Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $\mathrm{su}\left(2\right)\oplus \mathrm{su}\left(2\right)$ and $\mathrm{su}\left(2\right)\oplus \mathrm{su}\left(2\right)\oplus \mathrm{u}\left(1\right)$ subalgebras of the full SU(4) dynamical group of the system, the nontrivial part of the final calculation is reduced to a single Riccati (first-order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.

We show that the Hilbert space of even number $(⩾4)$ of qubits can always be decomposed as a direct sum of four orthogonal subspaces such that the normalized projectors onto the subspaces are activable bound entangled (ABE) states. These states also show a surprising recursive relation in the sense that the states belonging to $2N+2$ qubits are Bell correlated to the states of $2N$ qubits; hence, we refer to these states as Bell-correlated ABE (BCABE) states. We also study the properties of noisy BCABE states and show that they are very similar to that of two qubit Bell-diagonal states.

Given $N$ identical copies of the state of a quantum two-level system, we analyze its optimal estimation. We consider two situations: general pure states and (pure) states restricted to lie on the equator of the Bloch sphere. We perform a complete and comprehensive analysis of the optimal schemes based on local measurements, and give results (optimal measurements, maximum fidelity, etc.) for arbitrary $N$, not necessarily large, within the Bayesian framework. We also make a comparative analysis of the asymptotic limit of these results with those derived from a (pointwise) Cramér-Rao type of approach. We give explicit schemes based on local measurements and no classical communication that saturate the fidelity bounds of the most general collective schemes.

Ionization cross sections in collisions of antiprotons $\left(\overline{p}\right)$ with $\mathrm{H}_2{}^{+}$ molecules are calculated for incident energies in the range of $2–500\mathrm{keV}$ by using a semiclassical impact-parameter method. The electronic motion is solved in a numerically accurate manner by means of a discrete variable representation. A sudden approximation is applied to the description of the molecular rotation and vibration. The present $\overline{p}+\mathrm{H}_2{}^{+}$ ionization cross sections are compared with the theoretical results of the ionization in $\overline{p}+{\mathrm{He}}^{+}$ and the experimental results of the production of ${\mathrm{H}}^{+}$ ions in $\overline{p}+{\mathrm{H}}_2$.

We have developed a generalized nonunitary Lindblad equation and its quantum trajectory Monte Carlo implementation for the evolution of open quantum systems (OQSs) whose coupling to the environment features not only energy exchange but also probability flux to the environment. This generalization allows the treatment of a class of problems where the state space of the system includes bound and continuum states. We show the equivalence between the solution of the generalized Lindblad equation and the Monte Carlo average over open quantum trajectories. As a first test case we study the multilevel radiative decay of a hydrogenic ion. As a second test case we apply the theory to the time development of the internal state of fast highly charged ${\mathrm{Kr}}^{35+}$ ions traversing carbon foils with varying thickness subject to collisions and to spontaneous radiative decay. We find significantly improved agreement of the nonunitary transport theory with experimental data.

We adopt an effective-field-theory view to describe the low-energy excitations of trapped Bose gases, which allows a direct and systematic way to investigate the consequences of spontaneous symmetry breaking. The derivation of the effective Lagrangian can incorporate various approximations and can reproduce the results obtained by the standard hydrodynamic approach. Based on the effective Lagrangian, we calculate the energy spectrum and Matsubara Green’s function of trapped one-dimensional Bose gases with $\delta$-function repulsive interaction allowing the comparison of various results obtained by different approaches. We also analytically calculate the finite-temperature correlation function of trapped two-dimensional (2D) Bose gases. The calculation scheme can be easily extended to higher dimensions. We find that particle interactions will always decrease the coherence length of the condensate in 2D, confirming recent numerical results. The validation of various asymptotic expressions are given.

We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work on one- and two-dimensional lattices and study the entanglement between two groups of lattice sites as a function of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check [G. Giedke et al., Phys. Rev. Lett. 87, 167904 (2001)] for bound entanglement where appropriate. The short-range entanglement is found to grow approximately linearly with the group sizes and to be favored by strong interactions. Conversely, long-range entanglement is favored by relatively weak interactions. No examples of bound entanglement are found.

We study the dispersion and absorption spectra of a weak probe in a $\Lambda$-type three-level atomic system with closely ground sublevels driven by a strong field and damped by a broadband squeezed vacuum. We analyze the interplay between the spontaneous generated coherence and the squeezed field on the susceptibility of the atomic system. We find that by varying the intensity of the squeezed field the group velocity of a weak pulse can change from subluminal to superluminal. In addition we exploit the fact that the properties of the atomic medium can be dramatically modified by controlling the relative phase between the driving field and the squeezed field, allowing us to manipulate the group velocity at which light propagates. The physical origin of this phenomenon corresponds to a transfer of the atomic coherence from electromagnetically induced transparency to electromagnetically induced absorption. Besides, this phenomenon is achieved under nearly transparency conditions and with negligible distortion of the propagation pulse.

