An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.

The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ${\Gamma }^{-1}$ is relatively long, while the steady-state regime, formally such that $t⪢{\Gamma }^{-1}$, is appropriate for the evaluation of the forces and the dynamics for large $\Gamma$. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of ${\mathrm{Eu}}^{3+}$ that has a particularly small $\Gamma$. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.

Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity $\Delta \theta$ scaling with the total number of condensate particles $N$ as (i) the standard quantum limit $\Delta \theta \sim 1∕N^{1∕2}$, (ii) the sub shot-noise $\Delta \theta \sim 1∕N^{3∕4}$, and the (iii) the Heisenberg limit $\Delta \theta \sim 1∕N$. However, in a realistic dynamical BEC splitting, the $1∕N$ limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity $\Delta \theta \sim 1∕N^{3∕4}$ can be reached in a realistic experimental setting. We also show that the $1∕N^{3∕4}$ scaling is a rigorous upper bound in the limit $N\to \infty$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.

We investigate a nonaxisymmetric rotating Bose-Einstein condensate (BEC) in the limit of rotation frequency for which the BEC transforms into a quasi-one-dimensional system. We compute the vortex lattice wave function by minimizing the Gross-Pitaevskii energy functional in the lowest Landau level approximation for different confinement potentials. The condensate typically presents a changing number of vortex rows as a function of the interaction strength or rotation-confinement ratio. More specifically, the vortex lattices can be classified into two classes according to their symmetry with respect to the longitudinal axis. These two classes correspond to different local minima of the energy functional and evolve independently as a function of the various parameters.

The analytical expressions of the fractional parentage coefficients for the total spin states of a spinor $N$-boson system have been derived. Thereby an $S$-conserved theory for the spinor Bose-Einstein condensation has been proposed. A set of equations has been established to describe the first excited band of the condensates. Numerical solution for ${}^{23}\mathrm{Na}$ has been given as an example.

We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when the interparticle interaction increases over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the critical point due to quantum correlations. We also study the dynamical behavior of the instability by exploring the momentum distribution and the fringe visibility, which can be verified experimentally by releasing the trap.

We show that the stability of three-dimensional skyrmions in trapped Bose-Einstein condensates depends critically on scattering lengths, atom numbers, trap rotation, and trap anisotropy. In particular, for the ${}^{87}\mathrm{Rb}\mid F=1,m_f=-1⟩$, $\mid F=2,m_f=1⟩$ hyperfine states stability is sensitive to the scattering lengths at the 2% level, where the differences between them are crucial. In a cigar shaped trap, we find stable skyrmions with slightly more than $2\times {10}^6$ atoms, a number which scales with the inverse square root of the trap frequency. These can be stabilized against drift out of the trap by laser pinning.

We discuss collective monopole and quadrupole excitations of a collisionless gas of trapped Fermionic atoms in the superfluid BCS phase, comparing the fully microscopic Bogoliubov–de Gennes and quasiparticle random-phase approximation method with widely used semiclassical methods. In particular, the microscopic treatment allows us to address the questions of temperature dependence and nontrivial dependence on the trap parameters, which cannot be answered within the semiclassical approach. The main result concerning the temperature dependence is a strong Landau damping at intermediate temperature, which disappears in the limits of zero and critical temperature. However, even at zero temperature, considerable deviations from superfluid hydrodynamics are found if the trap frequency is of the same order of magnitude as the pairing gap.

We investigate the influence of ionization on the propagation and spectral effects of a few-cycle ultrashort laser pulse in a two-level medium. It is found that when the fractional ionization is weak, the production of higher spectral components makes no difference. However, when the two states are essentially depleted before the peak of the laser pulse, the impact of ionization on the higher spectral components is very significant.

Based on a two-mode boson model, we study nonclassical properties of the atom-molecule Bose-Einstein condensate. The effects of nonlinear collisions on the dynamics of the molecular formation is studied both in classical and quantum treatments. We find that the conversion from atoms to molecules can be suppressed strongly due to nonlinearity induced localization of the atomic population. In addition, we study statistical properties of the atom-molecule condensed system by calculating the intensity correlation functions numerically. We find that the effect of nonlinearity leads to the appearance of superchaotic molecular pulses, while maintaining the atomic field sub-Poissonian. The joint quantum statistical properties of the atoms and the molecules always show antibunching.

