We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine which is the Hamiltonian. We show that, in general, this requires a time $\Delta t$ that obeys the uncertainty relation $\Delta t\Delta H\gtrsim 1,$ where $\Delta H$ is a measure of how accurately the unknown Hamiltonian must be estimated. We apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can, in principle, be measured with arbitrarily large precision in an arbitrarily short time. On the other hand, we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time $\Delta t$ which obeys the uncertainty relation $\Delta t\Delta E\gtrsim 1,$ where $\Delta E$ is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.

Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically associated Bell states that serve as measuring rods by relating the metric geometry of the manifold to the observed Einstein-Podolsky-Rosen (EPR) correlations. It is further shown that these correlations can be accounted for by a hidden variable theory which is nonlocal but invariant under the stability group of the reference state.

Several no-go theorems showed the incompatibility between the locality assumption and quantum correlations obtained from maximally entangled spin states. We analyze these no-go theorems in the framework of Bohm’s interpretation. The mechanism by which nonlocal correlations appear during the results of measurements performed on distant parts of entangled systems is explicitly put into evidence in terms of Bohmian trajectories. It is shown that a GHZ-like contradiction of the type $+1=-1$ occurs for well-chosen initial positions of the Bohmian trajectories and that it is this essential nonclassical feature that makes it possible to violate the locality condition.

One-dimensional quantum-mechanical tunneling process from a finite range potential is considered. Analytical and asymptotical properties of the transmission amplitude are discussed, and dispersion relations between the real and the imaginary tunneling-time parameters are derived.

We investigate properties of the structural physical approximation (SPA) of the partial transposition map recently introduced by Horodecki and Ekert [Phys. Rev. Lett. 89, 127902 (2002)]. We focus on the case of two-qubit states and show that in this case the map has the structure of a generalized quantum measurement followed by the preparation of a suitable output state. We also introduce SPA for a map that transforms two copies of density matrix of a single qubit onto a square of that matrix. We prove that also this map is essentially a generalized quantum measurement.

This paper proposes a cryptographic quantum communication scheme analogous to one out of two oblivious transfers based on quantum conjugate coding defined in a four-dimensional Hilbert space. The quantum uncertainty principle ensures that our scheme can satisfy the following two conditions: (i) a sender, Bob, can encode two bits of information $X\in \{0,1\}$ and $Y\in \{0,1\},$ but a receiver, Alice, can only obtain either X or Y dependent on her choice; and (ii) honest Bob, who attempts to encode $\mathrm{}(X,Y),$ cannot reveal Alice’s choice. By contrast, when malicious Bob tries to reveal her choice, honest Alice can detect malicious Bob with a finite probability. Moreover, by using our proposed scheme many times, we can construct a protocol for quantum bit commitment (QBC) from Alice to Bob. Contrary to common belief, the security of our QBC protocol may not be violated by the well-known no-go theorem of QBC. This is because our QBC protocol does not meet the assumptions in which the no-go theorem holds.

We show how to characterize the temporal evolution of a single qubit interacting with a thermal bath by correlation functions of the bath under quite general hypotheses. The aim is to show how the qubit decoherence time depends on the degree of correlation of the bath. We explicitly study some spin-bath models where every spin of the environment interacts with the qubit either directly or by the mediation of a harmonic oscillator. In both cases we find an increase of the decoherence time as soon as a symmetry breaking occurs in the environment. In the latter case a possible experimental setup is discussed.

A scheme for entanglement teleportation is proposed to incorporate multipartite entanglement of four qubits as a quantum channel. Based on the invariance of entanglement teleportation under an arbitrary two-qubit unitary transformation, we derive relations for the separabilities of joint measurements at a sending station and of unitary operations at a receiving station. From the relations of the separabilities it is found that an inseparable quantum channel always leads to total teleportation of entanglement with an inseparable joint measurement and/or a nonlocal unitary operation.

We propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices. The quantum walk is taking place in position space and experimental implementation with present-day technology—even using existing setups—seems feasible. We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum walk to the classical random walk for increasing errors and decoherence.

The speedup of an unsorted database search has always been a challenging problem not only in classical computation but also in quantum computation. We propose a fetching algorithm for a Liouville space nuclear magnetic resonance (NMR) ensemble computing to fetch a marked item from an unsorted database directly. This algorithm achieves the absolute optimum in an unsorted database search problem: a single query. In fact, this algorithm also works well for fetching several unknown numbers of marked items. The computer simulation realization of the algorithm in a three-qubit homonuclear spin system is also presented. In addition, a compromised version of the algorithm, which reduces the demand on the structure of the molecules for the NMR experiment, is also devised.

Having the quantum correlations in a general mixed or pure bipartite state in mind, the part of information accessible by simultaneous measurement on both subsystems is shown never to exceed the part accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite-subsystem) observables is shown to be responsible both for the amount of quasiclassical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

The transition probability of the magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ transition ${2s}^{2}2p$ ${}^2{P}^o$ $J=1/2\mathrm{}$ to $J^{\prime }=3/2\mathrm{}$ $(\lambda =574.19\mathrm{}\mathrm{nm})$ in the B-like ion ${\mathrm{Cl}}^{12+}$ has been measured using two different light sources, the Heidelberg heavy-ion storage ring TSR and the Livermore electron-beam ion trap EBIT-I. Our results for the atomic level lifetime are $21.2\pm 0.6\mathrm{ms}$ from the heavy-ion storage ring and $21.0\pm 0.5\mathrm{ms}$ from the Livermore electron-beam ion trap. Particular attention has been paid to systematic errors, making this experiment a common reference for atomic level lifetime measurements in the visible spectrum.

