We calculate electron capture and ionization probabilities for ion–atom collisions in a strong laser field $(5\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2)$ by numerically solving the three-dimensional time-dependent Schrödinger equation. For circularly polarized laser fields and an impact energy of $1.2\mathrm{keV}∕\mathrm{amu}$, we find a substantial modification of the electronic dynamics in the ${\mathrm{H}}^{+}\text{–}\mathrm{H}$ collision system as compared to field-free collisions. In particular, we observe a strong dependence on the initial laser phase and the impact parameter for both capture and ionization, which can be explained using semiclassical arguments.

A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous eigenstate of the initial Hamiltonian is written as a power series which has a straightforward diagrammatic representation. Each term of the series corresponds to a sequence of “adiabatic” evolutions, during which the system remains in an instantaneous eigenstate of the Hamiltonian, punctuated by transitions from one state to another. The first term of this series is the standard adiabatic evolution, the next is the well known first correction to it, and subsequent terms can be written down essentially by inspection. Although the final result is perhaps not terribly surprising, it seems to not be widely known, and the interpretation is new, as far as we know. Application of the method to the adiabatic approximation is given, and some discussion of the validity of this approximation is presented.

Most quantum tomographic methods for massive particles using destructive measurement can only be used for motion in one dimension. We show how to infer the quantum state of a nonrelativistic, $N$-dimensional harmonic oscillator system by simple inverse Radon transforms. We assume a time-independent Hamiltonian for which the dynamics along each coordinate always occurs simultaneously with the others and measurements on all coordinates are performed simultaneously. This is unlike light systems where different modes can be delayed and phase shifted with respect to each other. A requirement of the procedure is that the angular frequencies of the $N$ harmonic potentials be incommensurable. We discuss the information available if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite-time measurements. As further examples, we consider free particles in $N$ dimensions with periodic boundary conditions and particles in an $N$-dimensional box, where we find a similar condition of incommensurability and finite recurrence time.

We present calculated cross sections and rate coefficients for dissociative recombination of the ${{\mathrm{Ar}}_2}^{+}$ molecular ion in the low-energy region $(<0.5\mathrm{eV})$. In this region, the cross section is dominated by resonances, the repulsive Rydberg states converging to the excited states of the ion, which cross the ground state of the ion near equilibrium geometry. The resonance curves and their parameters were determined from electron scattering calculations using the complex Kohn variational method and molecular quantum chemistry techniques. The nuclear dynamics were studied using a time-independent, nonlocal potential model solved using a discrete variable representation and exterior complex scaling. The calculated cross sections and rate coefficients are reported and compared to available experiments. The temperature dependence of the rate coefficients is examined as well as the branching fractions of the resulting atomic fragments.

We present a calculation of the low lying spectrum of a rotating Bose-Einstein condensate. We show that in a cylindrical geometry, there exist two linear branches, one associated with usual acoustic excitations, the other corresponding to a twisting mode of the vortex lattice. Using a hydrodynamical approach, we derive the elasticity coefficient of the vortex lattice and calculate the spectrum of condensate in a three-dimensional harmonic trap with cylindrical symmetry.

Much of the theory of entanglement concerns the transformations that are possible to a state under local operations with classical communication (LOCC); however, this set of operations is complicated and difficult to describe mathematically. An idea which has proven very useful is that of the entanglement monotone: a function of the state which is invariant under local unitary transformations and always decreases (or increases) on average after any local operation. In this paper we look on LOCC as the set of operations generated by infinitesimal local operations, operations which can be performed locally and which leave the state little changed. We show that a necessary and sufficient condition for a function of the state to be an entanglement monotone under local operations that do not involve information loss is that the function be a monotone under infinitesimal local operations. We then derive necessary and sufficient differential conditions for a function of the state to be an entanglement monotone. We first derive two conditions for local operations without information loss, and then show that they can be extended to more general operations by adding the requirement of convexity. We then demonstrate that a number of known entanglement monotones satisfy these differential criteria. Finally, as an application, we use the differential conditions to construct a new polynomial entanglement monotone for three-qubit pure states. It is our hope that this approach will avoid some of the difficulties in the theory of multipartite and mixed-state entanglement.

We first classify the quantum clone into irreversible and reversible types from the perspective of quantum-information distribution. We propose a scheme of continuous-variable reversible telecloning, which broadcast the information of an unknown state without loss from a sender to several spatially separated receivers exploiting multipartite entanglement as quantum channels. In this scheme, the quantum information of an unknown state is distributed into $M$ optimal clones and $M-1$ anticlones using $2M$-partite entanglement. For the perfect quantum-information distribution that is optimal cloning, $2M$-partite entanglement is required to be a maximum two-party entanglement.

Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5P_{1∕2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1∕R^3$ potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the $0_u^{+}$ states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

We study an atomic Bose gas with an $s$-wave Feshbach resonance in one dimension. Most of the parameter region is occupied by a phase in which the superfluid fluctuations of atoms and molecules are the predominant ones, due to the phase fluctuations of atoms and molecules being locked by a Josephson coupling between them. When the density difference between atoms and molecules is close to zero, two additional phases may exist: the two-component Luttinger liquid, which contains two branches of gapless excitations, and the interchannel charge density wave where the relative density fluctuations between atoms and molecules are frozen at low energy.

