Entanglement conditions for two-mode states

We provide a class of inequalities whose violation shows the presence of entanglement in two-mode systems. We initially consider observables that are quadratic in the mode creation and annihilation operators and find conditions under which a two-mode state is entangled. Further examination allows us to formulate additional conditions for detecting entanglement. We conclude by showing how the methods used here can be extended to find entanglement in systems of more than two modes.Comment: 4 pages, replaced with published versio

Entanglement criteria and nonlocality for multi-mode continuous variable systems

We demonstrate how to efficiently derive a broad class of inequalities for entanglement detection in multi-mode continuous variable systems. The separability conditions are established from partial transposition (PT) in combination with several distinct necessary conditions for a quantum physical state, which include previously established inequalities as special cases. Remarkably, our method enables us to support Peres' conjecture to its full generality within the framework of Cavalcanti-Foster-Reid-Drummond multipartite Bell inequality [Phys. Rev. Lett. 99}, 210405 (2007)] that the nonlocality necessarily implies negative PT entangled states.Comment: 4 pages, publishe

Dynamical theory of single photon transport in a one-dimensional waveguide coupled to identical and non-identical emitters

We develop a general dynamical theory for studying a single photon transport in a one-dimensional (1D) waveguide coupled to multiple emitters which can be either identical or non-identical. In this theory, both the effects of the waveguide and non-waveguide vacuum modes are included. This theory enables us to investigate the propagation of an emitter excitation or an arbitrary single photon pulse along an array of emitters coupled to a 1D waveguide. The dipole-dipole interaction induced by the non-waveguide modes, which is usually neglected in the literatures, can significantly modify the dynamics of the emitter system as well as the characteristics of output field if the emitter separation is much smaller than the resonance wavelength. Non-identical emitters can also strongly couple to each other if their energy difference is smaller than or of the order of the dipole-dipole energy shift. Interestingly, if their energy difference is close but non-zero, a very narrow transparency window around the resonance frequency can appear which does not occur for identical emitters. This phenomenon may find important applications in quantum waveguide devices such as optical switch and ultra narrow single photon frequency comb generator.Comment: 17 pages, 8 figure

Conservation relation of nonclassicality and entanglement for Gaussian states in a beam-splitter

We study the relation between single-mode nonclassicality and two-mode entanglement in a beam-splitter. We show that not all of the nonclassicality (entanglement potential) is transformed into two-mode entanglement for an incident single-mode light. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as the increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam-splitters.Comment: 10 pages, 8 figure