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We present a proposal to produce bipartite and tripartite entanglement in a hybrid magnon-cavity QED system. Two macroscopic yttrium iron garnet (YIG) spheres are coupled to a single-mode microwave cavity via magnetic dipole interaction, while the cavity photons are generated via the two photon process induced by a pump field. Using the mean field theory, we show that the second order nonlinearity can result in strong bipartite entanglement between cavity photons and magnonic modes under two conditions, i.e., $\delta_c \delta_{m}=2g^2$ and $\delta_c=-\delta_{m}$. For the later one, we also show the possibility for producing the bipartite entanglement between two magnonic modes and tripartite entanglement among the cavity photons and two magnonic modes. Combining these two conditions, we further derive a third condition, i.e., $\delta_m^2-\phi^2+2g^2=0$, where the tripartite entanglement can be achieved when two magnonic modes have different resonant frequencies.

We present a new paradigm in the field of cavity QED by bringing out remarkable features associated with the avoided crossing of the dressed state levels of the Jaynes Cummings model. We demonstrate how the parametric couplings, realized by a second order nonlinearity in the cavity, can turn the crossing of dressed states into avoided crossings. We show how one can generate coherence between the avoided crossing of dressed states. Such coherences result, for example, in quantum beats in the excitation probability of the qubit. The quality of quantum beats can be considerably improved by adiabatically turning on the parametric interaction. We show how these avoided crossings can be used to generate superpositions of even or odd Fock states with the remarkable property of equal weights for the states in superposition. The fidelity of generation is more than 95\%. In addition, we show strong entanglement between the cavity field and the qubit with the concurrence parameter exceeding 90\%.

In this paper, we are concerned with the asymptotic behavior of solutions to the Cauchy problem (or initial-boundary value problem) of one-dimensional Keller-Segel model. For the Cauchy problem, we prove that the solutions time-asymptotically converge to the nonlinear diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which is derived by Darcy's law, as in [11, 28]. For the initial-boundary value problem, we consider two cases: Dirichlet boundary condition and null Neumann boundary condition on (u, \rho). In the case of Dirichlet boundary condition, similar to the Cauchy problem, the asymptotic profile is still the self-similar solution of the corresponding parabolic equation, which is derived by Darcy's law, thus we only need to deal with boundary effect. In the case of null-Neumann boundary condition, the global existence and asymptotic behavior of solutions near constant steady states are established. The proof is based on the elementary energy method and some delicate analysis of the corresponding asymptotic profiles., Comment: 33 pages

We theoretically study the quantum interference induced photon blockade phenomenon in atom cavity QED system, where the destructive interference between two different transition pathways prohibits the two-photon excitation. Here, we first explore the single atom cavity QED system via an atom or cavity drive. We show that the cavity-driven case will lead to the quantum interference induced photon blockade under a specific condition, but the atom driven case can't result in such interference induced photon blockade. Then, we investigate the two atoms case, and find that an additional transition pathway appears in the atom-driven case. We show that this additional transition pathway results in the quantum interference induced photon blockade only if the atomic resonant frequency is different from the cavity mode frequency. Moreover, in this case, the condition for realizing the interference induced photon blockade is independent of the system's intrinsic parameters, which can be used to generate antibunched photon source both in weak and strong coupling regimes.

We investigate a single atom cavity-QED system directly driven by a broadband squeezed light. We demonstrate how the squeezed radiation can be used to sense the presence of a single atom in a cavity. This happens by transferring one of the photons from the field in a state with even number of photons to the atom and thereby populating odd number Fock states. Specifically, the presence of the atom is sensed by remarkable changing in the presence of one photon and the loss of squeezing of the cavity field. A complete study of quantum fluctuations and the excitation of multiphoton transitions is given.

We present a study of collective multi-photon blockade in coherently driven atoms in a single mode cavity. Considering two atoms strongly coupled to an optical cavity, we show that the two-photon blockade with two-photon anti-bunching, and the three-photon blockade with three-photon anti-bunching can be observed simultaneously. The three-photon blockade probes both dressed states in the two photon and three photon spaces. The two photon and three photon blockades strongly depend on the location of two atoms in the strong coupling regime. The asymmetry in the atom-cavity coupling constants opens new pathways for multiphoton blockade which is also shown to be sensitive to the atomic decay and pumping strengths. The work presented here predicts many new quantum statistical features due to the collective behavior of atoms and can be useful to generate non-classical photon pairs.

We examine a Kerr phase gate in a semiconductor quantum well structure based on the tunnelling interference effect. We show that there exist a specific signal field detuning, at which the absorption/amplification of the probe field will be eliminated with the increase of the tunnelling interference. Simultaneously, the probe field will acquire a -\pi phase shift at the exit of the medium. We demonstrate with numerical simulations that a complete 180^\circ phase rotation for the probe field at the exit of the medium is achieved, which may result in many applications in information science and telecommunication.