Scheme to Measure Quantum Stokes Parameters and their Fluctuations and Correlations

We propose a scheme to measure quantum Stokes parameters, their fluctuations and correlations. The proposal involves measurements of intensities and intensity- intensity correlations for suitably defined modes, which can be produced by a combination of half wave and quarter wave plates.Comment: Submitted to the Journal of Modern Optic

How much quantum noise of amplifiers is detrimental to entanglement

We analyze the effect of the quantum noise of an amplifier on the entanglement properties of an input state. We consider both phase insensitive and phase sensitive amplification and specialize to Gaussian states for which entanglement measures are well developed. In the case of phase insensitive amplification in which both the modes are symmetrically amplified, we find that the entanglement in the output state vanishes if the intensity gain exceeds a limiting value $2/(1+\exp[-E_N])$ where $E_N$ is the logarithmic negativity of the input state which quantifies the initial entanglement between the two modes. The entanglement between the two modes at the output is found to be more robust if only one mode is amplified.Comment: Latex, 9 pages, 4 figures

A non group theoretic proof of completeness of arbitrary coherent states D(α)∣f>D(\alpha)\mid f>

A new proof for the completeness of the coherent states $D(\alpha )\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed.Comment: 10 pages, latex, no figure

Quantum phase space distributions in thermofield dynamics

It is shown that the the quantum phase space distributions corresponding to a density operator $\rho$ can be expressed, in thermofield dynamics, as overlaps between the state $\mid \rho >$ and "thermal" coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an arbitrary initial condition are derived.Comment: 17 pages, revtex, no figures. number of pages were incorrectly stated as 3 instead of 17. No other correction

Linear amplification and quantum cloning for non-Gaussian continuous variables

We investigate phase-insensitive linear amplification at the quantum limit for single- and two-mode states and show that there exists a broad class of non-Gaussian states whose nonclassicality survives even at an arbitrarily large gain. We identify the corresponding observable nonclassical effects and find that they include, remarkably, two-mode entanglement. The implications of our results for quantum cloning outside the Gaussian regime are also addressed.Comment: published version with reference updat

Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ``doubly-infinite'' statistics, many representations of orthostatistics, Hubbard statistics and its variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43. Published versio

Quantum many-body simulations using Gaussian phase-space representations

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices.Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more reference

Proposal for measurment of harmonic oscillator Berry phase in ion traps

We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of Schr\"odinger cat states.Comment: Replaced with revised versio

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods