The critical temperature $T_c$ of an interacting Bose gas trapped in a general power-law potential $V\left(\mathbf{x}\right)={\sum }_i{U}_i{\mid x_i\mid }^{p_i}$ is calculated with the help of variational perturbation theory. It is shown that the interaction-induced shift in $T_c$ fulfills the relation $(T_c-T_c^0)∕T_c^0=D_1\left(\eta \right)\widehat{a}+D^{\prime }\left(\eta \right){\widehat{a}}^{2\eta }+\mathcal{O}\left({\widehat{a}}^2\right)$ with $T_c^0$ the critical temperature of the trapped ideal gas, $\widehat{a}$ the $s$-wave scattering length divided by the thermal wavelength at $T_c$, and $\eta =1∕2+{\sum }_i{p}_i^{-1}$ the potential-shape parameter. The terms $D_1\left(\eta \right)\widehat{a}$ and $D^{\prime }\left(\eta \right){\widehat{a}}^{2\eta }$ describe the leading-order perturbative and nonperturbative contributions to the critical temperature, respectively. This result quantitatively shows how an increasingly inhomogeneous potential suppresses the influence of critical fluctuations. The appearance of the ${\widehat{a}}^{2\eta }$ contribution is qualitatively explained in terms of the Ginzburg criterion.

Using resonant interaction between atoms and the field in a high-quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasiprobability distributions and demonstrate the nonclassicality of the superposition in terms of the zeros of the $Q$ function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by [Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.

We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations), any state chosen from the set of two-colorable graph states (Calderbank-Shor-Steane codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.

The monopole and quadrupole oscillations of a Bose-Einstein condensate (BEC) gas trapped in a spherically symmetric potential are calculated using the time-dependent Hartree approximation which enables us to use an orthonormal single-particle basis for the description of both the condensate and noncondensate components. It is found that the monopole mode has a much smaller damping rate than the quadrupole mode. The obtained temperature dependence of the frequency shifts and the damping rates of the collective oscillations are found to be consistent with experimental data obtained for BEC gases in anisotropic trapping potentials. A comparison between the time-dependent Hartree approximation and the time-dependent Hartree-Fock approximation is also made and it is found that there is a rather small difference.

A $d$-mode system is considered and the concepts of mode-position operator and mode-momentum operator are introduced. Their eigenvalues are integers in $Z_d$ and the mode phase space is $Z_d\times Z_d$. The exponentials of these operators are displacement operators in the mode phase space and they form a Heisenberg-Weyl group. The displacement operators perform a cyclic permutation of a state among the $d$ modes; and they also change its mode momentum (i.e., the rate with which this cyclic permutation takes place). In the case of entangled states the mode displacement operators permute the entanglement among the $d$ observers; and they also change the momentum with which the entanglement propagates.

We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalization of previous results for two- and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited-state population. Specifically, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential nondestructive optical measurement schemes.

Quantum remote rotation allows us to implement local quantum operation on remote systems with shared entanglement. Here we report an experimental demonstration of remote rotation on single photons using linear optical elements. The local dephase is also teleported during the process. The scheme can be generalized to any controlled rotation commuting with ${\sigma }_z$.

The spontaneous emission rate of an atom in a dielectric system with a single interface is calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The spontaneous emission rate is shown to exhibit a damping oscillation as the atomic distance from the interface is varied. The calculated frequency of the oscillation matches very well with the prediction from closed-orbit theory. This study provides a different perspective on the spontaneous emission of atoms in the presence of environments.

We show that the two-photon temporal (longitudinal) correlation of light is limited by its classical optical spectral width. We present examples of the sources of two-photon light approaching this limit.

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a “skyrmion” and a “meron-pair,” respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.

We have demonstrated the Talbot-Lau effect for atomic de Broglie waves in the time domain. This effect is based on Fresnel diffraction of matter waves from an incoherent source. In the experiment, de Broglie waves of atoms in a particular internal state have been manipulated and the resulting density directly imaged by resonant optical fields. These experiments allow us to probe the quantum dynamics of the atomic center of mass. We have also used this effect to create patterns in the density of the atoms with period as small as $1∕10$ of the optical wavelength, demonstrating the potential application of this technique for atom nanofabrication.

We propose a scheme to directly measure the Wigner function for the motion of a trapped ion. Unlike the previous scheme [Phys. Rev. Lett. 78, 2547 (1997)], the present scheme works in the intermediate-excitation regime, which may be of experimental importance in view of decoherence. The scheme can also be used to perform a quantum nondemolition measurement of the vibrational energy and prepare motional Schrödinger cat states.

We present a comprehensive study, using both analytical and numerical methods, of measurement-induced localization of relational degrees of freedom. Looking first at the interference of two optical modes, we find that the localization of the relative phase can be as good for mixed states—in particular, for two initially Poissonian or thermal states—as for the well-known case of two Fock states. In a realistic setup the localization for mixed states is robust and experimentally accessible, and we discuss applications to superselection rules. For an ideal setup we show how a relational Schrödinger cat state emerges and investigate circumstances under which such a state is destroyed. In our second example we consider the localization of relative atomic phase between two Bose Einstein condensates, looking particularly at the build up of spatial interference patterns, an area which has attracted much attention since the work of Javanainen and Yoo. We show that the relative phase localizes much faster than was intimated in previous studies focusing on the emerging interference pattern itself. Finally, we explore the localization of relative spatial parameters discussed in recent work by Rau, Dunningham, and Burnett. We retain their models of indistinguishable scattering but make different assumptions. In particular we consider the case of a real distant observer monitoring light scattering off two particles, who records events only from a narrow field of view. The localization is only partial regardless of the number of observations. This paper contributes to the wider debate on relationism in quantum mechanics, which treats fundamental concepts—reference frames and conservation laws—from a fully quantum and operational perspective.