Laser induced fluorescence spectra of the $C{}^1{\Sigma }^{+}–X{}^1{\Sigma }^{+}$ system of ${}^{23}{\mathrm{Na}}^{85}\mathrm{Rb}$ and ${}^{23}{\mathrm{Na}}^{87}\mathrm{Rb}$ have allowed vibrational levels of the electronic ground state up to $v^{″}=76,$ spanning 99.85% of the potential well to be observed. The ground-state term values have been fitted to a Dunham polynomial expansion, and also to a direct modified Lennard-Jones (MLJ) potential. The analytical MLJ construction allowed us to match previous measured term values for $v^{″}<~30$ with long-range behavior of the potential through the intermediate internuclear distance region covered by the present investigation.

The vibrational relaxation of ${\mathrm{H}}_3^{+}$ molecules from a conventional plasma ion source is studied performing Coulomb explosion imaging on the ions extracted from a storage ring after variable times of storage. Storage for 2 s is found sufficient for radiative relaxation of the breathing excitation and the fragment velocity distribution in the breathing coordinate then agrees well with simulations based on the calculated ground-state wave function. The radiative decay of the two lowest pure breathing levels ${(1,0\mathrm{}}^0)$ and ${(2,0\mathrm{}}^0)$ is seen to be considerably faster than expected from rotationless calculations. Assuming a high rotational excitation of the ${\mathrm{H}}_3^{+}$ ions, as suggested already in earlier experiments, the theoretical transition probabilities of the University College London line list for ${\mathrm{H}}_3^{+}$ [L. Neale, S. Miller, and J. Tennyson, Astrophys. J. 464, 516 (1996)] can explain the increase of the vibrational cooling rates and reproduce the observed decay curve for the lowest breathing-excited level, confirming the absolute transition probabilities of these line tables. The observations give evidence for a quasistable population of high-lying rotational levels in the stored ion beam, relevant for the interpretation of storage ring measurements on the rate coefficients for dissociative recombination of ${\mathrm{H}}_3^{+}$ ions with low-energy electrons.

The total electron scattering cross section of ${\mathrm{CH}}_4,$ ${\mathrm{C}}_2{\mathrm{H}}_2,$ ${\mathrm{C}}_2{\mathrm{H}}_4,$ and ${\mathrm{C}}_2{\mathrm{H}}_6$ molecules have been obtained for 200–1400-eV energy electrons by measuring the attenuation of the electron beam through a gas cell. The present cross sections are compared to existing experimental cross sections as well as to theoretical predictions. The correlation between the total electron scattering cross section and the number of target-molecule electrons is discussed.

The phase-integral approximation is used in the frame of the inverse scattering theory to reconstruct a potential of the type ${v=v}_1{+v}_2$ in which one component $v_1$ is assumed to be known a priori. It is shown that from the knowledge of this term and the phase shift, an analytic expression of the unknown term $v_2$ can be derived. A number of suggestions in order to enlarge the range of applications of this method are also presented. The case of He-Na elastic scattering is given as an example.

Ultracold collisions of polar OH molecules are considered in the presence of an electrostatic field. The field exerts a strong influence on both elastic and state-changing inelastic collision rate constants, leading to clear experimental signatures that should help disentangle the theory of cold molecule collisions. Based on the collision rates, we discuss the prospects for evaporative cooling of electrostatically trapped OH. We also find that the scattering properties at ultralow temperatures prove to be remarkably independent of the details of the short-range interaction, owing to avoided crossings in the long-range adiabatic potential curves. The behavior of the scattering rate constants is qualitatively understood in terms of a novel set of long-range states of the $[\mathrm{OH}{]}_2$ dimer.

Previous work on multielectron transitions in proton, antiproton, and ${\mathrm{He}}^{2+}$-ion impact on neon is extended to the case of argon targets for collision energies in the 5–1000 keV/amu range. Global quantities such as net electron loss from the target, net capture, and net ionization are predicted within experimental errors using a spherically symmetric optimized effective target atom potential with dynamical screening effects based on the time-dependent net ionization probability. The inclusion of target response is crucial in order to obtain correct positions and heights for the peaks in the net ionization cross sections. Effects due to cascading following multiple outer-shell excitation are found to be appreciable at energies between 10 and 100 keV/amu, but are overestimated by the statistical model. L-shell vacancy production is reported to affect recoil charge state production at energies above 200 keV/amu for charge states $q>~3.$ At low and intermediate energies, the independent-particle model is shown to overestimate q-fold recoil ion production significantly for $q>~3$ for proton impact signaling the role of electronic correlations for these channels. For antiproton impact the $q=3\mathrm{}$ cross section is consistent with the independent-particle model.