Amplification of superposition states in phase-sensitive amplifiers

Abstract

We study statistical properties of quantum superposition states (Schrodinger-cat states) amplified by phase-sensitive (squeezed) amplifiers. We show that the phase-sensitive amplifier with a properly chosen phase can preserve quantum coherences and nonclassical behavior of the Schrodinger-cat-state input even for a gain factor G larger than 2. In particular, we show that for an even coherent state (CS) phase-sensitive amplifiers can preserve squeezing for G) 2 but simultaneously in the process of amplification the noise added by the amplifier leads to a rapid increase of fluctuations in the photon number. Because of the finite maximum degree of squeezing obtainable for the even CS the maximum gain factor G for which squeezing can still be observed in the output state is finite. The phase-sensitive amplifier with a properly chosen phase can also reduce fluctuations in the photon number of the initial even CS. Nevertheless, one cannot amplify the initial even CS with super-Poissonian photon statistics into the state with sub-Poissonian photon statistics.PACS number(s): 42.50.Dv, 03.65.8zRecently Haroche and co-workers [1] have proposed a conceptually simple but elegant method to prepare quantum superposition states confined in a microwave cavity.

Effects of entanglement in an ideal optical amplifier

“…2. Earlier studies of the amplification of cat states [4,[17][18][19][20][21][22][23][24][25][26][27][28] did not consider the limit of 1 g → or the interferometer approach of Fig. 2.…”

Evolution of cat states in a dissipative parametric amplifier: decoherence and entanglement

“…On the other hand, the characteristic function of the single-mode case can be obtained from that of the two-mode case by simply setting the parameter related to the absent mode equal to zero, e.g. the characteristic function of the signal mode (first-mode) can be obtained by setting ζ 2 = 0 in (12) and (13).…”

“…This function may be used in studying the sum photon-number distribution and the reduced factorial moments for compound modes. For the general term (13), relation (15) can be calculated to obtain…”

“…where the subscript I in ( 19) and (20) means that these quantities have been calculated for the general term (13). Also in (19) and (20) L n (.)…”

“…Further, the evolution of cat states in several quantum systems has been intensively studied [11]- [18]. For convenience of the present work we refer to the interaction of these states with environment [11][12][13][14]18], where the common goal of such studies is the comprehension and description of the decoherence processes (decoherence is the rapid transformation of a pure linear superposition state into the corresponding statistical mixture state) in the system under observation, and the energy loss due to the interaction with the reservoir. Most of these papers adopt the Heisenberg-Langevin approach or the Markov master equation approach.…”