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Universe

On the General Entangled State and Quantum Decoherence

Abasalt Rostami, Javad T. Firouzjaee

Published Sep 26, 2022• 0 citations
Publisher

Abstract

We study the primary entanglement effect on the decoherence of reduced-density matrices of scalar fields, which interact with other fields or independent mode functions. We study the (leading) tree-level evolution of the scalar bispectrum due to a coupling between two scalar fields. We show that the primary entanglement has a significant role in the decoherence of the given quantum state. We find that the existence of such an entanglement could couple dynamical equations coming from a Schrödinger equation. We show that if one wants to see no effect of the entanglement parameter in the decohering of the quantum system, then the ground state eigenvalues of the interaction terms in the Hamiltonian cannot be independent of each other Generally, including the primary entanglement destroys the independence of the interaction terms in the ground state. We show that the imaginary part of the entanglement parameter plays an important role in the decoherence process without posing any specific restriction to the interaction terms. Our results could be generalized to every scalar quantum field theory with a well-defined quantization of its fluctuations in a given curved space-time.

DOI
10.3390/universe8100508

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We study the primary entanglement effect on the decoherence of reduced-density matrices of scalar fields, which interact with other fields or independent mode functions. We study the (leading) tree-level evolution of the scalar bispectrum due to a coupling between two scalar fields. We show that the primary entanglement has a significant role in the decoherence of the given quantum state. We find that the existence of such an entanglement could couple dynamical equations coming from a Schrödinger equation. We show that if one wants to see no effect of the entanglement parameter in the decohering of the quantum system, then the ground state eigenvalues of the interaction terms in the Hamiltonian cannot be independent of each other Generally, including the primary entanglement destroys the independence of the interaction terms in the ground state. We show that the imaginary part of the entanglement parameter plays an important role in the decoherence process without posing any specific restriction to the interaction terms. Our results could be generalized to every scalar quantum field theory with a well-defined quantization of its fluctuations in a given curved space-time.
We study the primary entanglement effect on the decoherence of fields reduced density matrix which are in interaction with another fields or independent mode functions. We show that the primary entanglement has a significant role in decoherence of the system quantum state. We find that the existence of entanglement could couple dynamical equations coming from Schrödinger equation. We show if one wants to see no effect of the entanglement parameter in decoherence then interaction terms in Hamiltonian can not be independent from each other. Generally, including the primary entanglement destroys the independence of the interaction terms. Our results could be generalized to every scalar quantum field theory with a well defined quantization in a given curved space time.
We study the entanglement dynamics in the system of coupled boson fields. We demonstrate that there are different natural notions of locality in this context leading to inequivalent notions of entanglement. We concentrate on the particle picture, when entanglement of one particle is determined by one-particle density matrix. We study, in detail, the effect of interaction preserving populations of individual one-particle states. We show that if the system is initially in a disentangled state with the definite total number of particles and the dimension of the one-particle Hilbert space is more than two, then only potentials of the special form admit complete entanglement, which is shown to be reached at NOON states. If the system is initially in Glauber’s coherent state, complete entanglement is not reached despite the presence of two entangling channels in this case. We conclude with studying the time evolution of entanglement of photons in a cavity with multiple quantum dots in the limit of large number of photons. We show that in a relatively short time scale the completely entangled states belong to the class of graph states and are formed due to the interaction with dots in resonance with the cavity modes.
We discuss the dynamical properties of quantum entanglement and partial entropy for moving three-level atom interacting with single-mode quantized field inside a phase-damped cavity for more general cases.The results show that the atomic motion and decoherence effects play an important role on the evolution of the system dynamics and quantum entanglement.Moreover, we show that the phenomena of long lived nonlocal correlation and short temporal disentanglement can be generated through specific values of phase damping and atomic motion parameter.
In this paper we study the interaction between two qutrits ([Formula: see text]-type three-level atoms) with a two-mode field in a high quality cavity, considering the field-field (F-F) correlation and dipole-dipole (D-D) interaction. By defining a Hamiltonian corresponds to D-D interaction related to the two three-level atoms, we introduce a generalized Hamiltonian of Jaynes-Cummings model for the desired system and then the associated Schrödinger equation is solved. Finally, by achieving the reduced density matrix and then the linear entropy as a criterion for the entanglement, we investigate the influence of the F-F and D-D coupling on the degree of entanglement of the system. Our results show that there exists specific initial superposition of atomic states wherein the stable value of linear entropy is accessible. In addition, in such cases the F-F correlation and D-D interaction have not considerable effect on the entropy. Moreover, in general, as we have shown, the entanglement can be tuned appropriately by choosing the parameters involve in the model.
Schroumloumloumldinger equation for joint bidirectional motion in time
The conventional time-dependent Schrödinger equation describes only unidirectional time evolution of the state of a physical system, i.e. forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the description of joint, and interactive, forward and backward time evolution within a physical system. The principal mathematical assumption for bidirectional evolution in general is that the space of states should be taken to be not merely a Hilbert space, but a more restricted entity known as a Kreĭn space, which is a complex Hilbert space with a Hermitian operator that has eigenvalues +1 and −1 only, and that therefore gives rise to an indefinite metric. The vector subspaces of states with positive or negative norm with respect to the indefinite metric will—for open channels—be construed to be states in forward or, respectively, backward evolution along the time axis. The quantum dynamics is generated by a pseudo-Hermitian Hamiltonian operator and conserves inner products with respect to the indefinite metric. Input and output states are defined in physically plausible ways such that the output comprises both reflected and transmitted states from a zone of interaction in time; a unitary transformation between input and output states is obtained from the pseudounitary transformation between the initial and final states. Three applications are studied: (1) a formal theory of collisions in terms of perturbation theory; (2) a relativistically invariant quantum field theory for a system that kinematically comprises the direct sum of two quantized real scalar fields, such that one subfield evolves forward and the other backward in time, and such that there is dynamical coupling between the subfields; (3) an argument that in the latter field theory, the dynamics predicts that in a range of values of the coupling constants, the expectation value of the vacuum energy of the universe is forced to be zero to high accuracy.