We consider a bipartite mixed state of the form $\rho ={\sum }_{\alpha ,\beta =1}^l{a}_{\alpha \beta }\mid {\psi }_{\alpha }⟩⟨{\psi }_{\beta }⟩$, where $\mid {\psi }_{\alpha }⟩$ are normalized bipartite state vectors, and matrix $\left(a_{\alpha \beta }\right)$ is positive semidefinite. We provide a necessary and sufficient condition for the state $\rho$ taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of $\mid {\psi }_{\alpha }⟩$ for $\alpha =1,2,\dots ,l$. Using this criterion, we can judge completely whether or not the state $\rho$ is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.

We propose a potential scheme, based on the achieved technique of a single-electron transistor, to implement the readout of an electronic spin state inside a doped ${\mathrm{C}}_{60}$ fullerene by means of the magnetic dipole-dipole coupling and spin filters. In the presence of an external magnetic field, we show how to perform the spin state detection by transforming the information contained in the spin state into the tunneling current. The robustness of our scheme against sources of error is discussed.

The transition from time advance to time delay in one-dimensional single barrier tunneling is investigated by considering the trajectories in the complex $k$ plane of the top-barrier transmission poles as a function of the opacity of the barrier. We show that such a transition is linked to the particular event where the first top-barrier transmission pole migrates under the barrier as the opacity of the system diminishes. It is also shown that the above situation has an effect on tunneling dynamics since it governs the presence of transient structures in the time evolution of the probability density.

We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes $\mathrm{N}@{\mathrm{C}}_{60}$ or $\mathrm{P}@{\mathrm{C}}_{60}$. The qubits are stored in electronic spin degrees of freedom of the doped atom N or P. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by the refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.

Unitary operations are the building blocks of quantum programs. Our task is to design efficient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given $n$-qubit system. The most common versions of this task are known as Hamiltonian simulation and gate simulation, where Hamiltonian simulation can be seen as an infinitesimal version of the general task of gate simulation. We present a Lie-theoretic approach to Hamiltonian simulation and gate simulation. From this, we derive lower bounds on the time complexity in the $n$-qubit case, generalizing known results to both even and odd $n$. To achieve this we develop a generalization of the so-called magic basis for two-qubits. As a corollary, we note a connection to entanglement measures of concurrence-type.

The possibility of using a solid medium to store few-photon laser pulses as coupled excitations between light and matter is investigated. The role of inhomogeneous broadening and nonadiabaticity are considered, and conditions governing the feasibility of the scheme are derived. The merits of a number of classes of solid are examined.

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); Phys. Rev. A65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the $1s2s{}^{3}S$ state of helium that generates the many-body electron density and shown that the corresponding $2s$ Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem.

Absolute total cross sections (TCS’s) for $0.5–370\text{−}\mathrm{eV}$ electrons scattered by nitrogen trifluoride $\left({\mathrm{NF}}_3\right)$ molecules have been measured using a linear transmission method under single collision conditions. It was found that the TCS energy function for ${\mathrm{NF}}_3$ is dominated with two pronounced enhancements: one resonantlike centered between 2 and $3\mathrm{eV}$ with the maximum value of $28\times {10}^{-20}{\mathrm{m}}^2$ followed with a minimum at around $7–12\mathrm{eV}\left(\sim 17\times {10}^{-20}{\mathrm{m}}^2\right)$, and the second much broader enhancement located around $40\mathrm{eV}$ ($19\times {10}^{-20}{\mathrm{m}}^2$ in the maximum). The low-energy enhancement is superimposed with some weak features located near 1.8, 2.2, and $2.8\mathrm{eV}$. The integral elastic cross section has been calculated at intermediate energies using an independent atom method with a static plus polarization model potential. The cross section for ionization has been computed as well using the binary-encounter-Bethe approach. The sum of calculated cross sections reasonably reproduces the intermediate-energy experimental TCS, with respect to the shape and value. The TCS for ${\mathrm{NF}}_3$ is also compared with the TCS for ammonia $\left({\mathrm{NH}}_3\right)$ which was supplementary measured and the effect of substitution of fluorine atoms for hydrogen (perfluorination effect) is demonstrated and discussed.

The outermost, singly ionized valence state of ${\mathrm{N}}_2$, the $X{}^2\Sigma _g^{+}$ state, is investigated in detail as a function of the photon frequency bandwidth for core excitation to the $\mathrm{N}1s\to {\pi }^{*}$ resonance, where the photon frequency is tuned in between the first two vibrational levels of this bound intermediate electronic state. We find a strong, nontrivial dependence of the resulting resonant photoemission spectral profile on the monochromator function width and the frequency of its peak position. For narrow bandwidth excitation we observe a well resolved vibrational fine structure in the final electron spectrum, which for somewhat broader bandwidths gets smeared out into a continuous structure. For even broader monochromator bandwidths, it converts again into a well resolved vibrational progression. In addition, spectral features appearing below the adiabatic transition energy of the ground state of $\mathrm{N}_2{}^{+}$ are observed for broadband excitation. A model taking into account the interplay of the partial scattering cross section with the spectral function is presented and applied to the $X{}^2\Sigma _g^{+}$ final state of $\mathrm{N}_2{}^{+}$.

