We investigate the phase transition of interacting Bose gases in general power-law traps in the thermodynamic limit. Using energy-shell renormalization and the $\epsilon$ expansion, we evaluate the partition function for the uncondensed gas phase within a renormalization-group framework. This approach allows a unified description of homogeneous as well as inhomogeneous and anisotropic systems. Results for the critical temperature are compared to mean-field theory as well as to a local-density approximation based on renormalization-group theory for the homogeneous Bose gas. This comparison indicates the consistency of our approach. We also make suggestions for an optimized trap design in experiments that measure the transition temperature.

A magnetically trapped ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate is used as a sensitive probe of short-range electrical forces. In particular, the electric polarization of, and the subsequent electric field generated by, ${}^{87}\mathrm{Rb}$ adsorbates on conducting and insulating surfaces is measured by characterizing perturbations to the magnetic trapping potential using high quality factor condensate excitations. The nature of the alterations to the electrical properties of $\mathrm{Rb}$ adsorbates is studied on titanium (metal) and silicon (semiconductor) surfaces, which exhibit nearly identical properties, and on glass (insulator), which displays a smaller transitory electrical effect. The limits of this technique in detecting electrical fields and ramifications for measurements of short-range forces near surfaces are discussed.

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

A pairwise correlation function in relative momentum space is discussed as a tool to characterize the properties of an incoherent source of noninteracting Abelian anyons. This is analogous to the Hanbury-Brown Twiss effect for particles with fractional statistics in two dimensions. In particular, using a flux tube model for anyons, the effects of source shape and quantum statistics on a two-particle correlation function are examined. Such a tool may prove useful in the context of quantum computing and other experimental applications where studying anyon sources are of interest.

An ultrashort weak pulse that propagates resonantly on the $\mid a⟩\to \mid b⟩$ transition of a three-level system $(\mid a⟩,\mid b⟩,\mid c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\mid b⟩\to \mid c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.

It has been proposed that photon-exchange effects associated with virtual atomic absorption could have widespread application in quantum information processing. Here we investigate simpler exchange effects associated with real absorption as modeled by an equivalent linear optical filter. Using nonclassical pairs of photons with variable time separation, we observe a maximum suppression of pair transmission by at least 5% with respect to the result for independent photons.

Complete electromagnetically induced transparency (EIT) in sodium vapor is demonstrated experimentally by means of excitation with a broadband multimode dye laser tuned on the $D_1$ line. One hundred percent transparency is observed by excitation of the Na vapor with circularly polarized laser light. The linear polarization excitation produces, instead, complete destruction of the EIT resonance. For laser power density in the $0.1\text{to}1\mathrm{W}∕{\mathrm{cm}}^2$ range, the linewidth of the EIT resonance remains in the interval of $90–400\mathrm{kHz}$. This complete transparency of the medium in a narrow frequency interval is interesting for many applications where the enhancement of the refractive index is important and where the improvement of the signal-to-noise ratio of the dark resonances allows a more sensitive measurement of weak magnetic fields.

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional “photon fluid” confined in a Fabry-Pérot resonator. With the atoms modeled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the “bare” strength of the anharmonic term. The resulting expression for the nonlinear Kerr susceptibility is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analyzed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that minimizes the probability of an inconclusive result. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.

Differential cross sections for elastic electron scattering in argon have been measured in the angular range of backward scattering from 130° to 180° at incident electron energies of 5, 7.5, and $10\mathrm{eV}$. In these measurements the magnetic angle-changing technique with a newly developed conical solenoid system has been employed. The differential cross sections measured in the above scattering angle range together with the cross sections of Gibson et al. [J. Phys. B 29, 3177 (1996)] have been integrated to obtain integral elastic and momentum transfer cross sections. Detailed comparison is presented of the differential and integral cross sections obtained with the results of various theoretical calculations. The results indicate that, in general, the theoretical cross sections at the above electron energies are overestimated at the larger scattering angles.

