Rydberg-Rydberg collisions in a cold, dense Rydberg gas can lead to the conversion of internal energy into center-of-mass energy of the colliding atoms, resulting in Rydberg-atom velocities much larger than the initial velocities in the gas. We prepare cold Rydberg-atom gases by laser excitation of laser-cooled atom clouds and use time-of-flight measurements to demonstrate the production of fast Rydberg atoms. The velocity distributions of Rydberg atoms emerging from the Rydberg-atom gases are obtained. State-selective field ionization spectra indicate a correlation between the production of fast Rydberg atoms and the presence of Penning ionization signatures. The dependence of the yield of fast Rydberg atoms on Rydberg atom density is measured.

Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-$1∕2$ subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete $2\pi$ rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.

A zero-area pulse produces no excitation in a two-state quantum system on exact resonance. We show analytically and numerically that off resonance the transition probability may acquire significant values, and as the Rabi frequency increases, it approaches steadily unity, a feature reminiscent of adiabatic passage. The nature of the transition is not, however, of adiabatic nature. We show that complete population transfer occurs as a result of a quasiresonant transition between the adiabatic states due to a $\delta$-function-type interaction with an area of $\pi$.

We separate a Bose-Einstein condensate into an array of two-dimensional (2D) sheets and excite quantized vibrational motion in the direction normal to the sheets. The measured collisional decay rates are suppressed due to the reduced dimensionality, a matter wave analog to inhibited spontaneous emission. After decay, the large excitation energy is transferred to back-to-back outgoing atoms, imaged as rings in the 2D plane. The ring diameters correspond to vibrational energy level differences, and edge-on imaging allows identification of the final vibrational states.

We have observed atomic line self-broadening of Cs near $7P_{3∕2}$ and $7P_{1∕2}$ atomic lines at ultracold temperatures using a magneto-optical trap and resonant ionization detection. We have observed blue satellite band features at detunings of 560 and $800\mathrm{MHz}$, respectively, as well as sharp hyperfine-split photoassociative spectra on the red wings of each line and also on the blue wings. Possible explanations of these features are discussed.

Based on the residual entanglement [Phys. Rev. A 71, 042331 (2005)], we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite state. The distinct characteristic of the global entanglement is that it consists of the sum of different entanglement contributions. The measure can provide sufficient and necessary condition of fully separability for pure states and be conveniently extended to mixed states by minimizing the convex hull. To test the sufficiency of the measure for mixed states, we evaluate the global entanglement of bound entangled states. The properties of the measure discussed finally show the global entanglement is an entanglement monotone.

A microcalorimeter with event mode capability for time-resolved soft-x-ray spectroscopy, and a high-resolution flat-field extreme ultraviolet spectrometer have been employed at the Livermore EBIT-I electron beam ion trap for observations and wavelength measurements of $M1$, $E2$, and $M3$ decays of long-lived levels in the Ni-like ions ${\mathrm{Xe}}^{26+}$, ${\mathrm{Cs}}^{27+}$, and ${\mathrm{Ba}}^{28+}$. Of particular interest is the lowest excited level, $3d^{9}4s{}^{3}D_3$, which can only decay via a magnetic octupole $\left(M3\right)$ transition. For this level in Xe, an excitation energy of $(590.40\pm 0.03\mathrm{eV})$ and a level lifetime of $(11.5\pm 0.5\mathrm{ms})$ have been determined.

We report photoionization measurements that help us interpret mechanisms leading to the control of the branching ratio for resonantly enhanced, two-color, two-photon ionization experiments. We measure intermediate state populations and photoelectron angular distributions to explore the ionization dynamics. Our measurements support the interpretation that ac Stark shifts are the primary mechanism of the product state control previously observed in a similar experimental setup. We discuss the role of interference in the ionization continuum and the effect of the ac Stark shift on the product state control.

Interaction of the internal states of an atom with spatially dependent standing-wave cavity field can impart position information of the atom passing through it leading to subwavelength atom localization. We recently demonstrated a different regime of atom localization [Phys. Rev. A 72, 013820 (2005)], namely sub-half-wavelength localization through phase control of electromagnetically induced transparency. This regime corresponds to extreme localization of atoms within a chosen half-wavelength region of the standing-wave cavity field. Here we present further investigation of the simplified model considered earlier and show interesting features of the proposal. We show how the model can be used to simulate a variety of energy-level schemes. Furthermore, the dressed-state analysis is employed to explain the emergence and suppression of the localization peaks, and the peak positions and widths. The range of parameters for obtaining clean sub-half-wavelength localization is identified.

A solid-state quantum computation protocol using controllable Heisenberg exchange interaction and a controllable global magnetic field is proposed. In this protocol, practical pulses can be used for controlling exchange interactions and the global magnetic field.

We demonstrate a compact solid-state laser source for high-resolution two-photon spectroscopy of the $1S\text{−}2S$ transition in atomic hydrogen. The source emits up to $20\mathrm{mW}$ at $243\mathrm{nm}$ and consists of a $972\mathrm{nm}$ diode laser, a tapered amplifier, and two doubling stages. The diode laser is actively stabilized to a high-finesse cavity. We compare the new source to the stable $486\mathrm{nm}$ dye laser used in previous experiments and record $1S\text{−}2S$ spectra using both systems. With the solid-state laser system, we demonstrate a resolution of the hydrogen spectrometer of $6\times {10}^{11}$, which is promising for a number of high-precision measurements in hydrogenlike systems.