Cold and ultracold collisions involving rotationally hot $\mathrm{CO}$ molecules are investigated using quantum mechanical coupled channel, coupled states, and effective potential scattering formulations. Quenching rate coefficients are given for initial rotational levels near the dissociation threshold. The stability of the $\mathrm{CO}$ “super rotors” against collisional decay is compared to previous investigations involving homonuclear molecules. It is found that quasiresonant transitions provide a significantly stronger contribution to the total relaxation rate than in the comparable case of ${\mathrm{O}}_2$. As in the case of ${\mathrm{H}}_2$, sharp structures in the distribution of total quenching rate coefficients are found at rotational levels where quasiresonant scattering is not allowed.

In this work we have measured the electronic energy loss of ${}^9\mathrm{Be}$ and ${}^{11}\mathrm{B}$ ions for the $⟨100⟩$ and $⟨110⟩$ directions in $\mathrm{Si}$ as a function of the incident ion energy. The channeling measurements cover a wide energy range between $100\mathrm{keV}∕\mathrm{amu}$ and $1\mathrm{MeV}∕\mathrm{amu}$. The Rutherford backscattering technique has been employed in the present experiments. An overall compilation of channeling energy loss values for several ions, including those for $\mathrm{He}$, $\mathrm{Li}$, and $\mathrm{O}$ measured previously, provides a clear picture of the Barkas contribution to the stopping power due to valence electrons in the present energy regime. A maximum of the relative contribution occurs for $\mathrm{Be}$ ions around $250\mathrm{keV}∕\mathrm{amu}$ while a saturation effect is observed for heavier ions. These results are interpreted in terms of a self-consistent nonlinear calculation based on the transport cross-section approach together with the unitary convolution approximation model, which describe the present data reasonably well at high projectile energies.

We investigate the relaxation effects on the quantum dynamics in a two-state molecular system interacting with a single-mode strongly amplitude-squeezed coherent field using the second-order Monte Carlo wave-function method. The molecular population inversion (collapse-revival behavior of Rabi oscillations) is known to show the echoes after each revival, which are referred to as ringing revivals, in the case of strongly squeezed coherent fields with oscillatory photon-number distributions due to the phase-space interference effect. Two types of relaxation effects, i.e., cavity relaxation (the dissipation of an internal single mode to outer mode) and molecular coherent (phase) relaxation caused by nuclear vibrations on ringing revivals are investigated from the viewpoint of the quantum-phase dynamics using the quasiprobability ($Q$ function) distribution of a single-mode field and the off-diagonal molecular density matrix $\mid {\rho }_{\mathrm{elec}1,2}\left(t\right)\mid$. It turns out that the molecular phase relaxation attenuates both the entire revival-collapse behavior and the increase in $\mid {\rho }_{\mathrm{elec}1,2}\left(t\right)\mid$ during the quiescent region, whereas a very slight cavity relaxation particularly suppresses the echoes in ringing revivals more significantly than the first revival but hardly changes a primary variation in envelope of $\mid {\rho }_{\mathrm{elec}1,2}\left(t\right)\mid$ in the nonrelaxation case.

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.

We analyze molecular bound states of atomic quantum gases near a Feshbach resonance. A simple, renormalizable field theoretic model is shown to have exact solutions in the two-body sector, whose binding energy agrees well with observed experimental results in both Bosonic and Fermionic cases. These solutions, which interpolate between BEC and BCS theories, also provide a more general variational ansatz for resonant superfluidity and related problems.

Dynamic instability in the transmission field of an optical ring cavity containing three-level $\Lambda$-type rubidium atoms is studied in detail both experimentally and theoretically. The onset and periodicity of such dynamic oscillations in the cavity field can be controlled by the experimental parameters, such as intensity and frequency detuning of the coupling field and∕or cavity field. Such nonlinear dynamic behavior is caused by competition between optical saturation of the cavity field and optical population pumping by the coupling field in the three-level atomic system.

The thermodynamic properties of $N$ two-level atoms coupled to radiation field are analyzed taking into account the diamagnetic term by a slight modification to the usual approach to quantizing the electromagnetic field. Following this procedure, we are able to solve the discrepancy originating in the use of different states as a basis for expressing the state of radiation field. We develop a perturbative expansion of partition function and a simple analytic expression is found for a high coupling constant. We show that, in this limit, the interaction of independent atomic spins with a single photon mode can be interpreted as an effective spin-spin interaction of long range nature. Even in this approach, if the diamagnetic term is taken into account, a phase transition at nonzero temperature cannot occur due to sum-rule arguments.

We evidence experimentally that the linewidth-enhancement factor $\alpha$ can take a rather large value ($\alpha \approx 1$) for a nonsemiconductor laser, here a ${\mathrm{Nd}}^{3+}$: YAG microchip laser. This measure is performed using an original and simple method adapted to this kind of laser and based on the variations of the laser relaxation frequency when the laser is subjected to an optical feedback.

We derive the general formula for Lorentz-transformed spin density matrix. It is shown that an appropriate Lorentz transformation can produce totally unpolarized state out of pure one. Further properties, as depurification by an arbitrary Lorentz boost and its relation to the localization properties are also discussed.

In this Brief Report we investigate the time evolution of entanglement in two-mode Bose-Einstein condensates (BEC’s) with various parameters of the scattering lengths of interatoms collisions, Josephson coupling strength, and initial states. The degree of entanglement increases by strengthening the tunnel coupling and keeping the balance of the collision interaction. In the latter stage we show that the two-mode BEC’s can be used for preparing the Greenberger-Home-Zeilinger state.

The Einstein-Podolsky-Rosen paradox and quantum entanglement are at the heart of quantum mechanics. Here we show that single-pass traveling-wave second-harmonic generation can be used to demonstrate both entanglement and the paradox with continuous variables that are analogous to the position and momentum of the original proposal.