In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even when considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.

We study experimentally interaction-driven spin oscillations in optical lattices in the presence of an off-resonant microwave field. We show that the energy shift induced by this microwave field can be used to control the spin oscillations by tuning the system either into resonance to achieve near-unity contrast or far away from resonance to suppress the oscillations. Finally, we propose a scheme based on this technique to create a flat sample with either singly or doubly occupied sites, starting from an inhomogeneous Mott insulator, where singly and doubly occupied sites coexist.

We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model.

We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states.

We investigate the Bell-type inequalities of graph states. In this paper, Bell-type inequalities can be derived based on two kinds of the associated subgraphs of the graph states. First, the star subgraphs lead to the maximal violation of the modified Seevinck-Svetlichny inequalities. Second, cycle subgraphs lead to maximal violation of Bell-type inequalities. As a result, once the associated graph of a graph state is given, the corresponding Bell operators can be immediatedly determined using stabilizing generators. In the above Bell-type inequalities, two measurement settings for each party are required.

A generalized teleportation protocol (GTP) for $N$ qubits is presented, where the teleportation channels are nonmaximally entangled and all the free parameters of the protocol are considered: Alice’s measurement basis, her sets of acceptable results, and Bob’s unitary operations. The full range of fidelity $\left(F\right)$ of the teleported state and the probability of success $\left(P_{\mathit{suc}}\right)$ to obtain a given fidelity are achieved by changing these free parameters. A channel efficiency bound is found, where one can determine how to divide it between $F$ and $P_{\mathit{suc}}$. A one-qubit formulation is presented and then expanded to $N$ qubits. A proposed experimental setup that implements the GTP is given using linear optics.

We consider the problem of evaluating the entanglement of non-Gaussian mixed states generated by photon subtraction from entangled squeezed states. The entanglement measures we use are the negativity and the logarithmic negativity. These measures possess the unusual property of being computable with linear algebra packages even for high-dimensional quantum systems. We numerically evaluate these measures for the non-Gaussian mixed states which are generated by photon subtraction with on/off photon detectors. The results are compared with the behavior of certain operational measures, namely the teleportation fidelity and the mutual information in the dense coding scheme. It is found that all of these results are mutually consistent, in the sense that whenever the enhancement is seen in terms of the operational measures, the negativity and the logarithmic negativity are also enhanced.

The possibility of obtaining the initial pure state in a usual Stern-Gerlach experiment through the recombination of the two emerging beams is investigated. We have extended the previous work of Englert, Schwinger, and Scully [Found Phys. 18, 1045 (1988)] including the fluctuations of the magnetic field generated by a properly chosen magnet. As a result we obtained an attenuation factor to the possible revival of coherence when the beams are perfectly recombined. When the source of the magnetic field is a superconducting quantum interference device (SQUID) the attenuation factor can be controlled by external circuits and the spin decoherence directly measured. For the proposed SQUID with dimensions in the scale of microns the attenuation factor has been shown unimportant when compared with the interaction time of the spin with the magnet.

Photoionization cross sections and angular distributions of silicon tetrafluoride have been calculated in the framework of the time-dependent density-functional theory approach. Both valence and inner shell ionizations have been considered in an extended photon energy range. Calculations have been carried out by using two different exchange-correlation (xc) potentials characterized by the correct asymptotic behavior. Theoretical results obtained with both the van Leeuwen–Baerends and statistical average of orbital potentials (SAOP) xc potentials are compared with photoabsorption, photoionization, and electron-scattering experiments as well as with previous theoretical calculations. It is suggested that even if both xc potentials provide a reasonably good description of the photoionization dynamics, correlation effects are phenomenologically better accounted for by the SAOP xc potential. Overall, the good accuracy attained with the linear combination of atomic orbitals-time dependent density-functional theory method in reproducing the experimental findings for ${\mathrm{SiF}}_4$ makes it a promising and powerful method for the characterization of the photoionization dynamics from medium and large-size molecules.

We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to $4\mathrm{T}$. We have followed the radiative cascade from completely $l,m$ mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\mid m\mid \sim n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\lesssim 20$. For higher $n$ manifolds, the electrons in the most negative $m$ states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\sim 35$ generated in antihydrogen experiments at $4\mathrm{K}$ will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative $m$ states due to the fact that only $\mid \Delta m\mid +\mid \Delta \pi \mid =1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\mid m\mid$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\gtrsim 20$.

We describe a simple experimental technique which allows us to store a single ${}^{87}\mathrm{Rb}$ atom in an optical dipole trap. Due to light-induced two-body collisions during the loading stage of the trap the maximum number of captured atoms is locked to one. This collisional blockade effect is confirmed by the observation of photon antibunching in the detected fluorescence light. The spectral properties of single photons emitted by the atom were studied with a narrow-band scanning cavity. We find that the atomic fluorescence spectrum is dominated by the spectral width of the exciting laser light field. In addition we observe a spectral broadening of the atomic fluorescence light due to the Doppler effect. This allows us to determine the mean kinetic energy of the trapped atom corresponding to a temperature of $105\mu \mathrm{K}$. This simple single-atom trap is the key element for the generation of atom-photon entanglement required for future applications in quantum communication and a first loophole-free test of Bell’s inequality.

The Friedel sum rule is generalized to relativistic systems of spin-$\frac{1}{2}$ particles in two dimensions. The change in energy due to the presence of an impurity is studied. The relation of the sum rule with the relativistic Levinson theorem is presented. Density oscillations in such systems are discussed. Since the Friedel theorem has been of major importance in understanding the impurity scattering in materials, the present results would be helpful to explain some phenomena in two-dimensional fermionic many body systems.

