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arXiv:2012.05910 · Journal of Modern Optics

Von Neumann entropy in a dispersive cavity

Ram Narayan Deb

Published Sep 1, 2021• 3 citations
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Abstract

We study the von Neumann entropy of the partial trace of a system of 2 two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single-mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanishes.

DOI
10.1080/09500340.2021.1970306

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We study the von Neumann entropy of the partial trace of a system of 2 two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single-mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanishes.
We show for a general pure entangled state of two two-level atoms, the von Neumann entropy of the partial traces can be directly measured from the magnitude of the mean spin vector of a single atom of the pair. We emphasize the fact that the von Neumann entropy of the partial traces for such a system can be obtained without knowing the exact form of the quantum state of the two atoms, if we have the value of the magnitude of the mean spin vector of a single atom of the pair. Mean spin vector, used in the context of spin squeezing and spectroscopic squeezing in population spectroscopy, is experimentally measurable and provides an exact measure of von Neumann entropy of the partial traces for such a system. The idea developed in this paper can be used in the context of other quantum mechanical two level systems as the algebra of two level systems can be described by that of spin- 12\frac{1}{2}21​ particles.
We study the entanglement in a system consisting of two non-interacting atoms located in separate cavities, both in their ground states. A single incoming photon has a non-zero probability of entering either of the two cavities. The Jaynes-Cummings interaction in the rotating wave approximation describes the coupling of each atom with the radiation field. We compute and analyze the atom-atom entanglement, the entanglement between the two photon modes, and also the entanglement between each atom and each photon mode. The measure of entanglement is the von Neumann entropy. For the case in which the two atom-photon systems have identical properties, but allowing for non-resonant conditions, the sum of the atom-atom and photon-modes-entanglement is time independent. The effect of detuning is to decrease the strength of the largest entanglement achieved and to shorten the time for it to occur. The results support the fact that the state of the photons after emergence from cavities is entangled, notwithstanding its single-particle nature. In addition, for the case of resonance and identical cavity parameters, we demonstrate that von Neumann entropy is always greater than or equal to the measure of entanglement known as negativity.
We consider a system of NNN two-level atoms (spins) interacting with the radiation field in a dispersive but high-QQQ cavity. Under an adiabatic condition, the interaction Hamiltonian reduces to a function of spin operators which is capable of producing spin squeezing. For a bipartite system (N=2)(N=2)(N=2), the expressions for spin squeezing get very simple, giving a clear indication of close to 100% noise reduction. We analyse this squeezing as a measure of bipartite entanglement.
We describe the entanglement of a Jaynes-Cummings system, where a two-level atom is also strongly driven by an external coherent field while it crosses a resonant cavity prepared in a coherent state. First we consider the atom-cavity field entanglement, described by the Von Neumann entropy. We find that it depends only on the interaction time and the initial atomic state. The entropy vanishes in the case of maximally polarized atom, independent of the interaction time, whereas it reaches its maximum value for atom in the upper or lower state and for long enough interaction times. Then we investigate the entanglement between two consecutive strongly driven atoms interacting with the cavity mode assumed in the vacuum state, showing that they never entangle in spite of the existence of atom-atom correlations.
In this paper, we are interested in studying entropy and dynamics entanglement between a single time dependent three-level atoms interacting with one-mode cavity field when the atomic motion is taken into account. An exact analytical solution for the wave function is given by using Schrodinger equation for a specific initial condition. The field entropy of this system is investigated in the non-resonant case. The influences of the detuning parameters and atomic motion on the entanglement degree are examined. We show that both of the detuning parameters and atomic motion play important roles in the evolution of von Neumann entropy and atomic populations. Finally, conclusion and some features are given.
We examine the single-atom entropy squeezing and the atom–field entanglement in a system of two moving two-level atoms interacting with a single-mode coherent field in a lossless resonant cavity. Our numerical calculations indicate that the squeezing period, the squeezing time and the maximal squeezing can be controlled by appropriately choosing the atomic motion and the field-mode structure. The atomic motion leads to a periodical time evolution of entanglement between the two-atom and the field. Moreover, there exists corresponding relation between the time evolution properties of the atomic entropy squeezing and that of the entanglement between the two atoms and the field.