A quantum-mechanical many-body system with a potential proportional to the pairwise inverse-square distance possesses a strong-weak coupling duality. Using this duality we construct a parent Hamiltonian describing the system of particles and quasiparticles. The construction of the Hamiltonian and the solutions found are of a hierarchical nature.

We investigate the spectrum of elementary excitations for $T=0\mathrm{}$ of a resonantly strongly driven two-component Bose-Einstein condensate (BEC) taking account of the Rabi oscillations. It is shown that the spectrum has two phononlike branches. Due to the inequality of the scattering lengths the Bogoliubov speed of sound of both branches differs from the Bogoliubov speed of sound for nondriven BEC, which leads to a modification of superfluidity. We have shown that the proposal to apply an additional resonant magnetic field in a scheme of the Feshbach resonance makes it possible to attain a very high sweep rate of the Feshbach resonance.

Theoretical information on dynamic stabilization (DS) of the ground state of H is still fragmentary, while its detection has remained open because of a lack of lasers with the required characteristics. The problem has been reactivated by the new light sources that are being developed, such as VUV-FEL’s or attosecond pulses from high-harmonic generation, which will offer adequate frequencies, intensities, and pulse durations. We are now presenting a mapping out of DS over an extended range of high frequencies, for pulses with various envelopes, peak intensities, and durations. We find prominent DS under conditions where our nonrelativistic, dipole approximation, and calculation should be valid. There is a marked dependence of DS on the pulse shape. The effect of quasistationary stabilization (of the rates) on DS is analyzed. We comment on the impact of our results on the detection possibility. We conclude that ground-state DS for H should be observable with the new light sources in a state-of-the-art experiment.

We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.

We test the applicability of density-functional theory (DFT) to spectral perturbations taking an example of a Cs atom surrounded by superfluid helium. The atomic DFT of helium is used to obtain the distribution of helium atoms around the impurity atom, and the electronic DFT is applied to the excitations of the atom, averaging over the ensemble of helium configurations. The shift and broadening of the $D_1$ and $D_2$ absorption lines are quite well reproduced by theory, suggesting that the DFT may be useful for describing spectral perturbations in more complex environments.

Intense ultranarrow resonances have been observed in the photoionization of Mg from the singly excited $3smd{}^{1}D$ $\mathrm{}(m=3,4,5,6\mathrm{})\mathrm{}$ states to the doubly excited $3png{}^{1}F$ $\mathrm{}(n=5,6,7\mathrm{})\mathrm{}$ autoionization states using stepwise laser excitation and time-of-flight mass spectrometry detection. The reported experimental energy resolution at an order of ${10}^{-7}$ of the photon energy represents a considerable improvement over the best photon energy resolution of about one part in ${10}^5$ for the synchrotron radiation light sources. The ultra-narrow $3png{}^{1}F$ resonances acquire a significant strength for the normally weak $3smd{}^1\overrightarrow{D}3png{}^{1}F$ two-electron transition due to a strong configuration interaction with an overlapping broad $3pnd{}^{1}F$ autoionization series and the $3s\epsilon f{}^{1}F$ continuum. The measured line positions and transition widths are in close agreement with the theoretical results derived from a B-spline-based configuration-interaction calculation.

We have studied the $4d$ photoabsorption process of I, ${\mathrm{I}}^{+},$ ${\mathrm{I}}^{2+},$ and ${\mathrm{I}}^{3+}$ by using linear density-response theory together with density-functional theory to take into account the dynamic electron correlation, which is crucially important in reproducing the $4d$ giant resonance. The current approach, however, differs from previous approaches of this type in that we use an optimized effective potential and explicitly incorporate a self-interaction correction. We found that the $4d$ photoabsorption spectrum of the ${\mathrm{I}}^{+}$ ion is almost the same as that of the neutral I atom, and that in moving from I to ${\mathrm{I}}^{3+}$ the spectrum changes from one notably characterized by a giant resonance into one with multiple sharp peaks. Convoluting the spectra with the experimental energy resolution yielded spectra in excellent agreement with absolute experimental photoabsorption cross-section spectra. Moreover, our results showed better agreement with experiment than earlier theoretical studies. In addition, increasing the energy resolution revealed peaks not observed in the experimental spectra.

Recently, a lot of attention has been devoted to finding physically realizable operations that realize as closely as possible certain desired transformations between quantum states, e.g., quantum cloning, teleportation, quantum gates, etc. Mathematically, this problem boils down to finding a completely positive trace-preserving (CPTP) linear map that maximizes the (mean) fidelity between the map itself and the desired transformation. In this communication, we want to draw attention to the fact that this problem belongs to the class of so-called semidefinite programming (SDP) problems. As SDP problems are convex, it immediately follows that they do not suffer from local optima. Furthermore, this implies that the numerical optimization of the CPTP map can, and should, be done using methods from the well-established SDP field, as these methods exploit convexity and are guaranteed to converge to the real solution. Finally, we show how the duality inherent to convex and SDP problems can be exploited to prove analytically the optimality of a proposed solution. We give an example of how to apply this proof method by proving the optimality of Hardy and Song’s optimal qubit $\theta$ shifter (e-print quant-ph/0102100).

We consider a charged Dirac particle bound in a scalar potential perturbed by a classical magnetic field derivable from a vector potential $\mathbf{A}\left(\mathbf{r}\right).\mathrm{}$ Using a procedure based on the Gordon decomposition of a field-induced current, we identify diamagnetic and paramagnetic contributions to the second-order perturbation-theory correction to the particle’s energy. In contradiction to earlier findings, based on the sum-over-states approach, it is found that the resulting diamagnetic term is ${\mathcal{E}}_{\mathrm{d}}^{\mathrm{}\left(2\right)\mathrm{}}{=(q}^2/2m)〈{\Psi }^{\mathrm{}\left(0\right)\mathrm{}}|\beta {\mathbf{A}}^2{\Psi }^{\mathrm{}\left(0\right)\mathrm{}}〉,$ where ${\Psi }^{\mathrm{}\left(0\right)\mathrm{}}\left(\mathbf{r}\right)$ is an unperturbed eigenstate and $\beta$ is the matrix associated with the rest-energy term in the Dirac Hamiltonian.

Parity- and time-invariance-violating $(P,T$-odd) nuclear forces produce $P,T$-odd nuclear moments. In turn, these moments can induce electric dipole moments (EDMs) in atoms through the mixing of electron wave functions of opposite parity. The nuclear EDM is screened by atomic electrons. The EDM of an atom with closed electron subshells is induced by the nuclear Schiff moment. Previously the interaction with the Schiff moment has been defined for a pointlike nucleus. No problems arise with the calculation of the electron matrix element of this interaction as long as the electrons are considered to be nonrelativistic. However, a more realistic model obviously involves a nucleus of finite size and relativistic electrons. In this work we have calculated the finite nuclear size and relativistic corrections to the Schiff moment. The relativistic corrections originate from the electron wave functions and are incorporated into a “nuclear” moment, which we term the local dipole moment. For ${}^{199}\mathrm{Hg}$ these corrections amount to $\sim 25\%.$ We have found that the natural generalization of the electrostatic potential of the Schiff moment for a finite-size nucleus corresponds to an electric-field distribution which, inside the nucleus, is well approximated as constant and directed along the nuclear spin, and outside the nucleus is zero. Also in this work the ${}^{239}\mathrm{Pu}$ atomic EDM is calculated.

Using the concept of the crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent Hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behavior of this prescription for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.

We investigate the quantum-classical transition in the $\delta$-function-kicked rotor and the attainment of the classical limit in terms of measurement-induced state localization. It is possible to study the transition by fixing the environmentally induced disturbance at a sufficiently small value, and examining the dynamics as the system is made more macroscopic. When the system action is relatively small, the dynamics is quantum mechanical and when the system action is sufficiently large there is a transition to classical behavior. The dynamics of the rotor in the region of transition, characterized by the late-time momentum diffusion coefficient, can be strikingly different from both the purely quantum and classical results. Remarkably, the early-time diffusive behavior of the quantum system, even when different from its classical counterpart, is stabilized by the continuous measurement process. This shows that such measurements can succeed in extracting essentially quantum effects. The transition regime studied in this paper is accessible in ongoing experiments.

