We show that any state which violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty relations provide a straightforward construction of nonlinear entanglement witnesses for the cross norm criterion. Entanglement plays a central role in quantum information processing. Thus its characterization is important for the field: It is crucial to be able to decide whether or not a given quantum state is entangled. However, this so-called separability problem remains one of the most challenging unsolved problems in quantum physics.Several sufficient conditions for entanglement are known. The first of such criteria was the criterion of the positivity of the partial transpose (PPT) [1]. This criterion is necessary and sufficient for 2 × 2 and 2 × 3 systems [2], but in higher dimensional systems some entangled states escape the detection. The characterization of these PPT entangled states is thus of great interest. Recently, the computable cross norm (CCN) or realignment criterion was put forward by O. Rudolph [3] and Chen and Wu [4]. The original condition has been reformulated in several ways and extended to multipartite systems [5][6][7]. The CCN criterion allows to detect the entanglement of many states where the PPT criterion fails, however, some states which are detected by the PPT criterion, cannot be detected by the CCN criterion [5]. In this way, one may view the CCN criterion as complementary to the PPT criterion. In addition to the CCN criterion, there are also algorithmic approaches to the separability problem which allow the detection of entanglement when the PPT criterion fails [8].A different approach to the separability problem tries to formulate separability criteria directly in mean values or variances of observables. Typically, these conditions are formulated as Bell inequalities [9], entanglement witnesses [2, 10] or uncertainty relations [11][12][13][14][15][16]. Here, the local uncertainty relations (LURs) by Hofmann and Takeuchi are remarkable [12]. They have a clear physical interpretation and are quite versatile: It has been shown that they can be used to detect PPT entangled states [13]. It is further known that in certain situations they can provide a nonlinear refinement of linear entanglement witnesses [14]. Consequently, the investigation of LURs has been undertaken in several directions [15,16].In this paper we investigate the relation between the CCN criterion and the LURs. We show that any state which can be detected by the CCN criterion can also be detected by a LUR. By providing counterexamples, we prove that the converse does not hold. Our results show that the LURs can be viewed as nonlinear entanglement witnesses for the CCN criterion. In this way, we demonstrate a surprising connection between permutation separability criteria (to which the CCN criterion belongs) [7], criteria in terms of covariance matrices, such as LURs [16,17], and the th...
A robust method for producing half-cycle-few-cycle pulses in mid-infrared to extreme ultraviolet spectral ranges is proposed. It is based on coherent undulator radiation of relativistic ultrathin electron layers, which are produced by microbunching of ultrashort electron bunches by a TW power laser in a modulator undulator. According to our numerical calculations it is possible to generate as short as 10 nm long electron layers in a single-period modulator undulator having an undulator parameter of only K = 0.25 and which is significantly shorter than the resonant period length. By using these electron layers the production of carrier-envelope-phase stable pulses with up to a few nJ energy and down to 30 nm wavelength and 70 as duration is predicted.PACS numbers: 41.60. Cr, 41.50.+h, 41.75.Ht Waveform-controlled few-cycle laser pulses enabled the generation of isolated attosecond pulses and their application to the study of electron dynamics in atoms, molecules, and solids [1]. Intense waveform-controlled extreme ultraviolet (EUV)/X-ray attosecond pulses could enable precision time-resolved studies of core-electron processes by using e.g. pump-probe techniques [2]. Examples are time-resolved imaging of isomerisation dynamics, nonlinear inner-shell interactions, or multiphoton processes of core electrons. EUV pump-EUV probe experiments can be carried out at free-electron lasers (FELs) [3,4]; however, the temporal resolution is limited to the fs regime and the stochastic pulse shape is disadvantageous.The shortest electromagnetic pulses reported to date, down to a duration of only 67 as, were generated by high-order harmonic generation (HHG) in gas targets [5,6]. Isolated single-cycle 130-as pulses were generated by HHG using driving pulses with a modulated polarization state [7]. One drawback of gas HHG is the relatively low EUV pulse energy due to the ionization depletion of the medium. The use of long focal length for the IR driving field, or using strong THz fields for HHG enhancement [8] were proposed to increase the EUV pulse energy. The generation of half-cycle 50-as EUV pulses with up to 0.1 mJ energy is predicted by coherent Thomson backscattering from a laser-driven relativistic ultrathin electron layer by irradiating a double-foil target with intense few-cycle laser pulses at oblique incidence [9,10]. Various schemes, such as the longitudinal space charge amplifier [11,12], or two-color enhanced self-amplified spontaneous emission (SASE) [13,14] were proposed for attosecond pulse generation at FELs. However, the realization of these technically challenging schemes has yet to be demonstrated and precise waveform control is difficult.In this Letter we propose a robust method for producing waveform-controlled pulses down to half-cycle durations in the mid-infrared (MIR) to the EUV spectral ranges. The method is based on coherent undulator radiation emitted by relativistic ultrathin electron layers, which are produced by microbunching of a picosecond electron bunch obtained from microwave electron inject...
We introduce a theoretical framework which is suitable for the description of all spatial and timemultiplexed periodic single-photon sources realized or proposed thus far. Our model takes into account all possibly relevant loss mechanisms. This statistical analysis of the known schemes shows that multiplexing systems can be optimized in order to produce maximal single-photon probability for various sets of loss parameters by the appropriate choice of the number of multiplexed units of spatial multiplexers or multiplexed time intervals and the input mean photon pair number, and reveals the physical reasons of the existence of the optimum. We propose a novel time-multiplexed scheme to be realized in bulk optics, which, according to the present analysis, would have promising performance when experimentally realized. It could provide a single-photon probability of 85% with a choice of experimental parameters which are feasible according to the experiments known from the literature.
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)] leads to the basic question: Can a light be enhanced and simultaneously localized in space and time by a subwavelength slit? To address this question, the spatial distribution of the energy flux of an ultrashort (femtosecond) wave-packet diffracted by a subwavelength (nanometer-size) slit was analyzed by using the conventional approach based on the Neerhoff and Mur solution of Maxwell's equations. The results show that a light can be enhanced by orders of magnitude and simultaneously localized in the near-field diffraction zone at the nmand fs-scales. Possible applications in nanophotonics are discussed.
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