Electron transfer in the presence of a laser field is explored for the prototype collision system ${\mathrm{He}}^{2+}\text{−}\mathrm{H}\left(1s\right)$ on the basis of a quantum-mechanical calculation. At collision energies $E_P⩾2\mathrm{keV}∕\mathrm{amu}$ the capture probabilities are found to be conisderably enhanced or suppressed depending on the exact synchronization of the time-dependent projectile and laser interactions. At lower collision energies the total capture cross section is strongly enhanced irrespective of the relative phase between both fields. This enhancement should be directly observable in future experiments.

We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of Anderson et al. [Phys. Rev. Lett. 90, 023001 (2003)] shows that it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display “system specific” features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival probability are found for a small shift of the potential. Next, a “semiclassical” expression for the averaged echo signal is presented and used to calculate the echo signal for atoms in a light sheet wedge billiard. Revivals in the echo coherence are found in this system, indicating that they may be a generic feature of dipole traps.

We present a detailed description of the formation of bright solitary waves in optical lattices. To this end, we have considered a ring lattice geometry with large radius. In this case, the ring shape does not have a relevant effect in the local dynamics of the condensate, while offering a realistic setup to implement experiments with conditions usually not available with linear lattices (in particular, to study collisions). Our numerical results suggest that the condensate radiation is the relevant dissipative process in the relaxation towards a self-trapped solution. We show that the source of dissipation can be attributed to the presence of higher-order dispersion terms in the effective mass approach. In addition, we demonstrate that the stability of the solitary solutions is linked with particular values of the width of the wave packet in reciprocal space. Our study suggests that these critical widths for stability depend on the geometry of the energy band, but are independent of the condensate parameters (momentum, atom number, etc.). Finally, the nonsolitonic nature of the solitary waves is evidenced showing their instability under collisions.

The interrelationship between the non-Markovian stochastic Schrödinger equations and the corresponding non-Markovian master equations is investigated in the finite-temperature regimes. We show that the general finite-temperature non-Markovian trajectories can be used to derive the corresponding non-Markovian master equations. A simple, yet important solvable example is the well-known damped harmonic oscillator model in which a harmonic oscillator is coupled to a finite-temperature reservoir in the rotating-wave approximation. The exact convolutionless master equation for the damped harmonic oscillator is obtained by averaging the quantum trajectories, relying upon no assumption of coupling strength or time scale. The master equation derived in this way automatically preserves the positivity, Hermiticity, and unity.

The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker’s map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.

Final-state probabilities are determined for the hydrogen atom which forms after the electron-positron pair annihilation in the positronium hydride PsH $\left(p^{+}{e}^{-}{e}^{+}{e}^{-}\right)$. It is shown that for the hydrogen atom the probability to be found in its ground state is $\approx 98.41\%$, while analogous probabilities for the excited $2s$, $2p$, and $3s$ states are $\approx 1.09\%$, $\approx 0.28\%$, and $\approx 0.13\%$, respectively. This means that the final hydrogen atom forms mainly in its ground $1s$ state.

The efficiency of recently proposed single-photon emitting sources based on tunable planar band-gap structures is examined. The analysis is based on the study of the total and “radiative” decay rates and the expectation value of the emitted radiation energy and its collimating cone. It is shown that the scheme operating in the frequency range near the defect resonance of a defect band-gap structure is more efficient than the one operating near the band edge of a perfect band-gap structure.

We give a fully analytical description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any intial state and we show that the atom-field steady state is, at most, classically correlated. For a chosen initial state, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. A result pertinent to quantum information is the quantification of concurrence during the dissipative dynamics. An analytical expression for the time evolution of the concurrence is given.

${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ ions with an energy of $25\mathrm{keV}$ are scattered under a grazing angle of incidence from a clean and flat $\mathrm{Cu}\left(001\right)$ surface. For specific azimuthal orientations of the crystal surface with respect to low index directions in the surface plane we observe the ion induced emission of electrons with a conventional $\mathrm{LEED}$ (low energy electron diffraction) setup. By operating the instrument in an energy dispersive mode we find intensity distributions of emitted electrons which can unequivocally be ascribed to diffraction effects at the target surface.