Approximately 40 years ago it was realized that the time development of decaying systems might not be precisely exponential. Winter [Phys. Rev. 123, 1503 (1961)] analyzed the simplest nontrivial system—a particle tunneling out of a well formed by a wall and $\delta$ function. He calculated the probability current just outside the well and found irregular oscillations on a short-time scale followed by an exponential decrease followed by more oscillations and finally by a decrease as a power of the time. We have reanalyzed this system, concentrating on the survival probability of the particle in the well rather than the probability current, and find a different short-time behavior.

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains “quantum,” this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.

We examine static single-spin measurements using magnetic-force microscopy methods. We show that these measurements could be carried out at millikelvin temperatures. A simple estimate of the decoherence time is presented. Possible experiments for measuring single-spin relaxation processes and the use of these measurements in quantum computations are discussed.

We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions, and measurements. The resources needed for an operation on a two-level system are one ebit and a bidirectional communication of two cbits, and for an n-level system, a pair of entangled n-level particles and two classical “nits.” In the latter case, there are $n-1$ possible distinct operations per n-level entangled pair. Similar results apply for generating interaction between a pair of remote systems, while for remote measurements only one-directional classical communication is needed. We further consider remote operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between the systems. Our results follow from the properties of a hybrid state-operator object (stator), which describes quantum correlations between states and operations.

In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical case and show that lossless compression is only possible if the message to be compressed is known to the sender. The lossless compression of an ensemble of messages is bounded from below by its von-Neumann entropy. We show that it is possible to reduce the number of qbits passing through a quantum channel even below the von Neumann entropy by adding a classical side channel. We give an explicit communication protocol that realizes lossless and instantaneous quantum data compression and apply it to a simple example. This protocol can be used for both online quantum communication and storage of quantum data.

The Jaynes entropy of the one-particle reduced density matrix is examined within the context of the convex set of N-representable one-matrices. The monotonic relationship of the Jaynes entropy with distance from the hull of the convex set is highlighted, and we show that the Jaynes entropy is monotonically related to the density-functional definition of the correlation energy, thus qualifying a conjecture of Collins which assumed a simple proportionality. It is further suggested that maximization of the Jaynes entropy subject to the constraints of fixed density and kinetic energy picks out the true one-matrix.

Collisional Stark rates for $p^4{\mathrm{He}}^{+}$ with $36\lesssim n\lesssim 38$ are estimated with coupled-channel calculations. Both an atomic and a molecular model are used. Matrix elements of the $\overline{p}{\mathrm{He}}^{+}-\mathrm{He}$ interaction for the atomic model are approximated with expressions having two or three parameters. Rough estimates for the molecular model are obtained using the generalized Born-Oppenheimer approximation, together with matrix elements for the atomic model. Guesswork, based on interactions of seemingly similar atoms, is used to set fairly wide limits to parameters for the atomic model, it being assumed that the potentials depend only on n, l, and R. Transitions are found to be unlikely. But the rates are sensitive to the potentials. Transitions can be likely if the potentials are different from what can reasonably be guessed by assuming a dependence on only n, l, and R. A potential with a minimum, preferably relatively deep, at relatively small R can cause transitions to be important. It is conjectured that this can occur because $\overline{p}{\mathrm{He}}^{+}-\mathrm{He}$ potentials depend on the component of $\overline{p}{\mathrm{He}}^{+}$ intrinsic angular momentum along $\mathbf{R}.$ Also, it is found that the difference in the reduced mass of $\overline{p}{\mathrm{He}}^{+}$ and He can cause the rate to be several times higher for $p^3{\mathrm{He}}^{+}$ than for comparable $p^4{\mathrm{He}}^{+}.$