We theoretically investigate the response of a two-component Fermi gas to vector potentials that couple separately to the two spin components. Such vector potentials may be implemented in ultracold atomic gases using optically dressed states. Our study indicates that light-induced gauge potentials may be used to probe the properties of the interacting ultracold Fermi gas, providing, among other things, ways to measure the superfluid density and the strength of pairing.

We derive a first-order differential equation for the decoherence of an orbital angular momentum entangled biphoton state propagating through a turbulent atmosphere. The derivation is based on the distortion that orbital angular momentum states experience due to propagation through a thin sheet of turbulent atmosphere. This distortion is treated as an infinitesimal transformation leading to a first-order differential equation, which we call an infinitesimal propagation equation. The equation is applied to a simple qubit case to show how the entanglement decays.

The spontaneous emission spectrum of a three-level $\Lambda$-type atom driven by a microwave field was studied. For the two transitions coupled to the same modified reservoir, we discussed the influence of photonic band gap and Rabi frequency of the microwave field on the emission spectrum. The emission spectrum is given for different locations of the upper band-edge frequency. With the transition frequencies moving from outside the band gap to inside, the number of peaks decreases in the emission spectrum and the multipeak structure of spectral line is finally replaced by a strong non-Lorentzian shape. With increase of the Rabi frequency of the microwave field, we find the spectral line changes from a multipeak structure to a two-peak structure, originating from the inhibition of spontaneous emission for the corresponding decay channel.

We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in the purification of different states. This approach enables us to achieve analytical expressions of the two measures for some quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-$2$ mixed states of $4\times 2$ systems. Moreover, we apply the scheme to characterize fully the dynamic behavior of quantum correlations for the specified physical systems under decoherence.

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases. However, so far, how to detect these quantum phases effectively remains an outstanding challenge. Here, we show that the optical Bragg scattering of cold atoms loaded on optical lattices can be used to detect many quantum phases, which include not only the conventional superfluid and Mott insulating phases, but also other important phases, such as various kinds of charge density wave (CDW), valence bond solid (VBS), CDW supersolid (CDW-SS) and Valence bond supersolid (VB-SS).

The physical mechanism underlying scattering properties of matter-wave gap solitons (GSs) by linear-optical-lattice defects is investigated. The occurrence of repeated reflection, transmission, and trapping regions for increasing strengths of an optical-lattice defect are shown to be due to resonances with impurity modes inside the defect potential with chemical potentials and numbers of atoms matching corresponding quantities of the incoming GSs. For small amplitude GSs the number of these resonances coincides with the number of bound states existing in the defect potential for the given defect strength. The dependence of the positions and widths of the transmission resonant peaks on incoming velocities is investigated by means of defect-mode analysis and effective-mass theory. The comparisons with direct integrations of the Gross-Pitaevskii equation provide good agreement confirming the correctness of our approach. Multiple resonant transmissions through arrays of optical lattice defects are also investigated and the possibility of using them for very precise GS dynamical filters is also suggested.

We demonstrate that directed transport of bright solitons formed in a quasi-one-dimensional Bose-Einstein condensate can be reliably controlled by tailoring a weak optical lattice potential, biharmonic in both space and time, in accordance with the degree of symmetry breaking mechanism. By considering the regime where matter-wave solitons are narrow compared to the lattice period, (i) we propose an analytical estimate for the dependence of the directed soliton current on the biharmonic potential parameters that is in good agreement with numerical experiments, and (ii) we show that the dependence of the directed soliton current on the number of atoms is a consequence of the ratchet universality.

We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.

We investigate the generation of continuous-variable (CV) entanglement of two separated atomic ensembles in coupled cavities. We find that under certain conditions, the entanglement between the two ensembles is gained periodically when the three-level $\Lambda$-type atoms in each ensemble dispersively interact with one classical field and one cavity mode. Generation of the entangled state does not completely depend on the cavity photon number. In addition, the effect of decoherence can be suppressed effectively.

Recent numerical investigations [K. Pál and T. Vértesi, Phys. Rev. A 82, 022116 (2010)] suggest that the I3322 inequality, arguably the simplest extremal Bell inequality after the CHSH inequality, has a very rich structure in terms of the entangled states and measurements that maximally violate it. Here we show that for this inequality the maximally entangled state of any dimension achieves the same violation than just a single EPR pair. In contrast, stronger violations can be achieved using higher dimensional states which are less entangled. This shows that the maximally entangled state is not the most nonlocal resource, even when one restricts attention to the most simple extremal Bell inequalities.

Due to electron-nucleus weak interaction, atomic bound states with different parities turn out to be mixed. We discuss a prospective method for measuring the mixing parameter between the nearly degenerate metastable states $1s_{1/2}2s_{1/2}:J=0$ and $1s_{1/2}2p_{1/2}:J=0$ in heliumlike uranium. Our analysis is based on the polarization properties of the photons emitted in the two-photon decays of such states.

We study atom-atom scattering in quasi-one-dimensional geometries with transverse anisotropy. By assuming an $s$-wave pseudopotential of contact interaction, we show that the system would exhibit a single confinement-induced resonance, where the scattering process degenerates to a total reflection as a one-dimensional gas of impenetrable bosons. For a general form of interaction, we present a formal calculation based on the two-channel model and draw the same qualitative conclusion of only one confinement-induced resonance. Our findings are inconsistent with a recent experiment by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], where a splitting of confinement-induced resonances has been observed in an anisotropic quasi-one-dimensional quantum gas of Cs atoms.

The optical bistability of an ultracold atomic ensemble located in a small-volume ultrahigh-finesse optical cavity is investigated. We find that a transverse pumping field can be used to control the bistable behavior of the intracavity photons induced by the input pumping along the cavity axis. This phenomenon can be used as a controllable optical switch.

We propose a robust and scalable scheme to generate an $N$-qubit $W$ state among separated quantum nodes (cavity-QED systems) by using linear optics and postselections. The present scheme inherits the robustness of the Barrett-Kok scheme [S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310(R) (2005)]. The scalability is also ensured in the sense that an arbitrarily large $N$-qubit $W$ state can be generated with a quasipolynomial overhead $~$$2^{O[(\log {}_{2}N){}^2]}$. The process to breed the $W$ states, which we introduce to achieve the scalability, is quite simple and efficient and can be applied for other physical systems.

In this paper, we discuss the atomic states in a vertical optical lattice in proximity of a surface. We study the modifications to the ordinary Wannier-Stark states in the presence of a surface, and we characterize the energy shifts produced by the Casimir-Polder interaction between atom and mirror. In this context, we introduce an effective model describing the finite size of the atom in order to regularize the energy corrections. In addition, the modifications to the energy levels due to a hypothetical non-Newtonian gravitational potential as well as their experimental observability are investigated.

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic $\mathrm{XY}$ spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the $\mathrm{XY}$ model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.

The presence of unique quantum correlations is the core of quantum-information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using correlation functions defined for quasiprobability distributions. In particular, we discuss the possibility of probing the negativity of a quasiprobability by comparing moments of the Wigner function. We show that one must take at least the fourth moments to find the negativity in general and the eighth moments for states with a rotationally invariant Wigner function.