Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is applied to the two-photon algebra and the corresponding algebra eigenstates are studied by using the Fock-Bargmann analytic representation. This formalism yields a unified analytic approach to various types of single-mode photon states generated by squeezing and displacing transformations.Comment: To appear in Annals of Physics, REVTeX with AMSsymbols, 27 pages, no figures. More information on http://www.technion.ac.il/~brif/science.htm

Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties

We discuss a scheme for generation of single-mode photon states associated with the two-photon realization of the SU(1,1) algebra. This scheme is based on the process of non-degenerate down-conversion with the signal prepared initially in the squeezed vacuum state and with a measurement of the photon number in one of the output modes. We focus on the generation and properties of single-mode SU(1,1) intelligent states which minimize the uncertainty relations for Hermitian generators of the group. Properties of the intelligent states are studied by using a ``weak'' extension of the analytic representation in the unit disk. Then we are able to obtain exact analytical expressions for expectation values describing quantum statistical properties of the SU(1,1) intelligent states. Attention is mainly devoted to the study of photon statistics and linear and quadratic squeezing.Comment: to appear in Quantum Semiclass. Opt., LaTeX, epsf style, 21 pages including 5 Postscript figures. More information on http://www.technion.ac.il/~brif/science.htm

Governing dynamics by squeezing in a system of cold trapped ions

We consider a system of laser-cooled ions in a linear harmonic trap and study the phenomenon of squeezing exchange between their internal and motional degrees of freedom. An interesting relation between the quantum noise reduction (squeezing) and the dynamical evolution is found when the internal and motional subsystems are prepared in properly squeezed (intelligent) states. Specifically, the evolution of the system is fully governed by the relative strengths of spectroscopic and motional squeezing, including the phenomenon of total cancellation of the interaction when the initial squeezing parameters are equal.Comment: REVTeX, 5 pages, 2 figures, to appear in Phys. Rev.

Reduction of optimum light power with Heisenberg-limited photon-counting noise in interferometric gravitational-wave detectors

We study how the behavior of quantum noise, presenting the fundamental limit on the sensitivity of interferometric gravitational-wave detectors, depends on properties of input states of light. We analyze the situation with specially prepared nonclassical input states which reduce the photon-counting noise to the Heisenberg limit. This results in a great reduction of the optimum light power needed to achieve the standard quantum limit, compared to the usual configuration

Improvement of measurement accuracy in SU(1,1) interferometers

We consider an SU(1,1) interferometer employing four-wave mixers that is fed with two-mode states which are both coherent and intelligent states of the SU(1,1) Lie group. It is shown that the phase sensitivity of the interferometer can be essentially improved by using input states with a large photon-number difference between the modes.Comment: LaTeX, 5 pages, 1 figure (compressed PostScript, available at http://www.technion.ac.il/~brif/graphics/interfer_graph/qopt.ps.gz ). More information on http://www.technion.ac.il/~brif/science.htm