We study the problem of optimal control of dissipative quantum dynamics. Although under most circumstances dissipation leads to an increase in entropy (or a decrease in purity) of the system, there is an important class of problems for which dissipation with external control can decrease the entropy (or increase the purity) of the system. An important example is laser cooling. In such systems, there is an interplay of the Hamiltonian part of the dynamics, which is controllable, and the dissipative part of the dynamics, which is uncontrollable. The strategy is to control the Hamiltonian portion of the evolution in such a way that the dissipation causes the purity of the system to increase rather than decrease. The goal of this paper is to find the strategy that leads to maximal purity at the final time. Under the assumption that Hamiltonian control is complete and arbitrarily fast, we provide a general framework by which to calculate optimal cooling strategies. These assumptions lead to a great simplification, in which the control problem can be reformulated in terms of the spectrum of eigenvalues of $\rho$, rather than $\rho$ itself. By combining this formulation with the Hamilton-Jacobi-Bellman theorem we are able to obtain an equation for the globally optimal cooling strategy in terms of the spectrum of the density matrix. For the three-level $\Lambda$ system, we provide a complete analytic solution for the optimal cooling strategy. For this system it is found that the optimal strategy does not exploit system coherences and is a “greedy” strategy, in which the purity is increased maximally at each instant.

Bose-Einstein condensates (BECs) are in many ways similar to laser light. In Fox-Li-type simulations, which involve free evolution of a two-dimensional BEC in combination with periodic focusing and localized loss, we model here numerically the BEC equivalent of transverse aspects of laser resonators. We discuss possible experimental realizations in the form of periodic series of light pulses interacting with the BEC. We show that such experiments can result in trapped, structurally stable, modes analogous to Hermite-Gaussian laser modes. This outlines a new way of trapping BECs and illustrates further the analogy between BECs and laser light.

We present semianalytical many-body results for energies and excitation frequencies for an inhomogeneous Bose-Einstein condensate over a wide range of atom numbers $N$ for both small $s$-wave scattering lengths, typical of most laboratory experiments, and large scattering lengths, achieved by tuning through a Feshbach resonance. Our dimensional perturbation treatment includes two-body correlations at all orders and yields analytical results through first order by taking advantage of the high degree of symmetry of the condensate at the zeroth-order limit. Because $N$ remains a parameter in our analytical results, the challenge of calculating energies and excitation frequencies does not rise with the number of condensate atoms. In this proof-of-concept paper the atoms are confined in a spherical trap and are treated as hard spheres. Our many-body calculations compare well to Gross-Pitaevskii results in the weakly interacting regime and depart from the mean-field approximation as the density approaches the strongly interacting regime. The excitation frequencies provide a particularly sensitive test of beyond-mean-field corrections. For example, for $N=2000$ atoms and an experimentally realized large scattering length of $a=0.433a_{ho}\left(a_{ho}=\sqrt{\hslash ∕m{\omega }_{ho}}\right)$ we predict a $75\%$ shift from the mean-field breathing mode frequency.

The destruction of quantum interference, decoherence, and the destruction of entanglement both appear to occur under the same circumstances. To address the connection between these two phenomena, we consider the evolution of arbitrary initial states of a two-particle system under open system dynamics described by a class of master equations which produce decoherence of each particle. We show that all initial states become separable after a finite time, and we produce the explicit form of the separated state. The result extends and amplifies an earlier result of Diósi. We illustrate the general result by considering the case in which the initial state is an Einstein-Podolsky-Rosen state (in which both the positions and momenta of a particle pair are perfectly correlated). This example clearly illustrates how the spreading out in phase space produced by the environment leads to certain disentanglement conditions becoming satisfied.

This paper investigates disentanglement as a result of evolution according to a class of master equations which include dissipation and interparticle interactions. Generalizing an earlier result of Diósi, the time taken for complete disentanglement iscalculated (i.e., for disentanglement from any other system). The dynamics of two harmonically coupled oscillators is solved in order to study the competing effects of environmental noise and interparticle coupling on disentanglement. An argument based on separability conditions for Gaussian states is used to arrive at a set of conditions on the couplings sufficient for all initial states to disentangle for good after a finite time.

We study the universality of scaling of entanglement in Shor’s factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the $NP$-complete exact cover problem as well as Grover’s problem. The analytic result for Shor’s algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore making it hard to generate an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution exact cover algorithm, which also shows universality of the quantum phase transition near which the system evolves. On the other hand, entanglement in Grover’s adiabatic algorithm remains a bounded quantity even at the critical point. The classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.

Decoherence properties of two Josephson charge qubits coupled via the ${\sigma }_x{\sigma }_x$ type are investigated. Considering the special structure of this new design, the dissipative effects arising from the circuit impedance providing the fluxes for the qubits’ superconducting quantum interference device loops coupled to the ${\sigma }_x$ qubit variables are considered. The results show that the overall decoherence effects are significantly strong in this qubit design. It is found that the dissipative effects are stronger in the case of coupling to two uncorrelated baths than are found in the case of one common bath.

Cold and ultracold collisions involving rotationally hot oxygen molecules are investigated using quantum-mechanical, coupled-channel, coupled-states, and effective-potential scattering formulations. Quenching rate coefficients are given for initial rotational levels near the dissociation threshold. The stability of the oxygen “super rotors” against collisional decay is compared to previous investigations involving hydrogen molecules where the rotational inertia was significantly smaller. In contrast to hydrogen, all possible states of rotationally hot oxygen are quenched very rapidly during a collision with a buffer gas helium atom, and the quenching efficiency is always dominated by pure rotational transitions.

In this work we report on a theoretical study on elastic electron collisions with ketenylidene radicals in the low and intermediate energy range. Calculated differential and momentum transfer cross sections for the $e^{-}-{\mathrm{C}}_2\mathrm{O}$ collision are reported in the (1–500)-eV range. A complex optical potential composed by static, exchange, correlation-polarization plus absorption contributions, derived from a fully molecular wave function, is used to describe the interaction dynamics. The Schwinger variational iterative method combined with the distorted-wave approximation is applied to calculate scattering amplitudes. Comparison made between our calculated cross sections with the theoretical and experimental results for elastic $e^{-}-{\mathrm{N}}_2\mathrm{O}$ collisions has revealed remarkable similarity for incident energies equal to 20 eV and above. Also, two shape resonances located at around 3 eV and 4.5 eV are observed and identified as due to the ${}^2\Pi$ and the ${}^4\Pi$ scattering channels, respectively.

A systematic study is reported on the convergence of computed triply differential cross sections for photo-double ionization of helium at 20 and $25\text{eV}$ above threshold, obtained using the hyperspherical $\mathcal{R}$ matrix with semiclassical outgoing waves method. Such a study has become feasible due to an essential improvement in the description of the radial correlation coordinate $\alpha =\arctan \left(r_2∕r_1\right)$ at short range, and to the implementation of the code on a more powerful computer. It shows that the size requirements of the inner region $R⩽R_0$, with $R=\sqrt{r_1^2+r_2^2}$, vary considerably depending on the dynamic situation considered. Typically, while $R_0\simeq 20\mathrm{a}\text{.u}\mathrm{.}$ proves sufficient in most circumstances, one has to increase the inner region up to $R_0\simeq 60\mathrm{a}\text{.u}\mathrm{.}$ in order to reach convergence in the triply differential cross sections obtained for very asymmetric energy sharings or in the particular case when one electron is ejected along the electric field for linearly polarized photons. The converged calculations are generally in very good agreement with new experimental data of high statistical quality recorded in the latter case, at $25\text{eV}$ above threshold, for various energy sharings. The dynamic situations identified here call for further experimental and theoretical studies.

Here we study a one-dimensional finite lattice formed by generalized contact interactions in a circular setup, i.e., under periodic boundary conditions. Considering only four such potentials, we show the emergence of different behaviors as revivals, bouncing, and trapping for the time evolution of wave packets. This is done by properly choosing the parameters that characterize the contact interactions. We also discuss possible physical applications for this type of system, such as using it to split an initially localized state into spatially separated and dynamically independent parts.

