The single-mode Dicke model is well known to undergo a quantum phase transition from the so-called normal phase to the superradiant phase (hereinafter called the 'superradiant quantum phase transition'). Normally, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study the role of the quantum Fisher information (QFI) of both the field mode and the atoms in the ground state of the Dicke Hamiltonian. For a finite but large number of atoms, our numerical results show that near the critical atom-field coupling, the QFI of the atomic and the field subsystems can surpass their classical limits, due to the appearance of nonclassical quadrature squeezing. As the coupling increases far beyond the critical point, each subsystem becomes a highly mixed state, which degrades the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present the analytical results of the QFI and their relationship with the reduced variances of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.Quantum phase transitions in many-body systems are of fundamental interest [1] and have potential applications in quantum information [2][3][4][5][6][7] and quantum metrology [8][9][10][11][12][13][14][15]. Consider, for instance, a collection of N two-level atoms interacting with a single-mode bosonic field, described by the Dicke model (with =  1) [16]:z 0 whereb andˆ † b are annihilation and creation operators of the bosonic field with oscillation frequency ω, which is nearly resonant with the atomic energy splitting ω 0 . The collective spin operators σ ≡ˆ±ˆ= ∑± ± J J iJ x y k k and σ = ∑Ĵ 2 z k k z obey the SU(2) Lie algebra, where σ ± k and σ k z are Pauli operators of the kth atom. The atom-field coupling strength λ ∝ N V depends on the atomic density N V . For a finite number of atoms N (= j 2 ), the Hamiltonian (1) commutes with the parity, where Tr A (Tr B ) is the partial trace of the ground state |g over the atomic (bosonic field) degrees of freedom. The QFI is one of the central quantities used to qualify the utility of an input state [35,36], especially in Mach-Zehnder (or, equivalently, Ramsey) interferometer-based phase or parameter estimation. The achievable phase sensitivity is well known to be limited by the quantum Cramér-Rao bound δφ ρ ∝ˆF G 1 ( , ) min in , where the QFI ρF G ( , ) in depends on the input state ρ in and the New J. Phys. 16 (2014) 063039 T-L Wang et al B 2 . Therefore, the ultimate sensitivity is limited by δφ =n 1/(2 ) min cl , known as New J. Phys. 16 (2014) 063039 T-L Wang et al

It is difficult for structural over-complete dictionaries such as the Gabor function and discriminative over-complete dictionary, which are learned offline and classified manually, to represent natural images with the goal of ideal sparseness and to enhance the difference between background clutter and target signals. This paper proposes an infrared dim target detection approach based on sparse representation on a discriminative over-complete dictionary. An adaptive morphological over-complete dictionary is trained and constructed online according to the content of infrared image by K-singular value decomposition (K-SVD) algorithm. Then the adaptive morphological over-complete dictionary is divided automatically into a target over-complete dictionary describing target signals, and a background over-complete dictionary embedding background by the criteria that the atoms in the target over-complete dictionary could be decomposed more sparsely based on a Gaussian over-complete dictionary than the one in the background over-complete dictionary. This discriminative over-complete dictionary can not only capture significant features of background clutter and dim targets better than a structural over-complete dictionary, but also strengthens the sparse feature difference between background and target more efficiently than a discriminative over-complete dictionary learned offline and classified manually. The target and background clutter can be sparsely decomposed over their corresponding over-complete dictionaries, yet couldn't be sparsely decomposed based on their opposite over-complete dictionary, so their residuals after reconstruction by the prescribed number of target and background atoms differ very visibly. Some experiments are included and the results show that this proposed approach could not only improve the sparsity more efficiently, but also enhance the performance of small target detection more effectively.

Track initiation for dim small moving target particularly in a heavy clutter environment is a theoretical and technological challenge for diverse tracking systems. The different spatial-temporal characteristics presenting in sequence scans are utilized to recognize target and initialize track in this paper. In spatial domain, the small target mapped in the image is a uniform gray spot other than pixel-sized object with high congregated degree, whereas, the false alarm is independent, irrelative and lower congregated degree. In temporal domain, the target's trajectory projected on image sequence is continuous for the continuity of target motion and will appear in the neighborhood at consecutive instants with the maximum probability, on the contrary, the false alarm is disorderly, and occurs in the neighborhood at consecutive instants is impossible. Based on the spatial-temporal characteristics mentioned above, a track initiation algorithm for dim small moving target based on spatial-temporal hypothesis testing, which consists of neighborhood clustering and trajectory continuity, is derived and analyzed in detail. The theory analysis and experimental results show that this method could effectively initialize the track for dim small moving target in heavy clutter environment.