Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson’s high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti-)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.     

Unconventional geometric quantum phase gates with two SQUIDs in a cavity

We present a potential scheme to implement two-qubit quantum phase gates through an unconventional geometric phase shift with two four-level SQUIDs in a cavity. The SQUID qubits undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, acquiring a geometric phase depending conditionally upon the SQUIDs’ states. Under certain conditions, the SQUID qubits are disentangled with the cavity mode and the SQUIDs’ states remain in their ground states during the gate operation, thus the gate is insensitive to both the SQUIDs’ “spontaneous emission” and the cavity decay.     

Van der Waals interactions and Photoelectric Effect in Noncommutative Quantum Mechanics

We calculate the long-range Van der Waals force and the photoelectric cross section in a noncommutative setup. It is argued that non-commutativity effects could not be discerned for the Van der Waals interactions. The result for the photoelectric effect shows deviation from the usual commutative one, which in principle can be used to put bounds on the space-space non-commutativity parameter.     

He-McKellar-Wilkens Effect in Noncommutative Space

The He-McKellar-Wilkens （HMW） effect in non-commutative （NC） space is studied. By solving the Dirac equations on NC space, we obtain topological HMW phase in NC space where the additional terms related to the space non-commutativity are given explicitly.     

Symplectic quantum mechanics

Using the notion of symplectic structure and Weyl (or star) product of non-commutative geometry, we construct unitary representations for the Galilei group and show how to rewrite the Schrödinger equation in phase space. This approach gives rise to a new procedure to derive Wigner functions without the use of the Liouville-von Neumann equation. Applications are presented by deriving the states of linear and nonlinear oscillators in terms of amplitudes of probability in phase space. The notion of coherent states is also discussed in this context.     

On a heuristic point of view related to quantum nonequilibrium statistical mechanics

In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to propose the coherent access by a particle to the available states of a system. By coherent access I mean the possibility for the particle to act as if it is populating more than one microstate at once. This hypothesis has experimental implications, since the thermodynamical probability and, as a consequence, the Bose-Einstein distribution as well as the argument of the Boltzmann factor is modified.     

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the “classical” trajectories is investigated, and we present numerical explorations of some semiclassical quantities.     

Teleportation fidelity as a probe of sub-Planck phase-space structure

We investigate the connection between sub-Planck structure in the Wigner function and the output fidelity of continuous-variable teleportation protocols. When the teleporting parties share a two-mode squeezed state as an entangled resource, high fidelity in the output state requires a squeezing large enough that the smallest sub-Planck structures in an input pure state are teleported faithfully. We formulate this relationship, which leads to an explicit relation between the fine-scale structure in the Wigner function and large-scale extent of the Wigner function, and we treat specific examples, including coherent, number, and random states and states produced by chaotic dynamics. We generalize the pure-state results to teleportation of mixed states.     

A unified theory of quantum holonomies

A periodic change of slow environmental parameters of a quantum system induces quantum holonomy. The phase holonomy is a well-known example. Another is a more exotic kind that exhibits eigenvalue and eigenspace holonomies. We introduce a theoretical formulation that describes the phase and eigenspace holonomies on an equal footing. The key concept of the theory is a gauge connection for an ordered basis, which is conceptually distinct from Mead-Truhlar-Berry’s connection and its Wilczek-Zee extension. A gauge invariant treatment of eigenspace holonomy based on Fujikawa’s formalism is developed. Example of adiabatic quantum holonomy, including the exotic kind with spectral degeneracy, are shown.     

Exotic quantum holonomy in Hamiltonian systems

We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.     

Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra

In this Letter, the “number-phase entropic uncertainty relation” and the “number-phase Wigner function” of generalized coherent states associated to a few solvable quantum systems with non-degenerate spectra are studied. We also investigate time evolution of “number-phase entropic uncertainty” and “Wigner function” of the considered physical systems with the help of temporally stable Gazeau-Klauder coherent states.     

Linear Optical Realization of Qubit Purification with Quantum Amplitude Damping Channel

We provide an experimental scheme which includes the realizatlon of quantum amplitude damping channel and the optimal two-qubit purification. Moreover, we discuss the purification of arbitrary input qubits and arbitrary N qubits. Our scheme only uses linear optical elements and the proposal may be useful in transmission of photons in fibres. This scheme is feasible in the laboratory with the current experimental technology.     

Magnetised black hole as a gravitational lens

We use the Ernst–Schwarzschild solution for a black hole immersed in a uniform magnetic field to estimate corrections to the bending angle and time delay due-to presence of weak magnetic fields in galaxies and between galaxies, and also due-to influence of strong magnetic field near super-massive black holes. The magnetic field creates a kind of confinement in space, that leads to increasing of the bending angle and time delay for a ray of light propagating in the equatorial plane.     

Nonclassicality of a single quantum excitation of a thermal field in thermal environments

The nonclassicality of single photon-added thermal states in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function. The Wigner functions become positive when the decay time exceeds a threshold value γtc, which only depends on the effective temperature of the thermal channel. Furthermore, we firstly demonstrate γtc is the same for arbitrary pure or mixed nonclassical optical fields with zero population in vacuum state.     

Simple Linear Optical ‘Binary Measurement Tree＇ for Single Photonic Polarization Qubit

Positive-operator-value-measurement （POVM） is one of the essential components of quantum information processing （ QIP）. Recently a ＇binary measurement tree＇ （BST） strategy （PRA 77, 052104） is suggested for implementing arbitrary POVM by sequential two-operator POVMs. We present a simple novel two-operator POVM module via linear optics, which is employed as block to construct a ＇binary measurement tree＇ for implementing arbitrary POVM on single photonic polarization qubit. The total complexity of the experimental setup is significantly reduced in contrast to the previous works. As an example, we give the detailed settings of a well-known POVM.     

Cavity-loss-induced Bell-nonlocality sudden death in the Tavis-Cummings model

The tripartite nonlocality is measured by the extent of violation of multipartite Bell inequality in Tavis-Cummings model with cavity loss. The effect of Bell-nonlocality sudden death is demonstrated. It is important that the study of tripartite system can exhibit fundamental characteristics which do not exist in bipartite systems.     

Convergent iterative solutions of Schroedinger equation for a generalized double well potential

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential . The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter a are discussed.     

Deterministic generation of squeezing for a cavity field with a collection of driven atoms

We propose an efficient scheme for realizing squeezing for a cavity mode. In the scheme, a collection of ladder-type three-level atoms are trapped in a cavity and driven by two classical fields. Under certain conditions, the cavity field deterministically evolves to a squeezed state. The scheme can also be used for conditional generation of superpositions of different squeezed vacuum states.     

Quantum Hall effect in noncommutative quantum mechanics

We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.