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International Journal of Modern Physics B

ORDINARY SQUEEZING AND AMPLITUDE-SQUARED SQUEEZING OF A SINGLE MODE COHERENT RADIATION IN INTERACTION WITH TWO TWO-LEVEL ATOMS

Hari Prakash, Rakesh Kumar Rai

Published Aug 10, 2007• 10 citations
Publisher

Abstract

In the present paper, we consider the interaction of a single mode radiation initially in a coherent state with an assembly of two two-level atoms in some different states using the Hamiltonian, H = ω(a+a + Sz)+g(a S+ + a+ S-) in the natural units, where a+ and a are the creation and annihilation operators for radiation, Sz, S± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and energy difference between the two atomic levels. We solve it exactly. We study ordinary squeezing and amplitude-squared squeezing of radiation for the general operators, [Formula: see text] and Yθ=1/2(a2e-iθ+a+2eiθ), when atoms are fully excited, super-radiant or in the ground state. We get a large ordinary squeezing (nearly 88% squeezing) for the super-radiant atomic state, at a time, which is 0.451 of the first revival time, and this should be easily observable. We also get a large amplitude-squared squeezing (nearly 20%) at the time, which is about 0.033 of the first revival time. Variation of variances near their minima with coupling time gt, square root of mean photon number |α| and phase are also discussed.

DOI
10.1142/s0217979207037570

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In the present paper, we consider the interaction of a single mode radiation initially in a coherent state with an assembly of two two-level atoms in some different states using the Hamiltonian, H = ω(a+a + Sz)+g(a S+ + a+ S-) in the natural units, where a+ and a are the creation and annihilation operators for radiation, Sz, S± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and energy difference between the two atomic levels. We solve it exactly. We study ordinary squeezing and amplitude-squared squeezing of radiation for the general operators, [Formula: see text] and Yθ=1/2(a2e-iθ+a+2eiθ), when atoms are fully excited, super-radiant or in the ground state. We get a large ordinary squeezing (nearly 88% squeezing) for the super-radiant atomic state, at a time, which is 0.451 of the first revival time, and this should be easily observable. We also get a large amplitude-squared squeezing (nearly 20%) at the time, which is about 0.033 of the first revival time. Variation of variances near their minima with coupling time gt, square root of mean photon number |α| and phase are also discussed.
We study sub-Poissonian photon statistics of light in interaction of a single mode radiation, initially either in a coherent state or in a superposed coherent state with an assembly of two-level atoms using the Hamiltonian, H = ω(a+a + Sz) + g(aS+ + a+ S–) in natural units, where a+ and a are creation and annihilation operators, Sz, S ± are the collective Dicke operators, g is the coupling constant, and ω is the energy of the photons and also the separation between the two atomic levels. We study the cases of (i) a single two-level and (ii) of two two-level atoms interacting with a single mode coherent or superposed coherent radiation. We find that for large coupling time gt, Fano factor shows collapses and revival phenomena, and that the variation is large for small mean number of photons. We also find that in the case of two two-level atoms, photon statistics shows larger sub-Poissonian than the case of a single two-level atom, and that there is no definite relationship between squeezing and sub-Poissonian photon statistics of light.
In the present paper we study higher-order sub-Poissonian photon statistics in interaction of a single mode radiation initially in the coherent state Ŧα〉 with an assembly of two excited two-level atoms using the Hamiltonian, H=ω(a+a+Sz)+g(aS++a+S.), in the natural system of units. Here, α=|α|eiθα, a is the annihilation operator for radiation, Sz and S± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and the energy difference between the two atomic levels. We solve it exactly and conclude that higher-order sub-Poissonian photon statistics can be obtained for an arbitrary order by choosing suitably the square root of mean photon number |α| of the coherent radiation and coupling time gt. Variations of higher-order sub-Poissonian photon statistics with parameters |α| and gt have also been discussed.
An analysis of the second-order and amplitude-squared (AS) squeezing is presented for the two atoms prepared in a two-atom squeezed state using coherent and squeezed field inputs. The system produce strong sqeezing and superposition angle (θ) is more effective for small values of average photon number [Formula: see text] as compared to that of large one. The degree of squeezing of both types increases as θ increases for coherent field input with small [Formula: see text]. Some values of θ for the initial field in a squeezed-vacuum state with any value of input squeezing can make one of the quadrature of the both types of squeezing permanently squeezed for T≥0. For the initial field in a more general squeezed state, the second-order and AS squeezing behave randomly for different values of θ.
Resonant interaction of a collection of two-level atoms with a single-mode coherent cavity field is considered in the framework of the Dicke model. We focus on the role of collective atomic effects in the phenomenon of collapses and revivals of the Rabi oscillations. It is shown that the behavior of the system strongly depends on the initial atomic state. In the case of the initial half-excited Dicke state we account for a number of interesting phenomena. The correlations between the atoms result in a suppression of the revival amplitude, and the revival time is halved, compared to the uncorrelated fully excited and ground states. The phenomenon of squeezing of the radiation field in the atom-field interaction is also discussed. For the initial fully excited and ground atomic states, the field is squeezed on the short-time scale, and squeezing can be enhanced by increasing the number of atoms. Some empirical formulas are found which describe the behavior of the system in excellent agreement with numerical results. For the half-excited Dicke state, the field can be strongly squeezed on the long-time scale in the case of two atoms. This kind of squeezing is enhanced by increasing the intensity of the initial coherent field and is of the same nature as revival-time squeezing in the Jaynes-Cummings model. The appearance of this long-time squeezing can be explained using the factorization approximation for semiclassical atomic states.