Related papers: Sub-Planck phase-space structure and sensitivity f…
We revisit the Perelomov SU(1,1) displaced coherent states states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation with photon counting and squeezing. In the non-displaced case we…
The effects of the spatiotemporal degrees of freedom on the practical implementation of an SU(1,1) interferometry is investigated. A recently developed Wigner functional approach is used to obtain the phase sensitivity of such an SU(1,1)…
We study some properties of the $SU(1,1)$ Perelomov number coherent states. The Schr\"odinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number…
We propose a method using the dispersive interaction between atoms and a high quality cavity to realize the mesoscopic superposition of coherent states which would exhibit sub-Planck structures in phase space. In particular we focus on a…
A basic introduction to the $su(1,1)$ algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of…
We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…
We implement a SU(1,1) covariant integral quantization of functions or distributions on the unit disk. The latter can be viewed as the phase space for the motion of a test "massive" particle on 1+1 Anti de Sitter space-time, and the…
The persistence of sub-Planck structure in phase space with loss of coherence is demonstrated in a mixed state, which comprises two terms in the density matrix. Its utility in carrying out Heisenberg-limited measurement and quantum…
We study quantum properties of SU$(2|1)$ supersymmetric (deformed ${\cal N}=4$, $d=1$ supersymmetric) extension of the superintegrable Smorodinsky--Winternitz system on a complex Euclidian space $\mathbb{C}^N$. The full set of wave…
Nonlinear SU(1,1) interferometers are fruitful and promising tools for spectral engineering and precise measurements with phase sensitivity below the classical bound. Such interferometers have been successfully realized in bulk and…
Multimode quantum light has promising applications in many areas of physics, such as quantum communications and quantum computing. However, its multimode nature also makes it challenging to measure its properties. Recently [Optica Quantum…
We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete…
We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock…
We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam…
We define the worldline harmonic SU(2|1) superspace and its analytic subspace as a deformation of the flat N=4, d=1 harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell (4,4,0) SU(2|1)…
GUT scale threshold corrections in minimal SU(5) supergravity grand unification are discussed. It is shown that predictions may be made despite uncertainties associated with the high energy scale. A bound relating the strong coupling…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…
Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and their properties are investigated. They represent a nontrivial generalization of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the points of…
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply…