Symmetries in Science II pp 471-482 | Cite as

# Squeezed States and Quadratic Hamiltonians: A Wigner Distribution Approach

## Abstract

For some time now there has been much interest in a special class of quantum states of the radiation field known as squeezed coherent states or simply squeezed states^{1–5}. In fact the first experimental observation of squeezing has been reported very recently^{6}. Squeezed states form a generalization of the coherent states in some sense, the latter being states which behave in the most possible classical way^{7}. Whereas coherent states are minimum uncertainty states having equal fluctuations (zero-point fluctuations) in the two quadratures of the annihilation operator of the field mode, squeezed states have less fluctuation in one at the expense of increased fluctuation in the other quadrature in a manner consistent with the uncertainty principle. From an operator point of view squeezed states are produced from the coherent states by what is equivalent to the Bogolubov transformation. It is interesting to note that different authors discovered or rediscovered the squeezed states under different names - two photon coherent states^{8}, new coherent states^{9}, correlated coherent states^{10}, pulsating states^{11} and twisted states^{12} - emphasising different view points of what is essentially one and the same thing.

## Keywords

Coherent State Unitary Evolution Gaussian State Phase Curvature Wigner Distribution## Preview

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