Squeeze Operator
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The squeeze operator for a single mode is hat{S}(z) = exp left ( {1 over 2} (z^ hat{a}^2 - z hat{a}^{dagger 2}) right ) , qquad z = r e^{itheta} where the operators inside the exponential are the ladder operators. The squeeze operator is ubiquitous in quantum optics and can operate on any state. For example, when acting upon the vacuum, the squeezing operator produces the squeezed vacuum state. The squeezing operator can also act on coherent states and produce…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The squeeze operator for a single mode is hat{S}(z) = exp left ( {1 over 2} (z^ hat{a}^2 - z hat{a}^{dagger 2}) right ) , qquad z = r e^{itheta} where the operators inside the exponential are the ladder operators. The squeeze operator is ubiquitous in quantum optics and can operate on any state. For example, when acting upon the vacuum, the squeezing operator produces the squeezed vacuum state. The squeezing operator can also act on coherent states and produce squeezed coherent states. The squeezing operator does not commute with the displacement operator: hat{S}(z) hat{D}(alpha) neq hat{D}(alpha) hat{S}(z) nor does it commute with the ladder operators, so one must pay close attention to how the operators are used.