Alkali-metal hydride molecules have large dipole moments in their ground electronic states. We explore the possibility of forming such molecules from a mixture of the ultracold atomic gases, employing a one-photon stimulated radiative association process. Using accurate molecular potential-energy curves and dipole moments, we have calculated the rate coefficients for populating each of the vibrational levels of the $X{}^1\Sigma ^{+}$ states of LiH and NaH. We have found that significant molecule formation rates into the upper vibrational levels can be realized with laser intensities and atomic densities that are easily attainable experimentally. We examine the spontaneous emission cascade which takes place from these upper vibrational levels on a time scale of milliseconds, and calculate the resulting rotational populations in $v=0$. We show that photon emission in the cascade process does not contribute to trap loss and that a large population of molecules in $v=0$ can be achieved.

We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction $\nu =5∕2$. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct short-range interactions between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for nontopological operations is above $14\%$. The total number of nontopological computational elements that one needs to simulate a quantum circuit with $L$ gates scales as $L(\ln L{)}^3$.

A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled-channel calculations. Using $R$-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.

We address the problem of calculating electromagnetic transition matrix elements between states of a particle in spherically symmetrical potentials with no assumed boundary conditions at finite distance (free-boundary-condition method). For this, the Schrödinger equation is solved in a finite box of radius $R$ and bound and continuum states, appropriately normalized, are numerically represented, through a variational finite-basis-set (B-spline) approach. The equivalence between the three transition operator forms (length, velocity, acceleration), within this approach, is discussed, and bound-continuum and continuum-continuum matrix elements are calculated in all three gauges. Results for the strong electromagnetic radiation of hydrogen are presented through the calculation of two-photon ionization cross sections and photoelectron angular distributions. It is demonstrated that the present approach is well suited for the calculation of multiphoton transitions when ionization in the continuum is allowed (above-threshold ionization). With the free-boundary-condition method complete control over the density of scattering states is feasible and, as the result of that, the degeneracy in the continuum between partial waves is preserved.

We use Bogoliubov-de Gennes (BdG) theory to describe a vortex in a neutral fermionic gas, for an attractive interaction that can be arbitrarily tuned to exhibit a crossover from BCS to Bose–Einstein condensation (BEC). We adopt the BCS–Leggett mean-field ground state for which a BdG approach is microscopically justified, and for which a Gross–Pitaevskii description emerges in the BEC limit. The local density of fermionic states is used to provide insight into the particle density depletion from BCS to BEC. We relate this depletion to the presence of unoccupied discrete states at the core center, as well as to a suppression of negative energy continuum states.

Optimal dense coding using a partially-entangled pure state of Schmidt rank $\overline{D}$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability ${\tau }_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-{\tau }_x$) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For $\overline{D}⩽D$ a bound is obtained for $L_d$ in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. [Phys. Rev. A71, 012311 (2005)]. For $\overline{D}>D$ it is shown that $L_d$ is strictly less than $D^2$ unless $\overline{D}$ is an integer multiple of $D$, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for $\overline{D}⩽D$, assuming ${\tau }_x>0$ for a set of $\overline{D}D$ messages, and a bound is obtained for the average $⟨1∕\tau ⟩$. A bound on the average $⟨\tau ⟩$ requires an additional assumption of encoding by isometries (unitaries when $\overline{D}=D$) that are orthogonal for different messages. Both bounds are saturated when ${\tau }_x$ is a constant independent of $x$, by a protocol based on one-shot entanglement concentration. For $\overline{D}>D$ it is shown that (at least) $D^2$ messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.

The concept of generalized quantum measurement is introduced as a transformation that sets a one-to-one correspondence between the initial states of the measured object system and final states of the object-meter system with the help of a classical informational index, unambiguously linked to a classically compatible set of quantum states. It is shown that the generalized quantum measurement concept covers all key types of quantum measurement—standard projective, entangling, fuzzy, and generalized measurements with a partial or complete destruction of initial information associated with the object. A special class of soft quantum measurements as a basic model for the fuzzy measurements widespread in physics is introduced and its information properties are studied in detail. Also, a special class of partially destructive measurements mapping all states of the Hilbert space of a finite-dimensional quantum system onto the basis states of an infinite-dimensional quantum system is considered.

Frequency shifts of the $\mathrm{Ag}I4d^{10}5s{}^{2}S_{1∕2}(F=0,M_F=0)$ to $4d^{9}5s^2{}^{2}D_{5∕2}(F^{\prime }=2,M_{F^{\prime }}=0)$ electric-quadrupole transition at $330.6\mathrm{nm}$ due to external fields are calculated using multiconfigurational self-consistent field methods. As this forbidden transition is free from first order Doppler and Zeeman effects, it is under investigation for the realization of an atomic optical clock. The calculated perturbations are the light shift, the blackbody frequency shift, and the quadratic Zeeman shift. Results show that a total uncertainty of ${10}^{-18}$ could be reach without confining the atoms in a Lamb-Dicke regime in an optical lattice.

A mode-locked femtosecond laser is used to physically map the laser frequency comb into the velocity comb of the excited Rb atoms at room temperature. Upon resonant excitation by discrete optical frequencies the velocity distribution of the excited Rb atoms shows comblike structure. Simultaneously, velocity-selective population transfer occurs between ground-state hyperfine levels. Both facts are observed by modified direct frequency comb spectroscopy and verified by a detailed density matrix treatment of the multilevel system in resonant field.

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms $\Gamma$ on sweep rate $\alpha$, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $\Gamma \propto \alpha$ is obtained when the initial molecular fraction is smaller than the $1∕N$ quantum fluctuations, and a cubic-root power law $\Gamma \propto {\alpha }^{1∕3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.