There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Table Of Integrals Series And Products

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

A scheme for measuring the quantum state for an arbitrary spin is proposed that is analogous to the symplectic tomography scheme used to measure quantum states associated with continuous observables such as position and momentum An invariant form for the spin state density operator is derived in terms of an integral, over the angles which specify the quantization axis, of a product of the measured probability of the values of the spin along a chosen direction and spherical harmonics summed with Clebsch-Gordan functions

Spin state tomography

Generalized uncertainty relation and correlated coherent states

'Nonclassical' States in Quantum Physics: Brief Historical Review. Squeezed States. Parametric Excitation and Generation of Nonclassical States in Linear Media. Even and Odd Coherent States and Tomographic Representation of Quantum Mechanics and Quantum Optics. The Binormial States of Light. Nonclassical States in Kerr Media. From the Jaynes-Cummings Model to Collective Interactions.

Theory of nonclassical states of light

It is shown that because of the radiation pressure a Schr\"odinger cat state can be generated in a resonator with an oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account by introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.

Vladimir I. Man’ko

Papers

Spin state tomography

Generalized uncertainty relation and correlated coherent states

Theory of nonclassical states of light

Ponderomotive control of quantum macroscopic coherence

Dynamical symmetry of vibronic transitions in polyatomic molecules and the Franck-Condon principle