We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks, or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.

We investigate a polarization- and frequency-selective feedback scheme to control the emission properties of multimode vertical-cavity surface-emitting lasers. A joint experimental and theoretical approach is used to study the modal and polarization dynamics of the system, with an emphasis on the role of anisotropies. Both experiments and theory reveal that selective feedback of a single transverse mode results in a drastic increase of the selected mode’s intensity. Furthermore, the influence of feeding back a single mode on the other transverse modes is discussed. Experimental measurements and numerical simulations also reveal that the emission and polarization dynamics can be considerably stabilized when this type of feedback is applied.

We extend the analysis of dense coding protocol based on displaced photon states. The phase transformations with a displaced qubit allow for someone to transform five states to each other. Each “particle-carrier” (displaced qubit) carries an equal number of photons. On the receiving side, it is possible to decode all five outcomes using a linear optical scheme with beam splitters and on-off photodetectors that cannot discriminate different number of detected photons. Summarizing, interacting with only a single displaced qubit, it is possible to transmit two bits of information more. Optimal conditions to guarantee maximal communication rate ${\log }_{2}5$ per “particle-carrier” (displaced qubit) and influence of decoherence on the communication rate are considered.

Laser-induced fluorescence (LIF) spectra $\left(4\right){}^1\Sigma ^{+}\to A{}^1\Sigma ^{+}–b{}^3\Pi$ and collisionally enhanced $A{}^1\Sigma ^{+}–b{}^3\Pi \to X{}^1\Sigma ^{+}$ LIF spectra measured by Fourier transform spectrometer with the resolution of $0.03–0.05{\mathrm{cm}}^{-1}$ provided about 1160 term values of the $e$-symmetry rovibronic levels of the fully mixed $A{}^1\Sigma ^{+}$ and $b{}^3\Pi$ states of a NaCs molecule. Direct deperturbation treatment of the experimental data field, covering rotational quantum numbers $J∊[5,151]$ of the $A\text{−}b$ complex in the energy region $E∊[10577,13668]{\mathrm{cm}}^{-1}$, was accomplished in the framework of the inverted channel-coupling approach by means of the $4\times 4$ Hamiltonian constructed on Hund’s coupling case $\left(a\right)$ basis functions. The nonequidistant spin-orbit splitting of the $b{}^3\Pi _{\Omega =0,1,2}$ substates and the indirect coupling $A{}^1\Sigma ^{+}–b{}^3\Pi _{\Omega =1}$ matrix element were introduced in the Hamiltonian phenomenologically to account for the regular perturbations by remote states manifold. The expanded Morse oscillator model was used to approximate both potential energy curves of the mutually perturbed states and spin-orbit coupling matrix elements as an analytical function of internuclear distance. Overall 31 fitting parameters have been required to reproduce 98% of experimental term values with a standard deviation of $0.006{\mathrm{cm}}^{-1}$, which is consistent with the uncertainty of the experiment. The term values deperturbation analysis was confirmed by a calculation of relative intensity distributions in the $A–b\to X$ LIF progressions. The predicted probabilities for both weakly and strongly perturbed levels agree with their experimental counterparts within the accuracy of measurements. The evaluated nonadiabatic $A\text{−}b$ wave functions were applied for a prediction of radiative lifetimes of the $A\text{−}b$ complex as well as transition probabilities of the $a\to A–b\to X$ cycle proposed in Stwalley, Eur. Phys. J. D 31, 221 (2004), for efficient transformation of ultracold molecules to their absolute ground level $v_X=0$; $J_X=0$.

Laser-induced electron recollisions are fundamental to many strong field phenomena in atoms and molecules. Using the recently developed quantitative rescattering theory, we demonstrate that the nonsequential double ionization (NSDI) of atoms by lasers can be obtained quantitatively in terms of inelastic collisions of the target ions with the free returning electrons where the latter are explicitly given by a spectrum-characterized wave packet. Using argon atoms as target, we calculated the NSDI yield including contributions from direct $(e,2e)$ electron-impact ionization and electron-impact excitation accompanied by subsequent field ionization. We further investigate the dependence of total NSDI on the carrier-envelope phase of few-cycle laser pulses, and showed that the effect can be experimentally observed by measuring the yield of doubly charged ions only.

In this paper we use a unidirectional decomposition capable of furnishing localized wave pulses, with luminal and superluminal peak velocities, in exact form and totally free of backward components, which have been a chronic problem for such wave solutions. This decomposition is powerful enough for yielding not only ideal nondiffracting pulses but also their finite energy versions still in exact analytical closed form, avoiding the need for time-consuming numerical simulations. Another advantage of the present approach is that, since the backward spectral components are absent, the frequency spectra of the pulses do not need to possess ultrawidebands, as it is required by the usual localized wave (LW) solutions obtained by other methods. Finally, the present results bring the LW theory nearer to the real experimental possibilities of usual laboratories.

We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap and its relation to the Uhlmann fidelity are interestingly illustrated by our approach.

Mutually unbiased bases encapsulate the concept of complementarity—the impossibility of simultaneous knowledge of certain observables—in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.

I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tripartite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tripartite Greenberger-Horne-Zeilinger (GHZ)-type and $W$-type entanglement and compare the evolution of their detection capabilities with the evolution of the negativity, bipartite concurrence, and tripartite negativity. Interestingly, I find a state in which there is no concurrence or tripartite negativity but there is entanglement. Finally, I utilize a three qubit quantum error correction code to address how ESD affects the abilities of quantum error correction.

Analytical calculations show that the mean motion of a quantum particle trapped by a rapidly oscillating potential can be significantly manipulated by inducing phase hops—i.e., by instantaneously changing the potential’s phase. A phase hop can be visualized as being the result of a collision with an imaginary particle which can be controlled. Several phase hops can have accumulating effects on the particle’s mean motion, even if they transform the particle’s Hamiltonian into its initial one. The theoretical predictions are verified by numerical simulations for the one-dimensional Paul trap.

An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted $\mathrm{O}+\mathrm{H}\to \mathrm{O}\mathrm{H}$ association reaction in an environment. The suggested approach is based on the application of the time-evolution operator to the “closed-system” part of the overall Hamiltonian and transformation of the open-system equation of motion to the Heisenberg picture suitable for numerical propagation. A dual role of the system-environment coupling with respect to the infrared (ir) laser-driven association of OH is demonstrated: the association probability is increased due to the coupling at relatively weak laser fields, but decreased at strong laser fields. Moreover, at a certain strength of the ir laser field, the association probability does not depend on the strength of the system-bath coupling at all.

We investigate the possible form of ideal intersections for two-dimensional rf trap networks suitable for quantum information processing with trapped ions. We show that the lowest order multipole component of the rf field that can contribute to an ideal intersection is a hexapole term uniquely determined by the tangents of the intersecting paths. The corresponding ponderomotive potential does not provide any confinement perpendicular to the paths if these intersect at right angles, indicating that ideal right-angle $\mathsf{X}$ intersections are impossible to achieve with hexapole fields. Based on this result, we propose an implementation of an ideal oblique-$\mathsf{X}$ intersection using a three-dimensional electrode structure.

Hard x-ray phase-contrast imaging provides high sensitivity to weakly absorbing low-$Z$ objects in medicine, biology, and materials science. Here, we describe a feasible method to obtain differential phase-contrast images directly with incoherent x-ray sources, avoiding the Talbot effect, which requires coherent x rays. This method was validated experimentally on material and biological samples, and the results prove that differential phase-contrast imaging can be realized under more relaxed conditions. It also demonstrates the feasibility of phase-contrast imaging with conventional x-ray tubes, and should benefit clinical diagnoses, biological examinations, and material inspections in the near future.

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific ${}^{40}\mathrm{Ca}^{+}+\mathrm{Na}$ system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge-exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of charge-neutral ultracold systems.