The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The semiclassical Casimir energies so defined coincide with those of zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are related to nonuniversal subtractions in the spectral density. The sign of the Casimir energy of a scalar field on a smooth manifold is estimated by the sign of the contribution due to the shortest periodic rays only. Demanding continuity of the Casimir energy under small deformations of the manifold, the method is extended to integrable systems. The Casimir energy of a massless scalar field on a manifold with boundaries includes contributions due to periodic rays that lie entirely within the boundaries. These contributions in general depend on the boundary conditions. Although the Casimir energy due to a massless scalar field may be sensitive to the physical dimensions of manifolds with boundary. In favorable cases its sign can, contrary to conventional wisdom, be inferred without calculation of the Casimir energy.

We have theoretically investigated the tuning of Casimir forces by means of an external magnetic field. We have found that the Casimir force between two homogeneous slabs can be tuned by the external field in two ways. One is to add cap layers to the two dielectric slabs. The other is to insert a new dielectric layer into the cavity made of the two slabs. Since the dielectric constants of the materials used as the cap layers or the inserted layers depend on the external magnetic field, the Casimir force can be modified significantly by the external magnetic field. Our results show that it is possible to control the Casimir interaction in the fabrication of materials by an external field.

We propose two quantum direct communication (QDC) protocols with user authentication. Users can identify each other by checking the correlation of Greenberger-Horne-Zeilinger (GHZ) states. Alice can directly send a secret message to Bob without any previously shared secret using the remaining GHZ states after authentication. Our second QDC protocol can be used even though there is no quantum link between Alice and Bob. The security of the transmitted message is guaranteed by properties of entanglement of GHZ states.

$R$-matrix method is used to calculate elastic differential, integral, and momentum transfer cross sections for electron-$\mathrm{S}{\mathrm{O}}_2$ collision. The electron-impact excitation cross sections for first seven low-lying electronic excited states of $\mathrm{S}{\mathrm{O}}_2$ molecule from the ground state of $\mathrm{S}{\mathrm{O}}_2$ molecule have been calculated for the first time. Sixteen low-lying electronic states of $\mathrm{S}{\mathrm{O}}_2$ molecule are included in the close coupling expansion of the wave function of the entire scattering system, which have vertical excitation energies up to $10.51\mathrm{eV}$. Configuration-interaction (CI) wave functions are used to calculate these excitation energies. In our CI model, we keep the core 14 electrons frozen in doubly occupied molecular orbitals $1a_1$, $2a_1$, $3a_1$, $4a_1$, $1b_1$, $1b_2$, $2b_2$ and the remaining 18 electrons span the relevant active space: $5a_1$, $6a_1$, $7a_1$, $8a_1$, $9a_1$, $2b_1$, $3b_1$, $3b_2$, $4b_2$, $5b_2$, $6b_2$, and $1a_2$. Our calculated dipole moment of the ground state of $\mathrm{S}{\mathrm{O}}_2$ at its equilibrium geometry is $0.79\mathrm{a.u.}$, which is in reasonable agreement with the corresponding experimental value $0.64\mathrm{a.u.}$ Our calculations detect one bound $\mathrm{S}\mathrm{O}_2{}^{-}$ state $\left({}^2\mathrm{B}_1\right)$ at the equilibrium geometry of $\mathrm{S}{\mathrm{O}}_2$ molecule. Both shape as well as core-excited shape resonances have been identified in the present work and are correlated with the experimental results on dissociative electron attachment study. A detailed analysis of resonances is provided. Cross sections are reported for the electron impact energy range $0–15\mathrm{eV}$. All cross section calculations are performed in the fixed-nuclei approximation at the experimental equilibrium geometry of the ground state of $\mathrm{S}{\mathrm{O}}_2$ molecule. We have also investigated dependence of resonances on the geometry of $\mathrm{S}{\mathrm{O}}_2$ molecule to probe the possible pathways for dissociation of resulting negative ion upon electron attachment. We have excellent agreement of differential, elastic integral, and momentum transfer cross sections calculated in the 16-state $R$-matrix approximation with the available experimental results for electron-impact energy range $0–15\mathrm{eV}$. Our resonant peaks correlate well with the peaks observed in the study of dissociative electron attachment (DEA) of electron with $\mathrm{S}{\mathrm{O}}_2$ molecule.

The generalized oscillator strengths for the valence-shell excitations to $3p^5(4s,4s^{\prime })$ and $3p^5(4p,4p^{\prime })$ of argon were measured by an angle-resolved fast-electron energy-loss spectrometer at an incident electron energy of $2500\mathrm{eV}$. The transition multipolarities for these excitations were elucidated with the help of the calculated intermediate coupling coefficients using the COWAN code. The generalized oscillator strength profiles for the electric dipole excitations to $3p^5(4s,4s^{\prime })$, the electric quadrupole and monopole excitations to $3p^5(4p,4p^{\prime })$ were analyzed and their positions of the extrema were determined. Furthermore, the generalized oscillator strength of the electric quadrupole excitation in $3p\to 4p$ was determined and its profile is in general agreement with the theoretical calculations. However, the generalized oscillator strength profile of the electric monopole excitation in $3p\to 4p$ is different from the theoretical calculations.

A detailed investigation has been carried out of ${\mathrm{N}}_2$ molecules in intense 55 and $220\mathrm{fs}$, linear and circular polarized, $790\mathrm{nm}$ laser pulses. Using an intensity selective scanning technique, ionization, dissociation, and dissociative ionization channels have been studied. Remarkably similar enhancements of signal with linear polarization observed for double ionization and dissociation channels demonstrate the dominance of dynamic alignment over rescattering effects. Fragmentation energies from dissociative ionization are reasonably well reproduced by classical trajectory calculations, the higher charged fragments displaying evidence of post dissociative ionization.