This paper deals with estimating the volume of the set of separable mixed quantum states when the dimension of the state space grows to infinity. This has been studied recently for qubits; here we consider larger particles and conclude that, in all cases, the proportion of the states that are separable is superexponentially small in the dimension of the set. We also show that the partial transpose criterion becomes imprecise when the dimension increases, and that the lower bound $6^{-N∕2}$ on the (Hilbert-Schmidt) inradius of the set of separable states on $N$ qubits obtained recently by Gurvits and Barnum is essentially optimal. We employ standard tools of classical convexity, high-dimensional probability, and geometry of Banach spaces. One relatively nonstandard point is a formal introduction of the concept of projective tensor products of convex bodies, and an initial study of this concept.

Quantum theory imposes a strict limit on the strength of nonlocal correlations. It only allows for a violation of the Clauser, Horne, Shimony, and Holt (CHSH) inequality up to the value $2\sqrt{2}$, known as Tsirelson’s bound. In this paper, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH inequality using semidefinite programming. As an example, we show that for any shared entangled state and observables $X_1,\dots ,X_n$ and $Y_1,\dots ,Y_n$ with eigenvalues $\pm 1$ we have $\mid ⟨X_1{Y}_1⟩+⟨X_2{Y}_1⟩+⟨X_2{Y}_2⟩+⟨X_3{Y}_2⟩+\cdots +⟨X_n{Y}_n⟩-⟨X_1{Y}_n⟩\mid ⩽2n\cos [\pi ∕\left(2n\right)]$. It is well known that there exist observables such that equality can be achieved. However, we show that these are indeed optimal. Our approach can easily be generalized to other inequalities for such observables.

We study two different decoherence modes for entangled qubits by considering a Liouville–von Neumann master equation. Mode A is determined by projection operators onto the eigenstates of the Hamiltonian and mode B by projectors onto rotated states. We present solutions for general and for Bell diagonal states and calculate for the latter the mixedness and the amount of entanglement given by the concurrence. We propose a realization of the decoherence modes within neutron interferometry by applying fluctuating magnetic fields. An experimental test of the Kraus operator decomposition describing the evolution of the system for each mode is presented.

We investigate accessibility and controllability of a quantum system $S$ coupled to a quantum probe $P$, both described by two-dimensional Hilbert spaces, under the hypothesis that the external control affects only $P$. In this context accessibility and controllability properties describe to what extent it is possible to drive the state of the system $S$ by acting on $P$ and using the interaction between the two systems. We give necessary and sufficient conditions for these properties and we discuss the relation with the entangling capability of the interaction between $S$ and $P$. In particular, we show that controllability can be expressed in terms of the SWAP and $\sqrt{\mathrm{SWAP}}$ operators acting on the composite system.

The uncertainty of a mixed state has two quite different origins: classical mixing and quantum randomness. While the classical aspect (mixedness) is significantly quantified by the von Neumann entropy, it seems that we still do not have a well accepted measure of quantum uncertainty. In terms of the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurements, we will propose an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigate its fundamental properties. We illustrate how it arises naturally from a naive hidden-variable approach to entanglement and how it exhibits a simple relation to the notion of negativity, which is an entanglement monotone introduced quite recently. We further show that it has a dramatic nonextensive feature resembling the probability law relating operations of two events. This measure of quantum uncertainty provides an alternative quantity complementary to the von Neumann entropy for studying mixedness and quantum correlations.

The dissociative recombination of small cluster cations with free, zero-energy electrons was studied at the ASTRID storage ring. It was found that only two-body fragmentation channels contribute: $\mathrm{C}+{\mathrm{C}}_2$ for $\mathrm{C}_3{}^{+}$, ${\mathrm{C}}_2+{\mathrm{C}}_2$ and $\mathrm{C}+{\mathrm{C}}_3$ for $\mathrm{C}_4{}^{+}$. For $\mathrm{C}_5{}^{+}$ and $\mathrm{C}_6{}^{+}$ the final channels were also characterized by two-body fragmentation, but the specific channels were not identified because of limited mass resolution. It is being speculated whether cluster ions larger than $\mathrm{C}_6{}^{+}$ may undergo recombination without dissociation. These clusters have a large heat capacity and a correspondingly lower temperature after electron capture. The decay of the intermediate neutral clusters may be influenced by infrared emission, which provides cooling and prevents dissociation.

The generation of high-order harmonics in diatomic molecules is investigated within the framework of the strong-field approximation. We show that the conventional saddle-point approximation is not suitable for large internuclear distances. An adapted saddle-point method that takes into account the molecular structure is presented. We analyze the predictions for the harmonic-generation spectra in both the velocity and length gauges. At large internuclear separations, we compare the resulting cutoffs with the predictions of the three-step semiclassical mechanism. Good agreement is obtained only by using the adapted saddle-point method combined with the velocity gauge.

Classical mechanics is not sufficient to describe ion confinement in the dynamic Kingdon trap. We compute quantum corrections to the classical pseudopotential and supplement classical stability criteria with quantum stability criteria. Considering a realistic experimental scenario we show that it is possible to operate the dynamic Kingdon trap in the quantum regime.