We combined adaptive closed-loop optimization, phase shaping with a restricted search space, and imaging to control dynamics and decipher the optimal pulse. The approach was applied to controlling the amplitude of the $\mathrm{C}{\mathrm{O}}_2$ bending vibration during strong-field Coulomb explosion. The search space was constrained by expressing the spectral phase as a Taylor series, which generated pulses with characteristics commensurate with the natural physical features of this problem. Optimal pulses were obtained that enhanced bending by up to 56% relative to what is observed with comparably intense, transform-limited pulses. We show that (1) this judicious choice of a reduced parameter set made unwrapping the dynamics more transparent and (2) the enhancement is consistent with field-induced structural changes to a bent excited state of $\mathrm{C}\mathrm{O}_2{}^{2+}$, which theoretical simulations have identified as the state from which the explosion originates.

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.

We consider, within the algebraic formalism, the time dependence of fidelity for qubits encoded in an open physical system. We relate the decay of fidelity to the evolution of correlation functions and, in the particular case of a Markovian dynamics, to the spectral gap of the generator of the semigroup. The results are applicable to the analysis of models of quantum memories.

Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of “Schrödinger cat” states.

By confining pairs of ions in a Penning trap, and alternating each ion between large and small cyclotron orbits, we have measured the cyclotron frequency ratios ${}^{12}\mathrm{CD}_3^{+}∕{}^{18}\mathrm{O}^{+}$, ${}^{12}\mathrm{C}_2\mathrm{D}_6^{+}∕{}^{18}\mathrm{O}_2^{+}$, ${}^{12}\mathrm{C}_3^{+}∕{}^{18}\mathrm{O}_2^{+}$, ${}^{13}\mathrm{CD}_3^{+}∕{}^{19}\mathrm{F}^{+}$, and ${}^{28}\mathrm{Si}\mathrm{H}_3^{+}∕{}^{12}\mathrm{C}{}^{19}\mathrm{F}^{+}$. Combined with other measurements for H, D, ${}^{13}\mathrm{C}$, and ${}^{28}\mathrm{Si}$, these ratios yield the atomic masses $M\left({}^{18}\mathrm{O}\right)=17.999$ 159 613 0(13) $\mathrm{u}$, and $M\left({}^{19}\mathrm{F}\right)=18.998$ 403 162 9(11) $\mathrm{u}$, which improve on previous values in the Atomic Mass Evaluation (AME2003) by factors of 500 and 60, respectively. Our value for $M\left({}^{18}\mathrm{O}\right)$ is lower than the AME2003 value by $1.4\left(7\right)\mu \mathrm{u}$.

The effects of strong magnetic fields $(B\sim {10}^4\mathrm{T})$ on charge exchange, excitation, and ionization processes in collisions of $\mathrm{H}\left(1s\right)$ atoms with fully stripped ions $A^{Z+}$ are studied by the classical trajectory Monte Carlo method in the energy range $25–2000\mathrm{keV}∕u$. The cases $\vec{B}\parallel \vec{v}$ and $\vec{B}\perp \vec{v}$, where $\vec{v}$ is the velocity vector of $A^{Z+}$ ion, are considered. It was found that in the considered energy range and for $B⩽5\times {10}^4\mathrm{T}$ and $Z=2,6$, the parallel magnetic field insignificantly affects the charge exchange cross section, but leads to an increase of excitation and ionization cross sections in the region below $100–200\mathrm{keV}∕u$ (up to a factor of 1.5–4 at $25\mathrm{keV}∕u$ for $Z=2$ and 6, respectively). The transverse magnetic field, however, causes a significant (up to a factor of 4) reduction of total charge exchange cross section in the entire energy range investigated and to a dramatic increase of excitation and ionization cross sections (up to one to two orders of magnitude for $Z=2$ and 6, respectively, at $E\sim 25\mathrm{keV}∕u$ and $B=5\times {10}^4\mathrm{T}$). The physics of magnetic field effects on considered processes is analyzed in terms of time evolution of interactions in the system, total electron energy, and electron trajectories. It was found that the major effects induced by the magnetic field are associated with the diamagnetic term in the interaction, continuum electron trapping in the projectile or target regions, and the Lorentz force. The energy distributions of captured and ionized electrons, as well as the momentum distributions of ionized electrons are also studied.