The eigenstates of nonrelativistic two-, three-, four-, and six-valence-electron atoms are classified according to their transformation properties under symmetry operations. In energy-favorable geometrical arrangements of the electrons, the spatial distribution of the wave function is constrained by the demand of invariance under rotation, inversion and permutation of particles. For a given term, the symmetry constraints may leave the energy-favorable arrangement accessible or inaccessible. In the latter case the term is not expected to belong to the low-energy part of the spectrum. Contrary, in the former case with no symmetry-induced inherent nodal surface in the multidimensional coordinate space of the multielectron wave function, the term is expected to belong to the low-energy part of the spectrum. The symmetry-based classification is confirmed by recent calculations.

We reveal that a repulsive Bose-Einstein condensate confined in a three-dimensional (3D) optical lattice supports vortex states which are spatially localized in all three dimensions and possess highly nontrivial particle flow. We demonstrate that the lattice stabilizes extended vortex lines that are normally unstable to transverse modulations, and show that stable vortices localized inside the 3D lattice may be easily generated via a nonadiabatic loading process.

The phase transition from a superfluid to a Mott insulator has been observed in a ${}^{23}\mathrm{Na}$ Bose-Einstein condensate. A dye laser detuned $\approx 5\mathrm{nm}$ red of the Na $3{}^{2}S\to 3{}^{2}P_{1∕2}$ transition was used to form the three-dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the time scale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the ${\mathrm{Na}}_2\left(1\right){}^3\Sigma _g^{+}$ state.

By driving photoassociation transitions, we form electronically excited molecules $\left({\mathrm{Na}}_2^{*}\right)$ from ultracold $(50–300\mu \mathrm{K})$ Na atoms. Using a second laser to drive transitions from the excited state to a level in the molecular ground state, we are able to split the photoassociation line and observe features with a width smaller than the natural linewidth of the excited molecular state. The quantum interference which gives rise to this effect is analogous to that which leads to electromagnetically induced transparency in three-level atomic $\Lambda$ systems, but here one of the ground states is a pair of free atoms while the other is a bound molecule. The linewidth is limited primarily by the finite temperature of the atoms.

We propose a scheme for realizing quantum gates [controlled-NOT (CNOT) and Toffoli] using a two-level quantum system by means of a pulsed bias. We show how to realize a CNOT gate using a two-qubit, two-level coupled system and a Toffoli gate using a three-qubit, two-level coupled system. For the CNOT gate, we show how to reduce the $4\times 4$ Hamiltonian of the coupled system to a $2\times 2$ Hamiltonian in order to solve for parameter values of the system. When these values are substituted into the coupled system equations for the two-qubit system, the simulation results confirm the CNOT gate operation. We further demonstrate our proposed scheme for a CNOT gate operation using a multilevel system of two coupled superconducting quantum interference devices as a particular example. We next use the same approach to implement a Toffoli gate using a three-qubit system.

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

A concept of CP-violating ($T$,$P$-odd) permanent molecular magnetic moments ${\mu }^{CP}$ is introduced. We relate the moments to the electric dipole moment of electron (eEDM) and estimate ${\mu }^{CP}$ for several diamagnetic polar molecules. The moments exhibit a steep, $Z^5$, scaling with the nuclear charge $Z$ of the heavier molecular constituent. A measurement of the CP-violating magnetization of a polarized sample of heavy molecules may improve the present limit on eEDM by several orders of magnitude.

In this paper, we give a characterization of all the unitary transformations that can be synthesized in a given time for a two-qubit system in the presence of general time varying coupling tensor. This characterization helps to compute the minimum time and the shortest pulse sequence for generating a general two-qubit transformation under nonstationary interactions. The methods presented here can be applied in design of time optimal pulse sequences for transferring coherence and polarization between coupled spins with time varying couplings as in solid-state NMR under magic angle spinning.

An efficient semiclassical optimal control theory applicable to multidimensional systems is formulated for controlling wave packet dynamics on a single adiabatic potential energy surface. The approach combines advantages of different formulations of optimal control theory: quantum and classical on one hand and global and local on the other. Numerical applications to the control of HCN-CNH isomerization demonstrate that this theory can provide an efficient tool to manipulate molecular dynamics of many degrees of freedom by laser pulses.

We address the question as to whether an entangled state that satisfies local realism will give a violation of the same after entanglement swapping in a suitable scenario. We consider such a possibility as a kind of superadditivity in nonclassicality. Importantly, it will indicate that checking for violation of local realism, in the state obtained after entanglement swapping, can be a method for detecting entanglement in the input state of the swapping procedure. We investigate various entanglement swapping schemes, which involve mixed initial states. The strength of violation of local realism by the state obtained after entanglement swapping is compared with the one for the input states. We obtain a kind of superadditivity of violation of local realism for Werner states, consequent upon entanglement swapping involving Greenberger-Horne-Zeilinger-state measurements. We also discuss whether entanglement swapping of specific states may be used in quantum repeaters with a substantially reduced need to perform the entanglement distillation step.

Density-wave structures are studied in a quasi-one-dimensional atomic gas mixture of one-component bosons and two-component fermions using the mean-field approximation at zero temperature. Owing to the Peierls instability in the fermion system, the ground state of the system shows a fermion density wave and periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in each component, and their phase difference distinguishes two types of ground states, the in-phase and the out-phase density waves. In this paper, a self-consistent method is presented to treat the density-wave states in a boson-fermion mixture with two-component fermions. The analysis of the effective potential and the interaction energies shows that the density waves appearing in the ground state are in phase or out of phase depending on the strength of the interfermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density wave of fermions, but, in the case of out of phase, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants.

