We used a cross capacitor to measure the relative dielectric permittivity ${\epsilon }_r$ of ${\mathrm{O}}_2$ at 273, 293, and $323\mathrm{K}$ and at pressures up to $6.5\mathrm{MPa}$. Simultaneously we measured oxygen’s complex refractive index $n$ using a quasispherical cavity resonator at frequencies between 2.4 and $7.3\mathrm{GHz}$. The combined results from these measurements determine oxygen’s frequency-dependent, relative magnetic permeability ${\mu }_r(f,p,T)$ with an uncertainty of less than 1% of $({\mu }_r-1)$ at pressures above $2\mathrm{MPa}$. Regression of these data to a model for oxygen’s impact—broadened microwave spectrum allowed us to determine two quantities that are, in principle, amenable to calculation: the molar magnetic susceptibility in the limits of zero pressure and zero frequency ${\chi }_{M00}^{\mathrm{meas}}\equiv {\chi }_M(0,0,293.15\mathrm{K})$ and the second magnetic virial coefficient $b_{\mu }$. With oxygen’s electronic $g$ factor constrained to $2.0039\pm 0.0003$ (the value known from laser magnetic resonance, EPR, and molecular beam experiments) we obtained ${\chi }_{M00}^{\mathrm{meas}}=(42.92\pm 0.06)\times {10}^{-9}{\mathrm{m}}^3{\mathrm{mol}}^{-1}$ and $b_{\mu }=-1.8\pm 0.5{\mathrm{cm}}^3{\mathrm{mol}}^{-1}$. The result for ${\chi }_{M00}^{\mathrm{meas}}$ is consistent with a recent ab initio calculation ${\chi }_{M00}^{\mathrm{meas}}∕{\chi }_{M00}^{\mathrm{calc}}=0.9998\pm 0.0014$. Our measurements of oxygen’s magnetic susceptibility are the first made relative to the susceptibility of helium calculated ab initio. All previous measurements were made relative to the diamagnetic susceptibility of water. These previous measurements, published in 1943 or earlier, span the wider range $0.975<{\chi }_{M00}^{\mathrm{meas}}∕{\chi }_{M00}^{\mathrm{calc}}<1.019$. Our measurements of ${\epsilon }_r$ determine the static molecular dielectric polarizability of oxygen: $(1.7456\pm 0.0003)\times {10}^{-40}\mathrm{F}{\mathrm{m}}^2$, which deviates by $+0.7$ and $-0.1\%$ from two recent ab initio calculations.

In a recent publication we presented detailed experimental and theoretical results for the electron-impact-induced ionization of ground-state helium atoms. The purpose of that work was to refine theoretical approaches and provide further insight into the Coulomb four-body problem. Cross section ratios were presented for transitions leading to excited states, relative to those leading to the ground state, of the helium ion. We now build on that study by presenting individual relative triple-differential ionization cross sections (TDCSs) for an additional body of experimental data measured at lower values of scattered-electron energies. This has been facilitated through the development of new electron-gun optics which enables us to accurately characterize the spectrometer transmission at low energies. The experimental results are compared to calculations resulting from a number of different approaches. For ionization leading to ${\mathrm{He}}^{+}{\left(1s^2\right)}^{1}S$, cross sections are calculated by the highly accurate convergent close-coupling (CCC) method. The CCC data are used to place the relative experimental data on to an absolute scale. TDCSs describing transitions to the excited states are calculated through three different approaches, namely, through a hybrid distorted-$\text{wave}+R$-matrix (close-coupling) model, through the recently developed four-body distorted-wave model, and by a first Born approximation calculation. Comparison of the first- and second-order theories with experiment allows for the accuracy of the different theoretical approaches to be assessed and gives insight into which physical aspects of the problem are most important to accurately model.

Ultracold sodium atoms have been trapped inside a hollow-core optical fiber. The atoms are transferred from a free-space optical dipole trap into a trap formed by a red-detuned Gaussian light mode confined to the core of the fiber. We show that at least 5% of the atoms held initially in the free-space trap can be loaded into the core of the fiber and retrieved outside.

The kinetic energy release (KER) and angular distribution for dissociation and ionization of $\mathrm{N}_2{}^{+}$ in an intense short pulse $\left(7\mathrm{fs}\right)$ laser at $790\mathrm{nm}$ was measured by employing a coincidence three-dimensional momentum imaging method that provides kinematically complete information on the dissociation. At an intensity of $6.0\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ a high-KER peak $(\sim 6.1\mathrm{eV})$ unexpectedly appears in the dissociation spectrum in addition to the usual low-KER peak $(\sim 0.6\mathrm{eV})$. Additionally, the KER distribution in ionization, which peaks around $7\mathrm{eV}$, has a tail that surprisingly extends well beyond the Coulomb explosion energy. Both these high-KER contributions result from dissociation pathways involving highly excited states of $\mathrm{N}_2{}^{+}$ with steep potential curves as indicated by the dressed state potential energy curves picture.

Recently, Pu et al. developed an efficient strategy to find the adiabatic condition of a nonlinear system—i.e., the atom-homonuclear dimer conversion [Phys. Rev. Lett. 98, 050406 (2007)]. Here, by applying their method, we extend it to study the adiabatic condition of coherent atom–heteronuclear-diatomic- or -triatomic-molecule conversion. The different adiabatic evolutions in creating the homo- or heteronuclear dimers are compared. The impact of the two different reaction paths on the adiabatic conditions in creating the heteronuclear triatomic molecules is also discussed.

We examine pairing and molecule formation in strongly interacting Fermi gases, and we discuss how radio-frequency (rf) spectroscopy can reveal these features. For the balanced case, the emergence of stable molecules in the Bose-Einstein condensation regime results in a two-peak structure in the rf spectrum with clearly visible medium effects on the low-energy part of the molecular wave function. For the highly imbalanced case, we show the existence of a well-defined quasiparticle (a spin polaron) on both sides of the Feshbach resonance, we evaluate its lifetime, and we illustrate how its energy may be measured by rf spectroscopy.

We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles for contending with noise in physical implementations of quantum information processing. Private subsystems (and subspaces) for quantum channels play a central role in cryptographic schemes such as quantum secret sharing and private quantum communication. We show that a subsystem is private for a channel precisely when it is correctable for a complementary channel. This result is shown to hold even for approximate notions of private and correctable defined in terms of the diamond norm for superoperators.

We derive an effective Hamiltonian to account for the geometric phase that occurs in the adiabatic separation of center-of-mass and internal motion of a molecule moving in external fields. We then apply this Hamiltonian to the determination of the coherence time of molecules confined in a region of space by an anisotropic electric field. We show that the coherence time is expected to scale as the load temperature of the molecules squared and that milli-K temperatures are likely to be required for a trapped molecule experiment to compete with a more conventional Ramsey beam resonance experiment.

We have measured the relative single and double photoionization cross section of magnesium from $22\text{to}54\mathrm{eV}$ photon energy using monochromatized synchrotron radiation. The corresponding double-to-single ionization ratio as well as the relative single photoionization cross section compares reasonably well with recent theoretical calculations [A.S. Kheifets and I. Bray, Phys. Rev. A 75, 042703 (2007)]. The photon energy dependence of the ratio can be modeled by a suitably scaled helium double-to-single photoionization ratio. However, to our surprise, a previously proposed scaling model for that ratio does not work in the case of Mg. From the near-threshold double-photoionization cross section we estimate the range of validity of the Wannier threshold law to be about $0.7\mathrm{eV}$ with a rather small cross section near threshold.

We consider the evolution of nonlinear optical pulses in cubic-quintic nonlinear media wherein the pulse propagation is governed by the generalized nonlinear Schrödinger equation with exponentially varying dispersion, cubic, and quintic nonlinearities and gain and/or loss. Using a self-similar analysis, we find the chirped bright soliton solutions in the anomalous and normal dispersion regimes. From a stability analysis, we show that the soliton in the anomalous dispersion regime is stable, whereas the soliton in the normal dispersion regime is unstable. Numerical simulation results show that competing cubic-quintic nonlinearities stabilize the chirped soliton pulse propagation against perturbations in the initial soliton pulse parameters. We characterize the quality of the compressed pulse by determining the pedestal energy generated and compression factor when the initial pulse is perturbed from the soliton solutions. Finally, we study the possibility of rapid compression of Townes solitons by the collapse phenomenon and the exponentially decreasing dispersion. We find that the collapse could be postponed if the dispersion increases exponentially.

We classify the completely positive maps acting on two $d$-dimensional systems which commute with all $U\otimes U$ unitaries, where $U∊\mathrm{SU}\left(d\right)$. This set of operations map Werner states to Werner states. We find a simple condition for a map to be implementable by stochastic local operations and classical communication (SLOCC). We show that all positive partial transpose (PPT) preserving maps can be implemented by SLOCC. This can be used to prove that the entanglement of Werner states cannot be stochastically increased, even if we allow PPT entanglement for free, which provides a necessary result for proving the result of Masanes [Phys. Rev. Lett. 96, 150501 (2006)], one of the central results in the theory of entanglement.

The origin of the SO(4) symmetry of the relativistic hydrogen atom discussed recently [Chen et al., Phys. Rev. A 77, 034102 (2008)] is clarified, thereby providing the background missing there. Some applications of this symmetry are listed.

A molecular synchrotron offers unique possibilities to study molecular collisions at low energies. For such a study, it is imperative that the velocity of the stored molecules can be tuned over a wide range. Bunching elements, used to provide the necessary longitudinal focusing forces in a synchrotron, introduce instabilities for certain velocities of the stored molecules. Here we present an experimental study of these motional resonances and show how they can be avoided. A packet of $\mathrm{N}{\mathrm{D}}_3$ molecules is stably confined in the synchrotron as its injection velocity is continuously scanned from $60\mathrm{m}∕\mathrm{s}$ $(E_{\mathrm{kin}}=3.0{\mathrm{cm}}^{-1})\text{to}87.5\mathrm{m}∕\mathrm{s}$ $(E_{\mathrm{kin}}=6.4{\mathrm{cm}}^{-1})$.

We present a detailed investigation of minimum detection efficiencies, below which local realism cannot be violated by any quantum system of any dimension in bipartite Bell experiments. Lower bounds on these minimum detection efficiencies are determined with the help of linear programming techniques. Our approach is based on the observation that any possible bipartite quantum correlation originating from a quantum state in an arbitrary dimensional Hilbert space is sandwiched between two probability polytopes, namely the local (Bell) polytope and a corresponding nonlocal no-signaling polytope. Numerical results are presented demonstrating the dependence of these lower bounds on the numbers of inputs and outputs of the bipartite physical system.

We propose a theoretical scheme to couple superconducting charge qubits (SCQs) via Raman transitions in a circuit QED architecture. Qubit array interacts a quantum data bus generated by a one-dimensional superconducting transmission line resonator (TLR). Based on the Raman transitions, the controllable and selective interqubit couplings mediated by the data bus can be obtained by just addressing the applied gate pulses, which provides the possibility for scaling up to many SCQs.

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.

We explicitly compute the optimal cost for a class of example problems in geometric quantum control. These problems are defined by a Cartan decomposition of $\mathrm{su}\left(2^n\right)$ into orthogonal subspaces $\mathfrak{l}$ and $\mathfrak{p}$ such that $[\mathfrak{l},\mathfrak{l}]\subseteq \mathfrak{p},[\mathfrak{p},\mathfrak{l}]=\mathfrak{p},[\mathfrak{p},\mathfrak{p}]\subseteq \mathfrak{l}$. Motion in the $\mathfrak{l}$ direction is assumed to have negligible cost, where motion in the $\mathfrak{p}$ direction does not. In the special case of two qubits, our results correspond to the minimal interaction cost of a given unitary.

Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling constant, these models can be understood as straight-line interpolations between different Hamiltonians $H_{\mathrm{I}}$ and $H_{\mathrm{F}}$. For finite-size realizations however, there will usually be a finite energy gap between ground and first excited state. By slowly changing the coupling constant through the point with the minimum energy gap one thereby has an adiabatic algorithm that prepares the ground state of $H_{\mathrm{F}}$ from the ground state of $H_{\mathrm{I}}$. The adiabatic theorem implies that in order to obtain a good preparation fidelity the runtime $\tau$ should scale with the inverse energy gap and thereby also with the system size. In addition, for open quantum systems not only nonadiabatic but also thermal excitations are likely to occur. It is shown that—using only local Hamiltonians—for the one-dimensional quantum Ising model and the cluster model in a transverse field the conventional straight-line path can be replaced by a series of straight-line interpolations, along which the fundamental energy gap is always greater than a constant independent on the system size. The results are of interest for adiabatic quantum computation since strong similarities between adiabatic quantum algorithms and quantum phase transitions exist.

We derive the distribution of eigenvalues of the reduced density matrix of a block of length $\ell$ in a one-dimensional system in the scaling regime. The resulting “entanglement spectrum” is described by a universal scaling function depending only on the central charge of the underlying conformal field theory. This prediction is checked against exact results for the $XX$ chain. We also show how the entanglement gap closes when $\ell$ is large.

We investigate experimentally the energy distribution of a single ${}^{87}\mathrm{Rb}$ atom trapped in a strongly focused dipole trap under various cooling regimes. Using two different methods to measure the mean energy of the atom, we show that the energy distribution of the radiatively cooled atom is close to thermal. We then demonstrate how to reduce the energy of the single atom, first by adiabatic cooling, and then by truncating the Boltzmann distribution of the single atom. This provides a nondeterministic way to prepare atoms at low micro-K temperatures, close to the ground state of the trapping potential.