Due to recent important work of Życzkowski and Sommers [J. Phys. A 36, 10115 (2003); 36, 10083 (2003)], exact formulas are available (in terms of both the Hilbert-Schmidt and the Bures metrics) for the $(n^2-1)$-dimensional and $\left[n\right(n-1)∕2-1]$-dimensional volumes of the complex and real $n\times n$ density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of $n=4$, that is, two-qubit systems. Making use of the density matrix $\left(\rho \right)$ parametrization of Bloore [J. Phys. A 9, 2059 (1976)], we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, $\nu ={\rho }_{11}{\rho }_{44}∕{\rho }_{22}{\rho }_{33}$. The associated integrand in each case is the product of a known Jacobian (highly oscillatory near $\nu =1$) and a certain unknown univariate function, which our extensive numerical (quasi Monte Carlo) computations indicate is very closely proportional to an (incomplete) Beta function $B_{\nu }(a,b)$, with $a=1∕2$, $b=\sqrt{3}$ in the real case, and $a=2\sqrt{6}∕5,b=3∕\sqrt{2}$ in the complex case. Assuming the full applicability of these specific incomplete Beta functions, we undertake separable-volume calculations.

We report on the use of depletion spectroscopy to detect ultracold ground-state KRb molecules with rotational resolution. The population of a specific ground-state vibrational level $v^{″}$, produced by photoassociation of ultracold atoms, is monitored by one-color two-photon pulsed-laser ionization. When a cw laser is resonant with a rovibrational transition to an excited state, the ground-state population, and hence the ion signal, is depleted. This narrow-band spectroscopic technique allows the individual rotational levels in both ground and excited states to be resolved, and thus the population of a single ground-state rovibrational level to be monitored. These resolved transitions are a necessary first step in transferring population from high vibrational levels of the ground state, such as produced by photoassociation, to the absolute molecular ground state $X{}^1\Sigma ^{+}$ ($v^{″}=0$, $J^{″}=0$). This technique can also be used to determine binding energies of high-$v^{″}$ molecules. Combining our binding energy measurement with the results of previous spectroscopy yields an improved dissociation energy of the $X$ state: $D_e=4217.822\pm 0.003{\mathrm{cm}}^{-1}$. We also report on the two-color pulsed-laser ionization used to locate the depletion transitions.

Experimental studies of the absorption spectrum of the ${\mathrm{Rb}}_2$ dimer are performed in the $600–1100\mathrm{nm}$ wavelength range for temperatures between 615 and $745\mathrm{K}$. The reduced absorption coefficient is measured by spatially resolved white light absorption in overheated rubidium vapor with a radial temperature gradient, which enables simultaneous measurements at different temperatures. Semiclassical and quantum spectral simulations are obtained by taking into account all possible transitions involving the potential curves stemming from the 5 ${}^{2}S+5$ ${}^{2}S$ and 5 ${}^{2}S+5$ ${}^{2}P$ asymptotes. The most accurate experimental potential curves are used where available, and newly calculated potential curves and transition dipole moments otherwise. The overall consistency of the theoretical model with the experimental interpretation is obtained only if the radial dependence of both the calculated transition dipole moments and the spin-orbit coupling is taken into account. This highlights the low-resolution absorption spectroscopy as a valuable tool for checking the accuracy of molecular electronic structure calculations.

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density ${\rho }_s$ in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter $\Delta$ and Fermi chemical potential $\mu$, using the Nozières–Schmitt-Rink approximation. This treatment is shown to be necessary for consistent treatment of ${\rho }_s$ over the entire BCS-BEC crossover. We also calculate the condensate fraction $N_c$ as a function of the temperature, a quantity which is quite different from the superfluid density ${\rho }_s$. We show that the mean-field expression for the condensate fraction $N_c$ is a good approximation even in the strong-coupling BEC regime. Our numerical results show how ${\rho }_s$ and $N_c$ depend on temperature, from the weak-coupling BCS region to the BEC region of tightly bound Cooper pair molecules. In a companion paper [Phys. Rev. A 74, 063626 (2006)], we derive an equivalent expression for ${\rho }_s$ from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.

We present fully differential measurements of $730\text{−}\mathrm{eV}$ electron-impact single ionization of the ground state of helium with 205- or $100\text{−}\mathrm{eV}$ outgoing electrons. Internormalized data are obtained for coplanar geometries with the fast electron detected at ${\theta }_A=6°$, 9°, and 12°. The data are compared, where possible, with the corresponding data of Catoire et al. [J. Phys. B 39, 2827 (2006)] and the convergent close-coupling theory. An improved agreement is found between the present measurements and the theory.

