Displaced and squeezed number states

LA - UR - 96 - 4789 Displaced and Squeezed Number States

After beginning with a short historical review of the concept of displaced (coherent) and squeezed states, we discuss previous (often forgotten) work on displaced and squeezed number states. Next, we obtain the most general displaced and squeezed number states. We do this in both the functional and operator (Fock) formalisms, thereby demonstrating the necessary equivalence. We then obtain the t...

Supersymmetric Displaced Number States

We introduce, generate and study a family of supersymmetric displaced number states (SDNS) that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation,...

Displaced squeezed number states: Position space representation, inner product, and some applications.

Towards Even and Odd Squeezed Number States

The time evolution of even and odd squeezed states, as well as that of squeezed number states, has been given in simple, analytic form. This follows experimental work on trapped ions which has demonstrated even and odd coherent states, number states, and squeezed (but not displaced) ground states. We review this situation and consider the extension to even and odd squeezed number states. Questi...

Temporal second-order coherence function for displaced-squeezed thermal states

We calculate the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz. a displaced– squeezed thermal state. The calculation involves first dynamical generation at time t of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time τ ≥ 0 apart. The generatio...