  We investigate superpositions of two-mode squeezed states (TMSSs), which have
potential applications to quantum information processing and quantum sensing.
Firstly we study some properties of these nonclassical states such as the
statistics of each mode and the degree of entanglement between the two modes,
which can be higher than that of a TMSS with the same degree of squeezing. The
states we consider can be prepared by inducing two-mode Jaynes-Cummings and
anti-Jaynes-Cummings interactions in a system of two modes and a
spin-$\tfrac{1}{2}$ particle, for instance in the trapped ion domain, as
described here. We show that when two harmonic oscillators are prepared in a
superposition of two TMSSs, each reduced single-mode state can be
advantageously employed to sense arbitrary displacements of the mode in phase
space. The Wigner function of this reduced state exhibits a symmetrical peak
centered at the phase-space origin, which has the convenient peculiarity of
getting narrower in both quadratures simultaneously as the average photon
number increases. This narrow peakcan be used as the pointer of our quantum
sensor, with its position in phase space indicating the displacement undergone
by the oscillator.