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.

In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations.

In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation between the noise operator and the conserved quantity or from the recently developed universal uncertainty principle for the noise-disturbance trade-off in general measurements. However, the problem of obtaining the precision limit to realizing the quantum NOT gate has eluded a solution from these approaches. Here, we develop a method for this problem based on analyzing the trace distance between the output state from the realization under consideration and the one from the ideal gate. Using the mathematical apparatus of orthogonal polynomials, we obtain a general lower bound on the error probability for the realization of the quantum NOT gate in terms of the number of qubits in the control system under conservation of the total angular momentum of the computational qubit plus the control system along the direction used to encode the computational basis. The lower bound turns out to be more stringent than one might expect from previous results. Our method is expected to lead to more accurate estimates for physical realizations of various types of quantum computations under conservation laws and to contribute to related problems such as the accuracy of programmable quantum processors.

The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU-equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. A 71, 062323 (2005)]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence $(\mathrm{LU}\iff \mathrm{LC})$ to include all stabilizer states represented by graphs with cycles of length neither 3 nor 4. To compare our result with Van den Nest et al.’s, we show that any stabilizer state of distance $\delta =2$ is beyond their criterion. We then further prove that $\mathrm{LU}\iff \mathrm{LC}$ holds for a more general class of stabilizer states of $\delta =2$. We also explicitly construct graphs representing $\delta >2$ stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with $2^m-1$ $(m⩾4)$ vertices using quantum error-correcting codes which have non-Clifford transversal gates.

We study the optical excitation spectrum of an atom in the vicinity of a dielectric surface. We calculate the rate of the total scattering as well as the rate of the scattering into the evanescent modes. With a proper assessment of the limitations, we demonstrate the portability of the flat-surface results to an experimental situation with a nanofiber. The effect of the surface-induced potential on the excitation spectrum for free-to-bound transitions is shown to be weak. On the contrary, the effect for bound-to-bound transitions is significant leading to a large excitation linewidth, a substantial negative shift of the peak position, and a strong long tail on the negative side and a small short tail on the positive side of the field frequency detuning.

The photoabsorption spectrum of Xe-like ${\mathrm{La}}^{3+}$ and I-like ${\mathrm{La}}^{4+}$ has been obtained in the extreme ultraviolet (euv) spectral region with the dual laser produced plasma technique. Photoexcitation from the $4d$ subshell is the dominant process in the $80–150\mathrm{eV}$ energy range. Strong discrete structure, corresponding to $4d\to np$, $mf$ ($n>6$, $m>4$) transitions in ${\mathrm{La}}^{3+}$ was observed at lower laser power densities, but with increasing laser flux the discrete features were suppressed and replaced by broad features in the $4d\to 5p$ and $4d\to 4f$ regions. This behavior can be attributed to the presence of absorption from excited states containing open $5p$ and $4f$ subshells in ${\mathrm{La}}^{3+}$ and the onset of similar absorption in ${\mathrm{La}}^{4+}$.

The lifetime broadening and molecular field splitting of the sodium dimer $2p$ core level is studied by x-ray photoelectron spectroscopy and by Auger electron spectroscopy. The lifetime of the Na $2p$ core hole has been determined to be $15\pm 8\mathrm{fs}$, much shorter than what has previously been reported for solid sodium. The molecular field splitting of this core level has been determined to be $42\pm 10\mathrm{meV}$. The Auger measurements have experimentally confirmed that the sodium dimer is a good example of when the Coulomb explosion mechanism determines the spectral shape.

We present a joint theoretical and experimental study of the time evolution of electronic states of highly charged hydrogenic ions formed by capture during transmission through solids as they undergo multiple collisions and radiative decay. For this transport problem we have developed an inhomogeneous nonunitary Lindblad master equation that allows for a description of open quantum systems with both sinks (electron loss) and source (capture) present. We apply this theoretical framework to study transient coherences created in electron capture by $13.6\mathrm{MeV}∕\mathrm{amu}$ ${\mathrm{Ar}}^{18+}$ ions transmitted through amorphous carbon foils and decoherence during subsequent interaction with the foil. In the limit of thin targets we can directly probe electron capture cross sections under single collision conditions, while for thicker targets we follow the partially coherent dynamics of the open quantum system in interaction with the solid as a function of interaction time. The calculated results are in close agreement with experimental data obtained at the LISE facility in GANIL. Photon intensities from excited argon ions were determined through high resolution x-ray spectroscopy in which individual fine structure components were resolved. Measurements were performed for a wide range of carbon foil thickness to study the time development of the excited state populations.