Closed-loop optimal quantum control experiments operate in the inherent presence of laser noise. In many applications, attaining high quality results [i.e., a high signal-to-noise $(S∕N)$ ratio for the optimized objective] is as important as producing a high control yield. Enhancement of the $S∕N$ ratio will typically be in competition with the mean signal, however, the latter competition can be balanced by biasing the optimization experiments towards higher mean yields while retaining a good $S∕N$ ratio. Other strategies can also direct the optimization to reduce the standard deviation of the statistical signal distribution. The ability to enhance the $S∕N$ ratio through an optimized choice of the control is demonstrated for two condensed phase model systems: second harmonic generation in a nonlinear optical crystal and stimulated emission pumping in a dye solution.

High-order above-threshold ionization by few-cycle laser pulses is analyzed in terms of quantum orbits. For a given carrier-envelope phase, the number of contributing orbits and their ionization and rescattering times determine the shape of the angle-resolved spectrum in all detail. Conversely, analysis of a given spectrum reveals the carrier-envelope phase and the various interfering pathways from which the electron could choose.

Recent experiments have shown that fullerene and fluorofullerene molecules can produce interference patterns. These molecules have both rotational and vibrational degrees of freedom. This leads one to ask whether these internal motions can play a role in degrading the interference pattern. We study this by means of a simple model. Our molecule consists of two masses a fixed distance apart. It scatters from a potential with two or several peaks, thereby mimicking two or several slit interference. We find that in some parameter regimes the entanglement between the internal states and the translational degrees of freedom produced by the potential can decrease the visibility of the interference pattern. In particular, different internal states correspond to different outgoing wave vectors, so that if several internal states are excited, the total interference pattern will be the sum of a number of patterns, each with a different periodicity. The overall pattern is consequently smeared out. In the case of two different peaks, the scattering from the different peaks will excite different internal states so that the path the molecule takes becomes entangled with its internal state. This will also lead to degradation of the interference pattern. How these mechanisms might lead to the emergence of classical behavior is discussed.

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialize the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to the reciprocal of the square root of the number of measurements.

We describe a phase transition for long-range entanglement in a three-dimensional cluster state affected by noise. The partially decohered state is modeled by the thermal state of a short-range translation-invariant Hamiltonian. We find that the temperature at which the entanglement length changes from infinite to finite is nonzero. We give an upper and lower bound to this transition temperature.

This paper explores several aspects of the adiabatic quantum-computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum-computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an $n$-local Hamiltonian, we will study whether approximation is possible using previous results on ground-state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

We prove a special case of the Helstrom theorem by using the no-signaling condition in the special theory of relativity that faster-than-light communication is impossible.

We consider the dissociation of a molecular Bose-Einstein condensate due to a magnetic-field sweep that starts on the molecular side of a Feshbach resonance and ends either on the atomic or on the molecular side. We determine both the time-dependent response of the molecular condensate wave function and the energy distribution of the atoms produced after the sweep. In the cases where experiments have been performed, our analytic and numerical calculations provide good agreement with experimental atomic energy distributions.

It was shown by Kocharovskaya and Khanin [Sov. Phys. JETP 63, 945 (1986)] that a comb of optical pulses can induce a ground-state atomic coherence and change the optical response of an atomic medium. In our experiment, we studied the propagation of a comb of optical pulses produced by a mode-locked diode laser in rubidium atomic vapor. Electromagnetically induced transparency (EIT) was observed when the pulse repetition rate is a subharmonic of the hyperfine splitting of the ground state. The width of the EIT resonance is determined by the relaxation rate of the ground-state coherence. Possible applications to magnetometery, atomic clocks, and frequency chains are discussed.

We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.

We present a quantum theory of the decay of an autoionizing state created in the attosecond xuv (extreme ultraviolet) pump and laser probe measurements within the strong field approximation employing resonance parameters from Fano’s theory. From the electron spectra versus the pump-probe time delay, we show how the lifetimes of the resonances can be extracted directly from the time domain measurements.

We present the simultaneous cooling and trapping of an isotopic mixture in a magneto-optical trap and describe the transfer of the mixture into a conservative, far-off-resonant dipole trap. The mixture is prepared with a technique that applies to intermediate and heavy alkaline-earth-metal-like atoms. In this work, ${}^{88}\mathrm{Sr}$ and ${}^{86}\mathrm{Sr}$ are simultaneously loaded first into the magneto-optical trap operated on the ${}^{1}S_0\text{−}{}^{3}P_1$ spin-forbidden line at 689 nm, and then transferred into the dipole trap. We observe fast interspecies thermalization in the dipole trap which allows one to set a lower bound on the ${}^{88}\mathrm{Sr}\text{−}{}^{86}\mathrm{Sr}$ elastic cross section.