Using the linear entropy as a measure of entanglement, we investigate the effect of a beam splitter on the Perelomov coherent states for the q-deformed Uq(su(2)) algebra. We distinguish two cases: in the classical q → 1 limit, we find that the states become Glauber coherent states as the spin tends to infinity; whereas for q ≠ 1, the states, contrary to the earlier case, become entangled as they pass through a beam splitter. The entanglement strongly depends on the q-deformation parameter and the amplitude Z of the state.
Recently, Markham and Vedral [Phys. Rev. A 67, 042113 (2003)] investigated the effect of beam splitting on the spin, or SU(2), coherent states for a single mode field. The spin coherent state is a binomial coherent state related to the Holstein-Primakoff realization of the su(2) Lie algebra given in terms of a set of single mode bose annihilation and creation operators. Upon beam splitting, the ordinary (or Glauber) coherent states merely split into products of ordinary coherent states with reduced amplitudes without becoming entangled, as one would expect for a classical-like field. The above authors expected the spin coherent states to go over to the ordinary coherent states in the limit of high spin, $j\ensuremath{\rightarrow}\ensuremath{\infty}$, and thus to become product states after beam splitting. But this expectation was not confirmed through numerical calculation of the entropy which, instead of going to zero, leveled off with increasing spin. In this paper we find similar behavior for SU(1,1) coherent states of the Perelomov type for large Bargman index
k, but also find that the Barut-Girardello SU(1,1) coherent states appear to rapidly become product states after beam splitting for increasing
k. We explain these results by showing that, in reality, neither the spin coherent states nor the Perelomov SU(1,1) coherent states go over to ordinary coherent states in the limits of large
j or
k, and that the Barut-Girardello coherent states merely go over to the vacuum in the large
k limit. Finally, we examine the correct limiting procedure for obtaining separable states (i.e., products of coherent states) upon beam splitting by performing contractions of the su(2) and su(1,1) Lie algebras and of their associated coherent states.
Some years ago Katriel and Solomon [1] described applications to the characterization of the photon statistics of nonideal lasers, nonclassical light, and deformed photon states using f -deformed coherent states. In this letter, we study the effect of a beam splitter on these nonlinear coherent states. We find that these states are useful for generating quantum entanglement as the deformation parameter gets farther form the unity and for strong input field regimes. The results are confirmed through the Werhl entropy.
We trace the resistance to entanglement generation of spin-coherent states when passed through a beam splitter as we vary S through $S=1/\stackrel{\ensuremath{\rightarrow}}{2}\ensuremath{\infty}.$ In the infinite S limit the spin-coherent states are equivalent to the high-amplitude limit of the optical coherent states. These states generate no entanglement and are completely distinguishable. This transition is discussed in terms of the classicality of the states. The decline of the generated entanglement, and in this sense increase in classicality with S, is very slow and dependent on the amplitude z of the state. Surprisingly, we find that, for
∣z∣>1, there is an initial increase in entanglement followed by an extremely gradual decline to zero. Other aspects of classicality are also discussed over the transition in S, including the distinguishability, which decreases quickly and monotonically. We illustrate the distinguishability of spin-coherent states using the representation of Majorana.
The Morse potential is relatively closed to the harmonic oscillator quantum system. Thus, following the idea used for the latter, we study the possibility of creating entanglement using squeezed coherent states of the Morse potential as an input field of a beam splitter. We measure the entanglement with the linear entropy for two types of such states and we study the dependence with the coherence and squeezing parameters. The new results are linked with observations made on probability densities and uncertainty relations of those states. The dynamical evolution of the linear entropy is also explored.
Coherent state (also called Glauber state) refer to a special kind of pure quantum-mechanical state of the light field corresponding to a single resonator mode which describe closest quantum state to a classical sinusoidal wave such as a continuous laser wave. In this paper we manipulate entangled two mode coherent states using beam splitter (BS) and Kerr medium and then evaluate the amount of entanglement by concurrence measure. We show that it is possible to construct maximal entangled state by transmitting a laser beam from a BS and Kerr medium.