Field’s entropy in the atom–field interaction: Statistical mixture of coherent states

Zúñiga-Segundo, Arturo; Juárez-Amaro, R.; Aguilar-Loreto, O.; Moya‐Cessa, H.

doi:10.1016/j.aop.2017.02.007

Cited by 8 publications

(8 citation statements)

References 29 publications

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“…In figure 1 we plot the entropy, S F , and the purity parameter, ξ F , which as should be expected, show the same behaviour. We calculated in Reference [11] the field entropy for certain periods of time, which agrees with the plots presented here, except for the period of time from about λt ≈ 10 to λt ≈ 17. Note that, although we are considering a two-level atom, the maximum of the entropy goes up to ln 4, defined by our four-level virtual system.…”

Section: Initial Field In a Mixed State And Atom In An Excited Statesupporting

confidence: 83%

“…The figure presented there coincides with the

of Figure 1 for several time intervals. As stated before, in [ 18 ], we were able calculate correctly the entropy for some time intervals, precisely the ones where they match. Therefore, Figure 1 extends the validity to intervals of time from about

.…”

Section: Interaction Between a Two-level And A Quantized Fieldsupporting

confidence: 60%

“…In Figure 1 , we plot the entropy,

, and the purity parameter,

, which, as should be expected, show the same behavior. We were able to calculate in [ 18 ] the field entropy, analytically, only for certain periods of time. The figure presented there coincides with the

of Figure 1 for several time intervals.…”

Section: Interaction Between a Two-level And A Quantized Fieldmentioning

confidence: 99%

“…A question arises: Is it possible to calculate the entropy of the field when it is initially in a mixed state, namely a mixture of coherent states? Recently, we tried to give an answer to this question, but were only able to deliver a positive answer for certain periods of time, but not for the complete evolution [ 18 ]. This is because in such a case, the above triangle inequality seems to be useless, and there is not a general answer.…”

Section: Introductionmentioning

confidence: 99%

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The von Neumann Entropy for Mixed States

Anaya-Contreras

Moya‐Cessa

Zúñiga-Segundo

2019

Entropy

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The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. We show here that it is possible to use the Araki-Lieb inequality in this case and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction. arXiv:1804.09698v1 [quant-ph]

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Section: Initial Field In a Mixed State And Atom In An Excited Statesupporting

confidence: 83%

“…The figure presented there coincides with the

.…”

Section: Interaction Between a Two-level And A Quantized Fieldsupporting

confidence: 60%

“…In Figure 1 , we plot the entropy,

, and the purity parameter,

of Figure 1 for several time intervals.…”

Section: Interaction Between a Two-level And A Quantized Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The von Neumann Entropy for Mixed States

Anaya-Contreras

Moya‐Cessa

Zúñiga-Segundo

2019

Entropy

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“…One of the main tasks in the present manuscript is to calculate the entropy of the field for kaleidoscope states or a statistical mixture of coherent states, in the Jaynes-Cummings framework, which we will do with the aid of the Araki-Lieb inequality [6]. Because we will consider mixtures as initial states [7], in principle, it will not be possible to use the Araki-Lieb inequality to calculate the entropies, especially the field entropy. However via purification of the mixed density matrix of the quantized field [8], we will be able to use such inequality in order to calculate the field von Neumann entropy even in the case of initial statistical mixtures, either for the atom or the field.…”

Section: Introductionmentioning

confidence: 99%

Kaleidoscope States as a Statistical Mixture in the Jaynes-Cummings Model: Entropy and Purification

Anaya-Contreras¹,

Zúñiga-Segundo²,

Moya‐Cessa³

2022

Preprint

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We investigate some of the fundamental features of the interaction of mixed kaleidoscope states, namely, particular statistical mixtures of coherent states, with two-level atoms in the Jaynes-Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field which is determined with help of the virtual atom method. Oscillations appear in this entropy that indicate a state of purity greater than the initial state, {it i.e.}, a purification of the initial state is achieved. In this oscillatory region, we obtain the field Wigner function that resembles Schrodinger's cats.

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