Displacement operator

The displacement operator for one mode in quantum optics is the shift operator

where $\alpha$ is the amount of displacement in optical phase space, $\alpha^*$ is the complex conjugate of that displacement, and $\hat{a}$ and $\hat{a}^\dagger$ are the lowering and raising operators, respectively. The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude $\alpha$ . It may also act on the vacuum state by displacing it into a coherent state. Specifically, $\hat{D}(\alpha)|0\rangle=|\alpha\rangle$ where $|\alpha\rangle$ is a coherent state, which is the eigenstates of the annihilation (lowering) operator.

单词	Displacement operator
释义	Displacement operator 英语百科 Displacement operator The displacement operator for one mode in quantum optics is the shift operator where $\alpha$ is the amount of displacement in optical phase space, $\alpha^*$ is the complex conjugate of that displacement, and $\hat{a}$ and $\hat{a}^\dagger$ are the lowering and raising operators, respectively. The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude $\alpha$ . It may also act on the vacuum state by displacing it into a coherent state. Specifically, $\hat{D}(\alpha)\|0\rangle=\|\alpha\rangle$ where $\|\alpha\rangle$ is a coherent state, which is the eigenstates of the annihilation (lowering) operator.
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