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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generation of sub-Poissonian light via the correlated absorption of photons by the dressed atom

Michail Z. Smirnov

Published Jan 6, 1999• 0 citations
Publisher

Abstract

Here we study the open modification of the Jaynes-Cummings model that is the coupled system of the dressed atom and the quantized mode. The mode is initially in the coherent quantum state exhibiting the Poissonian photon statistics. When the quasienergy levels of the dressed atom cross the mean number of photons (n) in the mode undergoes high- amplitude oscillations. Numeric results show that each time the value of (n) falls the photon statistics becomes more regular. Instantaneously, the statistics can become sub- Poissonian with the Fano factor F equalsV (Delta) n2/(n) being many times as small as unity. The above observation provides the evidence that the photons undergo correlated absorption, i.e., they tend to disappear in twos, in threes, etc.

DOI
10.1117/12.335829

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Here we study the open modification of the Jaynes-Cummings model that is the coupled system of the dressed atom and the quantized mode. The mode is initially in the coherent quantum state exhibiting the Poissonian photon statistics. When the quasienergy levels of the dressed atom cross the mean number of photons (n) in the mode undergoes high- amplitude oscillations. Numeric results show that each time the value of (n) falls the photon statistics becomes more regular. Instantaneously, the statistics can become sub- Poissonian with the Fano factor F equalsV (Delta) n2/(n) being many times as small as unity. The above observation provides the evidence that the photons undergo correlated absorption, i.e., they tend to disappear in twos, in threes, etc.
We study the coupled system of the dressed atom and the quantized mode of the electromagnetic field (an open modification of the Jaynes-Cummings model). The mode is initially excited to the coherent quantum state and exhibits Poissonian photon statistics. When the quasienergy levels of the dressed atom cross, the mean number of photons in the mode oscillates at high amplitude. Numerical results show that the photon statistics in the mode regularizes, correlating as the value of falls. Near the local minima of , the statistics can become sub-Poissonian with Fano factor many times smaller than unity.
The nonlinear dynamics of an open quantum system consisting of a “dressed” atom, i.e., an atom coupled with an external multifrequency electromagnetic field, and a single quantized mode of an electromagnetic field is studied. At different crossing points of the quasilevels of the dressed atom, the average number of photons in the quantized mode may either increase without limit with the passage of time or oscillate within finite limits. In the latter case a decrease of the number of photons is accompanied by regularization of their statistics, which may become sub-Poissonian.
The Jaynes-Cummings model describes the interaction between a two-level atom and a single mode of the radiation field. This system has a conservation law which restricts its dynamics. On the basis of this conservation law alone one can make useful statements about the photon statistics of the fields which arise in the model. Two cases are considered. In the first the field is initially in a coherent state. Here it is found that the field statistics become less sub-Poissonian as the amplitude of the initial state increases. The case of an initial thermal state is also considered. In that situation, if the average number of photons present in the initial state is greater than 2.55, then the field statistics can never become sub-Poissonian.
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.
According to the exact solution of a two-level atomic system interacting with a single-mode field in a cavity and including a pumping mechanism, sub-Poissonian photon statistics can be generated either by regular pumping or by resonance absorption of the lower level. When the atomic lifetime is much smaller than the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\gg}1), which corresponds to a usual laser system, the sub-Poissonian photon distribution can be obtained only by regular pumping. On the other hand, if the atomic lifetime is comparable with the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\le}1), the sub-Poissonian photon distribution can be generated by both mechanisms.
In the representation of dressed states, which diagonalizes the Hamiltonian in the Jaynes-Cummings model, the Bose operator for excitation annihilation Â, the spin operator Σ^_\hat \Sigma \_Σ^_ , and the corresponding Hermitian-conjugate operators are found. Using these operators, correlated coherent states were constructed and statistical properties of a field mode and an atom in these states are studied. Nonclassical field properties, such as the deviation of the probability distribution for the number of photons from the Poissonian distribution, its time dependence, and the squeezing of quadrature field components are found. For small interaction coefficients k, all these characteristics of the model vary weakly in time in the resonance case.