We exploit the process of asymmetry amplification by stimulated emission which provides an original method for parity violation (PV) measurements in a highly forbidden atomic transition. The method involves measurements of a chiral, transient, optical gain of a cesium vapor on the $7S\text{−}6P_{3∕2}$ transition, probed after it is excited by an intense, linearly polarized, collinear laser, tuned to resonance for one hyperfine line of the forbidden $6S\text{−}7S$ transition in a longitudinal electric field. We report here a 3.5-fold increase of the one-second-measurement sensitivity and subsequent reduction by a factor of 3.5 of the statistical accuracy compared with our previous result [J. Guéna et al., Phys. Rev. Lett. 90, 143001 (2003)]. Decisive improvements to the setup include an increased repetition rate, better extinction of the probe beam at the end of the probe pulse, and, for the first time to our knowledge, the following: a polarization-tilt magnifier, quasisuppression of beam reflections at the cell windows, and a Cs cell with electrically conductive windows. We also present real-time tests of systematic effects and consistency checks on the data, as well as a 1% accurate measurement of the electric field seen by the atoms, from atomic signals. PV measurements performed in seven different vapor cells agree within the statistical error. Our present result is compatible with the more precise result of Wood et al. within our present relative statistical accuracy of 2.6%, corresponding to a $2\times {10}^{-13}$ atomic-unit uncertainty in $E_1^{\mathit{pv}}$. Theoretical motivations for further measurements are emphasized and we give a brief overview of a recent proposal that would allow the uncertainty to be reduced to the 0.1% level by creating conditions where asymmetry amplification is much greater.

We study the influence of a continuous measurement in a composite quantum system C on the evolution of the states of its parts. It is shown that the character of the evolution (decoherence or recoherence) depends on the type of measured quantity and on the initial state of the system. A number of conditions under which the states of the subsystems of C decohere during the measuring process are established. We propose a model of the composite system and specify the observable the measurement of which may result in the recoherence of the state of one of the subsystems of C. In the framework of this model we find the optimal regime for the exchange of information between the parts of C during the measurement. The main characteristics of such a process are computed. We propose a scheme of detection of the recoherence under the measurement in a concrete physical experiment.

To show the feasibility of a long-distance partial Bell-state measurement, a Hong-Ou-Mandel experiment with coherent photons is reported. Pairs of degenerate photons at telecommunication wavelength are created by parametric down-conversion in a periodically poled lithium niobate waveguide. The photon pairs are separated in a beam splitter and transmitted via two fibers of $25\mathrm{km}$. The wave packets are relatively delayed and recombined on a second beam splitter, forming a large Mach-Zehnder interferometer. Coincidence counts between the photons at the two output modes are registered. The main challenge consists in the trade-off between low count rates due to narrow filtering and length fluctuations of the $25\text{−}\mathrm{km}$-long arms during the measurement. For balanced paths a Hong-Ou-Mandel dip with a net visibility of 47.3% is observed, which is close to the maximal theoretical value of 50% developed here. This proves the practicability of a long-distance Bell-state measurement with two independent sources, as, e.g., required in an entanglement swapping configuration in the scale of tens of kilometers.

Symmetric and nonsymmetric muonic three-body systems have been predicted to form in collisions between muonic atoms and hydrogen molecules. The hyperspherical adiabatic expansion is a representation for the investigation of muonic three-body bound states. In this research we have used hyperspherical “surface” functions for muonic helium hydride ions (isotopes of helium-tritium-muon molecules). Through this approach, the binding energy and lowest eigenpotentials for the muonic molecular ions are calculated in an extreme adiabatic approximation. The obtained results are close to the calculations of others.

Photodetached $d$-electron angular distributions have been measured for the processes ${\mathrm{V}}^{-}{\left(3d^{4}4s^2\right)}^{5}D+h\nu \to \mathrm{V}{\left(3d^{3}4s^2\right)}^{4}F+e^{-}$, ${\mathrm{V}}^{-}{\left(3d^{4}4s^2\right)}^{5}D+h\nu \to \mathrm{V}{\left(3d^{3}4s^2\right)}^{4}P+e^{-}$, and at discrete wavelengths in the region 457.9–647.1 nm using the laser photoelectron spectroscopy technique. Photoelectron yields were obtained by measuring the laboratory frame energy spectra of photodetached electrons as a function of the angle between the velocity vector of the outgoing photoelectrons and the polarization direction of the linearly polarized photon beam. A nonlinear curve-fitting routine was used to extract the value of the asymmetry parameter for a particular transition at fixed photon energies. Asymmetry parameters are also reported for photodetached $s$ electrons in the transitions ${\mathrm{V}}^{-}{\left(3d^{4}4s^2\right)}^{5}D+h\nu \to \mathrm{V}{\left(3d^{4}4s\right)}^{6}D+e^{-}$ and ${\mathrm{V}}^{-}{\left(3d^{4}4s^2\right)}^{5}D+h\nu \to \mathrm{V}{\left(3d^{4}4s\right)}^{4}D+e^{-}$ at four photon energies.