Decoherence of interacting Majorana modes

We study the decoherence of Majorana modes of a fermion chain, where the fermions interact with their nearest neighbours. We investigate the effect of dissipation and dephasing on the Majorana modes of a fermionic chain. The dissipative and dephasing noises induce the non-parity- and parity-preserving transitions between the eigenstates of the system, respectively. Therefore, these two types of noises lead to the different decoherence mechanisms. In each type of noise, we discuss the low- and high-frequency regimes to describe the different environments. We numerically calculate the dissipation and dephasing rates in the presence of long-range interactions. We find that the decoherence rate of interacting Majorana modes is different to that of non-interacting modes. We show the examples that the long-range interactions can reduce the decoherence rate. It is advantageous to the potential applications of quantum information processing.Comment: 11 pages, 14 figure

Topological phases in spin-orbit coupled dipolar lattice bosons

We study the topological phases in spin-orbit coupled dipolar bosons in a one-dimensional optical lattice. The magnetic dipolar interactions between atoms give rise to the inter-site interactions. In the Mott-insulating regime, this system can be described by the quantum XYZ spin model with the Dzyaloshinskii-Moriya interactions in a transverse field. We focus on investigating the effect of dipolar interactions on the topological phase. The topological phase can be shown when spin-orbit coupling incorporates with the repulsive dipolar interaction. We find that the dipolar interaction can broaden the range of parameters of spin-orbit coupling and transverse field for exhibiting the topological phase. The sum of spin correlations between the two nearest neighbouring atoms can be used to indicate the topological phase. This may be useful for detecting topological phases in experiments.Comment: 6 pages, 5 figures, revised versio

Quantum-limited measurement of magnetic-field gradient with entangled atoms

We propose a method to detect the microwave magnetic-field gradient by using a pair of entangled two-component Bose-Einstein condensates. We consider the two spatially separated condensates to be coupled to the two different magnetic fields. The magnetic-field gradient can be determined by measuring the variances of population differences and relative phases between the two-component condensates in two wells. The precision of measurement can reach the Heisenberg limit. We study the effects of one-body and two-body atom losses on the detection. We find that the entangled atoms can outperform the uncorrelated atoms in probing the magnetic fields in the presence of atom losses. The effect of atom-atom interactions is also discussed.Comment: 8 pages, 12 figure

Production of mesoscopic superpositions with ultracold atoms

We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomenon. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are generalized Schr\"{o}dinger cat states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.Comment: 4 pages, 2 figure

Particle-hole entanglement of ultracold atoms in an optical lattice

We study the ground state of two-component bosonic atoms in a one-dimensional optical lattice. By applying an external field to the atoms at one end of lattice, the atoms are transported and becomes localized at that site. The holes are then created in the remaining sites. The particle-hole superpositions are produced in this process. We investigate the entanglement entropy between the atoms in the two different parts of a lattice. A large degree of particle-hole entanglement is generated in the ground state. The particle-hole quantum correlations can be probed by the two-site parity correlation functions. The transport properties of the low-lying excited states are also discussed.Comment: 5 pages, 8 figure

Nonequilibrium dynamics of spin-orbit coupled lattice bosons

We study the non-equilibrium dynamics of two component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin XXZ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and non-stationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is useful to characterize the many-body dynamics. The effects of even and odd numbers of sites are discussed. Our result sheds light on non-equilibrium dynamics due to the interplay between spin-orbit coupling and atomic interactions.Comment: 8 pages, 6 figure

An iterative approach for amplitude amplification with nonorthogonal measurements

Using three coupled harmonic oscillators, we present an amplitude-amplification method for factorization of an integer. We generalize the method in [arXiv:1007.4338] by employing non-orthogonal measurements on the harmonic oscillator. This method can increase the probability of obtaining the factors by repeatedly using the nonlinear interactions between the oscillators and non-orthogonal measurements. However, this approach requires an exponential amount of resources for implementation. Thus, this method cannot provide a speed-up over classical algorithms unless its limitations are resolved.Comment: 21 pages, 5 figures; title changed, major revision

Vacuum Fluctuations induced Entanglement between Two Mesoscopic Systems

We study the dynamics of a pair of molecular ensembles trapped inside a superconducting resonator through which they are strongly coupled via a microwave field mode. We find that entanglement can be generated via "vacuum fluctuations" even when the molecules and cavity field are initially prepared in their ground state. This entanglement is created in a relatively short time and without the need for further manipulation of the system. It does, therefore, provide a convenient scheme to entangle two mesoscopic systems, and may well be useful quantum information processing.Comment: 4 pages, 4 figure

Relaxation dynamics in an isolated long-range Ising chain

We consider a chain of trapped ions to interact with each other via long-range interactions. This system can be used to simulate the long-range Ising model. We study the dynamics of quantum coherence of a single spin in the chain, where the spins are initially prepared in their upper states. The relaxation dynamics exhibits due to the genuine long-range interaction. The degree of quantum coherence of a single spin rapidly decreases and vanishes in the steady state. However, our numerical result suggests that the conventional spin chain model, which truncates the interactions between the distant spins, cannot show the relaxation dynamics. This implies that the usual truncation in approximating the long-range interaction is not applicable to describing the non-equilibrium dynamics. The effect of the interaction range on the relaxation dynamics is studied. The higher relaxation rate will show if a system has a longer range of interaction. However, it takes a longer relaxation time in the vicinity of infinite interaction range. We also examine the dynamics of quantum coherence of a block of spins. Our result may shed light on the relationship between long-range interaction and the coherence dynamics of a quantum many-body system.Comment: 7 pages, 5 figure

Dynamical stability of entanglement between spin ensembles

We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be very useful to generate and detect macroscopic entanglement in a common noisy environment and even a stable macroscopic memory.Comment: 4 pages, 1 figur