We compare the resonant neutralization dynamics of hydrogen anions in front of plane Ag surfaces of symmetries (100) and (111) using a Crank–Nicholson wave-packet propagation method. For the $\text{Ag}\left(100\right)$ surface, the surface state, degenerate with the valence band, rapidly decays while being populated by the ion. For $\text{Ag}\left(111\right)$, in contrast, the population of a quasi-local Shockley surface state inside the projected $L$-band gap impedes the electron decay into the bulk along the direction normal to the surface. This difference in the decay pattern strongly affects the survival of $1\text{keV}$ ions scattered from these surfaces. Scattering off the $\text{Ag}\left(111\right)$ surface results in about an order of magnitude higher ion-survival as a function of the exit angle with respect to the surface plane compared to that off $\text{Ag}\left(100\right)$. Results for $\text{Ag}\left(111\right)$ show good agreement with measurements [Guillemot and Esaulov, Phys. Rev. Lett. 82, 4552 (1999)].

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin spatial as well as generalized time-reversal symmetries are established and shown to lead to a twofold degeneracy of the electronic states in the presence of the field. Low lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and, in particular, the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.

The interactions between a two-level atom and a coherent field with a time-varying frequency have been investigated. The two typical cases—the frequency of the field varying with time in the forms of sine and rectangle—have been considered. It is found that the collapse-revival phenomena of the atomic population inversion are deformed as the frequency changing with time in sine form and the rectangular frequency modulation can lead to some new collapses and new revivals in the evolution of the atomic population inversion.

Recent fluorescence studies suggest that ultrashort pulse laser excitation may be highly selective. Selective high-intensity laser excitation holds important consequences for the physics of multiphoton processes. To establish the extent of this selectivity, we performed a detailed comparative study of the vacuum ultraviolet fluorescence resulting from the interaction of ${\mathrm{N}}_2$ and $\text{Ar}$ with high-intensity infrared ultrashort laser pulses. Both ${\mathrm{N}}_2$ and $\text{Ar}$ reveal two classes of transitions, inner-valence $ns\leftarrow np$ and Rydberg $np\leftarrow n^{\prime }{\ell }^{\prime }$. From their pressure dependence, we associate each transition with either plasma or direct laser excitation. Furthermore, we qualitatively confirm such associations with the time dependence of the fluorescence signal. Remarkably, only ${\mathrm{N}}_2$ presents evidence of direct laser excitation. This direct excitation produces ionic nitrogen fragments with inner-valence $\left(2s\right)$ holes, two unidentified transitions, and one molecular transition, the $\mathrm{N}_2{}^{+}:X{}^2\Sigma _g^{+}\leftarrow \mathrm{C}{}^2\Sigma _u^{+}$. We discuss these results in the light of a recently proposed model for multiphoton excitation.

Magnetic solitons in spinor Bose-Einstein condensates confined in a one-dimensional optical lattice are studied by the Holstein-Primakoff transformation method. It is shown that due to the long-range light-induced and static magnetic dipole-dipole interactions, there exist different types of magnetic solitary excitations in different parameter regions. Compared to conventional solid-state materials, the parameters of this type of magnetic solitons in an optical lattice can be easily tuned by the above dipole-dipole interactions, which are highly controllable in experiments.

We analyze the entanglement properties of the ground state for a system of spins half embedded in a magnetic field, mutually interacting antiferromagnetically. Contrary to the ferromagnetic case where a second-order quantum phase transition occurs, a first-order transition is obtained at zero field and the so-called concurrence which measures the two-spin entanglement displays a jump at the transition point.

In the context of quantum information, both Shannon entropy and the different Jaynes entropy for a two-electron “entangled artificial” atom proposed by Moshinsky are studied here. The Jaynes entropy in this model is shown to be intimately related to the correlation kinetic energy. A generalization of the customary Shannon entropy based on the electron density is then proposed in terms of the electron pair correlation function. Both definitions behave in a similar way to the Jaynes entropy when considered as a function of the strength of the model electron-electron interaction.

We study the mode entanglement in the one-dimensional Frenkel-Kontorova model, and found that quantum entanglement is distinct before and after the transition by breaking of analyticity. We show that the more extended the electron is, the more entangled the corresponding state. Finally, a quantitative relation is given between the average square of the concurrence quantifying the degree of entanglement and the participation ratio characterizing the degree of localization.

A theory is presented for the retarded resonance interaction in dielectric media between a ground state atom and an excited atom. We demonstrate in the retarded limit large deviations compared to earlier incorrect evaluations of this important quantity.