We consider a mixture of fermionic and bosonic atoms near interspecies Feshbach resonances, which have been observed recently in ${}^6\mathrm{Li}\text{−}{}^{23}\mathrm{Na}$ mixture by the MIT group and in ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ mixture by the JILA group. We point out that the fermion-boson bound state, namely the heteronuclear molecules, will coexist with the fermionic atoms in a wide parameter region, and the attraction between fermionic atoms and molecules will lead to the formation of atom-molecule pairs. The pairing structure is studied in detail, and, in particular, we highlight the possible realization of the Fulde-Ferrel-Larkin-Ovchinnikov state in this system.

The entanglement in a general Heisenberg antiferromagnetic chain of arbitrary spin-$s$ is investigated. The entanglement is witnessed by the thermal energy which equals the minimum energy of any separable state. There is a characteristic temperature below that an entangled thermal state exists. The characteristic temperature for thermal entanglement is increased with spin $s$. When the total number of lattice is increased, the characteristic temperature decreases and then approaches a constant. This effect shows that the thermal entanglement can be detected in a real solid state system of larger number of lattices for finite temperature. The comparison of negativity and entanglement witness is obtained from the separability of the unentangled states. It is found that the thermal energy provides a sufficient condition for the existence of the thermal entanglement in a spin-$s$ antiferromagnetic Heisenberg chain.

In this paper, we propose a scheme to generate two-ion maximally entangled states from either pure product states or mixed states using linear optics. Our new scheme is mainly based on the ionic interference. Because the proposed scheme can generate pure maximally entangled states from mixed states, we denote it as a purificationlike generation scheme. The scheme does not need a Bell state analyzer as the existing entanglement generation schemes do, it also avoids the difficulty of synchronizing the arrival time of the two scattered photons faced by the existing schemes, thus the proposed new entanglement generation scheme can be implemented more easily in practice.

By means of a $\mathrm{mod}\left(N\right)$-invariant operator basis, $s$-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of $s$-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.

Quantum information is a valuable resource which can be encrypted in order to protect it. We consider the size of the one-time pad that is needed to protect quantum information in a number of cases. The situation is dramatically different from the classical case: we prove that one can recycle the one-time pad without compromising security. The protocol for recycling relies on detecting whether eavesdropping has occurred, and further relies on the fact that information contained in the encrypted quantum state cannot be fully accessed. We prove the security of recycling rates when authentication of quantum states is accepted, and when it is rejected. We note that recycling schemes respect a general law of cryptography which we introduce relating the size of private keys, sent qubits, and encrypted messages. We discuss applications for encryption of quantum information in light of the resources needed for teleportation. Potential uses include the protection of resources such as entanglement and the memory of quantum computers. We also introduce another application: encrypted secret sharing and find that one can even reuse the private key that is used to encrypt a classical message. In a number of cases, one finds that the amount of private key needed for authentication or protection is smaller than in the general case.

Collinear collisions, with exponential repulsive potential, between a mass point and a harmonic oscillator are studied in the limit of high frequency. Multiple encounters during single collisions and an arbitrary value of the mass parameter $m$ are permitted. Methods are analytical and numerical. The main results are the following: For an initially resting oscillator the energy $E$ after the collision decays exponentially with frequency. The limiting decay constant for high frequency is independent of $m$ and identical to the golden rule prediction $2\pi ∕\lambda$ where ${\lambda }^{-1}$ is a dimensionless frequency. In the high-frequency domain the energy of the oscillator has the form $E=2{\pi }^2\varphi {\left(m\right)}^2\exp \{-2\pi ∕\lambda \}$ where $\varphi \left(m\right)=2m-\frac{2}{3}(1+\ln 4)m^2+\cdots$. The first term is the golden rule result, and the second term is new. A series of polynomials ${\varphi }_n$ is constructed that converges to $\varphi \left(m\right)$. It is suggested that $\varphi \left(m\right)$ is an entire function of the complex variable $m$ which has the form of an infinite product $\varphi \left(m\right)=2m\prod (1-m∕m_n)$ where the $m_n$ are the positive roots of $\varphi \left(m\right)$. The first 15 roots have been determined numerically which suggests an asymptotic behavior $\sqrt{m_n}\sim an+b$. Agreement with the numerical data is excellent.

We show that very large nonlocal nonlinear interactions between pairs of colliding slow-light pulses can be realized in atomic vapors in the regime of electromagnetically induced transparency. These nonlinearities are mediated by strong, long-range dipole-dipole interactions between Rydberg states of the multilevel atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of $\pi$ even for weakly focused single-photon pulses, thereby allowing a deterministic realization of the photonic phase gate.

A mean field theory for Raman superradiance (SR) with recoil is presented, where the typical SR signatures are recovered, such as quadratic dependence of the intensity on the number of atoms and inverse proportionality of the time scale to the number of atoms. A comparison with recent experiments and theories on Rayleigh SR and collective atomic recoil lasing (CARL) are included. The role of recoil is shown to be in the decay of atomic coherence and breaking of the symmetry of the SR end-fire modes.

A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the $N$ agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement ${\sigma }_x\otimes {\sigma }_x$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. With a new notation for the multipartite entanglement, the sender need only publish two bits of classical information for each measurement, which reduces the information exchanged largely.