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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Amplitude Nth-power squeezing of a field in the Jaynes-Cummings model

Ji‐Suo Wang, Qingmei Sui, Chuan‐Kui Wang

Published Oct 1, 1995• 8 citations
Publisher

Abstract

The properties of amplitude Nth-power squeezing (ANPS) of a field in the Jaynes-Cummings model for the initial atom being in the ground state and the radiation field being in a coherent state are investigated. It is found that the field may exhibit ANPS (N>or=2) in this system. The variations of the degree of the squeezing with the initial average photon numbers of the field and the powers of N are discussed.

DOI
10.1088/1355-5111/7/5/012

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The properties of amplitude Nth-power squeezing (ANPS) of a field in the Jaynes-Cummings model for the initial atom being in the ground state and the radiation field being in a coherent state are investigated. It is found that the field may exhibit ANPS (N>or=2) in this system. The variations of the degree of the squeezing with the initial average photon numbers of the field and the powers of N are discussed.
We have studied the properties of the amplitude- N -th powered squeezing of an electromagnetic field in the k -photon Jaynes-Cummings model of an atom initially being in the ground state and coupling with the superposition state. The results show that, under the condition of n ⩾ k , where n is the photon number of the superposition state, the field exhibits not only the amplitude- N = n -th powered squeezing but also the amplitude- N = ( n /2)-th powered squeezing for even n . The variations of the amplitude- N -th powered squeezing of the field with the powers N and k are discussed.
An analysis of the effects of detuning and the superposition angle on amplitude-squared (AS) squeezing is presented for the one- and two-photon Jaynes-Cummings model (JCM) using coherent and squeeze inputs. In the one-photon JCM for squeezed inputs, it is shown that the degree of AS squeezing increases as the detuning increases. The two-photon JCM, on the other hand, displays this characteristic only for coherent input in a small range of values of the detuning. The superposition angle affects the degree of AS squeezing more significantly for a detuned field than for a tuned one. The behavior of AS squeezing becomes independent of the value of the superposition angle in both the models for large initial average photon number, n\ifmmode\bar\else\textasciimacron\fi{}, with any value of detuning and for large detuning with any value of n\ifmmode\bar\else\textasciimacron\fi{}.
The quatum statistical properties of two-photon radiation from two-level atomic system are investigated by using complete set in the nth subspace of generalized Jaynes-Cummings hamiltonian, and the general expression for field variance is obtained. The conditions for optimum squeezing as well as the optimum squeezed quantity are found out for an arbitrary initial state, and the time evolution of the optimum squeezed state is then analysed. As an example, the squeezing in an initial state with bare atomic system in thermal equilibrium is discussed, which demonstrates the dependence of squeezing on several parameters, such as, temperature, detuning, coupling strength. The conditions for squeezing are given analytically and numerically. Finally, the physical picture of the squeezing is pointed out.
We use the recently-established asymptotic solution (AS) for large fields to study squeezing in the Jaynes-Cummings model. Arbitrary initial atomic states (including atomic coherence) are considered. We find that most features of squeezing can be understood from the properties of the asymptotic field states, and from the observation, which we establish numerically, that for large fields the interference between the two branches of the wavefunction does not contribute significantly to the squeezing (not even near the revival times, when the two field states being superposed have very nearly the same phase). We obtain a limit on the time over which the field may show any squeezing and find that it scales as the 3/4 power of the number of photons. We also obtain a bound on the maximum achievable squeezing for a given number of photons, which is an improvement over earlier estimates. Finally, we discuss some of the shortcomings of the AS, and in particular the existence of a small ghost peak in the field Q function for initial conditions where the AS predicts a single peak, which is enough to destroy the squeezing for certain times.
Amplitude-squared squeezing is investigated for the two-photon Jaynes-Cummings model with the field initially in a squeezed vacuum or a more general squeezed state. For small values of the coherence parameter and large values of the squeeze parameter, the amplitude-squared variances show threefold oscillatory behavior on the long time scale. It is found that a ground-state atom (as against an excited one) leads to considerable enhancement of the input amplitude-squared squeezing. The behavior of photon number squared and its relationship to the amplitude-squared squeezing is commented upon.