Squeezing with classical Hamiltonians

Abstract

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric downconversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.

14 pages, 10 figures, PRA

References in corpus (2)

• Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity
• Twisting tensor and spin squeezing

Cited by in corpus (5)

• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• Nuclear spin squeezing via electric quadrupole interaction
• Loschmidt echo driven by hyperfine and electric-quadrupole interactions in nanoscale nuclear spin baths
• Entanglement storage by classical fixed points in the two-axis countertwisting model
• Asymmetric Foucault pendulum dynamics with analogies to the Lipkin-Meshkov-Glick quantum phase transitions and other quantum phenomena