A family of monotonically convergent algorithms is presented for solving a wide class of quantum optimal control problems satisfying an inhomogeneous integrodifferential equation of motion. The convergence behavior is examined using a four-level model system under the influence of non-Markovian relaxation. The results show that high quality solutions can be obtained over a wide range of parameters that characterize the algorithms, independent of the presence or absence of relaxation.

We have theoretically studied the space-time entangled biphoton state generated from a two-level atomic system. In the photon counting measurement, the two-photon coincidence counting rate is a damped oscillation. The oscillation period is determined by the effective Rabi frequency and the damping rate is determined by the linewidth of the inhomogeneous-broadened ground state and the dipole dephasing rate. In an optical-pathway-balanced configuration, the two-photon temporal correlation shows an antibunching effect which corresponds to the interference between two types of nonlinear four-wave mixing processes occurring in such a two-level system. The visibility of the normalized second-order quantum coherence function $g^{\left(2\right)}\left(\tau \right)$ increases along with the increase of the effective Rabi frequency, but has an upper limit at 45%. We find agreement between the theory and the experiments [P. Kolchin et al., Phys. Rev. Lett. 97, 113602 (2006); S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, ibid 98, 053601 (2007)].

The phenomenon of spontaneous emission cancellation has been investigated in photonic-band-gap materials in the presence of dipole-dipole interaction. The material is densely doped with an ensemble of five-level nanoparticles. The mean field theory is used to calculate the effect of the dipole-dipole interaction whereas the linear response theory is used to calculate the expressions for the real and imaginary susceptibilities. Numerical simulations are performed for an isotropic photonic-band-gap material. Interesting results are predicted such as the control of the spontaneous emission cancellation by moving the resonance energies between the energy band and energy gap. It is also found that the photonic-band-gap material can be switched between absorptive and nonabsorptive states by changing the strength of the dipole-dipole interaction and the resonance energies in the energy band.

We extend to finite temperature the fidelity approach to quantum phase transitions (QPTs). This is done by resorting to the notion of mixed-state fidelity that allows one to compare two density matrices corresponding to two different thermal states. By exploiting the same concept we also propose a finite-temperature generalization of the Loschmidt echo. Explicit analytical expressions of these quantities are given for a class of quasifree fermionic Hamiltonians. A numerical analysis is performed as well showing that the associated QPTs show their signatures in a finite range of temperatures.

It is widely believed that the standard model of particle physics is just an intermediate step in understanding the properties of the elementary physics in nature and the interactions between them. Over the past twenty years, studies of the parity nonconservation in atomic systems based on nonaccelerator methods have made remarkable progress. An experiment to measure parity nonconservation in singly ionized barium has been proposed as an independent test of the standard model. We have employed the relativistic coupled-cluster theory to calculate the parity nonconserving $6s{}^{2}S_{1∕2}\to 5d{}^{2}D_{3∕2}$ transition amplitude and associated properties. We have also shown contributions from various intermediate states which play a significant role in the determination of this transition amplitude.

We report on a study of electron-hydrogen scattering, using a combination of a modified method of polarized orbitals and the optical potential formalism which does not require projection operators. The calculation is restricted to $S$ waves in the elastic region, where the correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia and Temkin [Phys. Rev. A 64, 032709 (2001)]. This indicates that the correlation function is general enough to include the target distortions (polarization) in the presence of the incident electron, except for the scattering lengths for which the inclusion of polarization is essential for precision results. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts.

Concentration depth profiles at liquid surfaces can be determined by means of neutral impact collision ion scattering spectroscopy. The energy resolution of the spectra is influenced by the energy loss straggling of the projectiles. Energy loss straggling is a measure of the width of the energy loss distribution of particles passing through matter. Knowledge of the energy loss straggling is especially important for determining concentration depth profiles of aqueous surfaces. Here it is shown that the energy loss in the gas phase and the energy loss distribution can be determined with a series of spectra taken at different vapor pressures of the aqueous solution. The projectiles used are $3\mathrm{keV}$ helium ions. The gas phase causes a shift of the spectra to lower energies and a broadening of the structure due to energy loss straggling. Both the energy loss in the gas phase and the energy loss straggling must be gauged in order to determine concentration depth profiles quantitatively. Knowledge of the energy loss distribution can be used to determine accurate concentration depth profiles by means of deconvolution.