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to $4\mathrm{K}$, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.

We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results—which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains—are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic $XY$ model. For the $XX$ model, we provide the asymptotic scaling of $\sim (1∕6){\log }_2\left(L\right)$, and contrast it with the block entropy.

We demonstrate that even under positive-partial-transpose-preserving operations in an asymptotic setting Greenberger-Horne-Zeilinger (GHZ) and $W$ states are not reversibly interconvertible. We investigate the structure of minimal reversible entanglement generating set (MREGS) for tripartite states under positive-partial-transpose- (PPT-) preserving operations. We demonstrate that the set consisting of $W$ and Einstein-Podolsky-Rosen (EPR) states alone cannot be an MREGS. In this context we prove the surprising result that the relative entropy of entanglement can be strictly subadditive for certain pure tripartite states which is crucial to keep open the possibility that the set of GHZ state and EPR states together constitute an MREGS under PPT-preserving operations.

We showed through experiments that the magnetochiral index is polarization invariant and reported its wavelength dependence. These properties were investigated with limonene and using a specially-designed ${\mathrm{Ar}}^{+}$-ring active interferometer. A Fresnel drag-type optical bias inside the discharge tube, combined with two calibrations and the circumvention of systematic errors, allowed us to reach a detection level in the range of ${10}^{-12}$ when measuring the change in the magnetochiral index of intracavity liquid samples. Our results are in agreement with the different predictions made for magnetochiral refraction.

We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modeled as a coupled discrete nonlinear Schrödinger (DNLS) equation. The excitation spectrum and the modulational instability condition of the total system are presented analytically. In the long-wavelength limit, our results agree with the homogeneous two-component Bose-Einstein condensates case. The discreteness effects result in the appearance of the modulational instability for the condensates in miscible region. The numerical calculations confirm our analytical results and show that the interspecies coupling can transfer the instability from one component to another.

An array of planar Penning traps, holding single electrons, can realize an artificial molecule suitable for NMR-like quantum-information processing. The effective spin-spin coupling is accomplished by applying a magnetic field gradient, combined to the Coulomb interaction acting between the charged particles. The system lends itself to scalability, since the same substrate can easily accommodate an arbitrary number of traps. Moreover, the coupling strength is tunable and under experimental control. Our theoretical predictions take into account a realistic setting, within the reach of current technology.

An algorithm is proposed which transfers the quantum information of a wave function (analog signal) into a register of qubits (digital signal) such that $n$ qubits describe the amplitudes and phases of $2^n$ points of a sufficiently smooth wave function. We assume that the continuous degree of freedom couples to one or more qubits of a quantum register via a Jaynes-Cummings Hamiltonian and that we have universal quantum computation capabilities on the register as well as the possibility to perform bang-bang control on the qubits. The transfer of information is mainly based on the application of the quantum phase estimation algorithm in both directions. Here, the running time increases exponentially with the number of qubits. We pose it as an open question which interactions would allow polynomial running time. One example would be interactions which enable squeezing operations.

We study a diatomic homonuclear molecule incident upon a potential barrier in three dimensions. We study various initial states for the molecule and allow transitions between rotational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also find that the probability of transmission can be enhanced by the addition of a second potential barrier. These results are in qualitative agreement with those found for the tunneling of a molecule in a one-dimensional model studied previously.

Synchronized chaotic dynamics are investigated theoretically and experimentally in a system of unidirectionally-coupled semiconductor lasers subject to delayed, polarization-rotated optical feedback and injection. Experimental data in the time and frequency domains demonstrate chaos synchronization with a lag between transmitter and receiver equal to the injection time, also known as driving synchronization. The natural polarization mode of the transmitter is shown to synchronize most efficiently to the orthogonal state of the receiver which is being injected. A full two-polarization model is used for both lasers, and is in good agreement with polarization-resolved experimental measurements.