{X}_4$ $(X=\mathrm{H},$ F, Cl) using the Schwinger variational method with Padé corrections. We present a comparative study that shows the influence of the identity of the X atom on the computed cross sections. Predicted cross sections are in good agreement with available photoionization and photoabsorption experimental data. We conclude that the presence of heavy outer atoms produces resonance structures in the photoionization cross sections and in the asymmetry parameters. We find a single nonvalence resonant state in the photoionization of ${\mathrm{CF}}_4$ and multiple resonances in ${\mathrm{CCl}}_4$ that have significant d-orbital character in the vicinity of the Cl atoms.

We prove that conical intersections are much more likely than local minima of the electronic energy gap. Therefore, if one encounters a very small electronic energy gap along a path through configuration space, it is much more likely to be associated with the neighborhood of a conical intersection than with an avoided intersection.

A recent approach to arrival times used the fluorescence of an atom entering a laser illuminated region, and the resulting arrival-time distribution was close to the axiomatic distribution of Kijowski, but not exactly equal, neither in limiting cases nor after compensation of reflection losses by normalization on the level of expectation values. In this paper we employ a normalization on the level of operators, recently proposed in a slightly different context. We show that in this case the axiomatic arrival-time distribution of Kijowski is recovered as a limiting case. In addition, it is shown that Allcock’s complex potential model is also a limit of the physically motivated fluorescence approach and connected to Kijowski’s distribution through operator normalization.

A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent-state semiclassical wave-packet method which avoids singularity issues arising in the usual Green’s function approach. We discuss the general conditions under which it is approximately correct to discuss quantum decoherence in terms of a “dephasing” picture and we derive semiclassical expressions for the phase and phase distribution. Remarkably, an effective system wavefunction emerges whose norm measures the decoherence and is equivalent to a density-matrix formulation.

We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the outcome of the tomography is consistent with unbiased noise in the channel. We study the incoherent eavesdropping attacks that are still permissible and establish under which conditions a secure cryptographic key can be generated. The whole analysis is carried out for channels that transmit quantum systems of any finite dimension.

The quantum key distribution (QKD) system with two-mode squeezed states has been demonstrated by Pereira et al. [Phys. Rev. A 62, 042311 (2000)]. They evaluate the security of the system based on the signal to noise ratio attained by a homodyne detector. In this paper, we discuss its security based on the error probability individually attacked by eavesdropper with the unambiguous or the error optimum detection. The influence of the energy loss at transmission channels is also taken into account. It will be shown that the QKD system is secure under these conditions.

Grover’s quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi 〉$ of n qubits. It is shown that the optimal time to perform the measurement is independent of $|\phi 〉,$ namely, it is identical to the optimal time in the original algorithm in which $|\phi 〉=|0〉,$ with the same number of marked states, r. The probability of success $P_{\mathrm{s}}$ is obtained in terms of the amplitudes of the state $|\phi 〉$ and is shown to be independent of r. A class of states, which includes fixed points and cycles of the Grover iteration operator, is identified. The relevance of these results in the context of using the success probability as an entanglement measure is discussed. In particular, the Groverian entanglement measure, previously limited to a single marked state, is generalized to the case of several marked states.

In high-$L$ Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-$L$ term, coming from the two electrons’ spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a ${}^2{S}_{1/2}$ state. However, observations in barium Rydberg states and recent observations in Rydberg states of ${\mathrm{Si}}^{2+}$ reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron’s radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, ${\mathrm{Si}}^{2+},$ and barium.

The isotope shifts of forbidden transitions in Be- and B-like argon ions are calculated. It is shown that only using the relativistic recoil operator can provide a proper evaluation of the mass isotope shift, which strongly dominates over the field isotope shift for the ions under consideration. Comparing the isotope shifts calculated with the current experimental uncertainties indicates very good perspectives for a first test of the relativistic theory of the recoil effect in middle-$Z$ ions.