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Physical review. E

Dynamics of an entangled pair of spin- 12 particles under correlated random magnetic fields

Venkata Satya Surya Phaneendra Pydimarri, Timothy R Field

Published Jan 25, 2023• 1 citation
Publisher

Abstract

The dynamics of a maximally entangled pair of spin-1/2 particles is obtained in the presence of random magnetic fields which are correlated. The two spin-1/2 particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.

DOI
10.1103/physreve.107.014135

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The dynamics of a maximally entangled pair of spin-1/2 particles is obtained in the presence of random magnetic fields which are correlated. The two spin-1/2 particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.
The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the same random magnetic field, are studied. The dynamics of the pure joint state of the pair are derived using stochastic calculus. An ensemble of such pure states is combined using the modified spin joint density matrix, and the joint relaxation time for the pair of spin-1/2 particles is obtained. The dynamics can be interpreted as a special kind of correlation involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles.
Abstract We examine the quantum dynamics of both a single spin- J particle and a pair of spin- J particles in the presence of static and rotating magnetic fields, which can be important for qudit-based quantum technologies. Notably, we find resonant, periodic oscillations between two maximally stretched states, irrespective of the value of J . Additionally, we observe periodic transitions between sublevels with magnetic quantum numbers of opposite signs. The dynamics also exhibit a periodic transfer of the spin to the maximally stretched state, starting from the ground state of the initial Hamiltonian. For a pair of spins, we derive various resonance conditions and further analyze the entanglement generated by dipole–dipole interactions. In the case of two spin-1/2 particles, the entanglement dynamics reveal resonances and kinks in the maximum entanglement, and their criteria can be obtained from the energy spectrum. Strikingly, we show that the kink can be exploited to engineer the entanglement dynamics. Finally, we briefly discuss the regime of weak dipolar interactions, which are relevant for dipolar Bose–Einstein condensates.
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.
In this paper, the effect of homogeneous and non-homogeneous magnetic fields as an external noisy on the entanglement dynamics over partial entangled state quantum network is studied. The Dzyaloshiniskii-Moriya (DM) interaction is used to generate entangled network from partially entangled states in the presence of the spin-orbit coupling. The entanglement between any two nodes is quantified using Wootter concurrence. The effect of homogeneous and non-homogeneous magnetic field in presence and absence of the spin coupling on the entanglement between any two nodes of the network is investigated. The results show that the homogeneous magnetic field has no effect on the entanglement without the presence of the spin-orbit interaction. The non-homogeneous magnetic field has a strong impact on the entanglement either with or without spin-orbit couplings. For initially entangled channels, the upper bound does not exceed its initial value, whereas for the channels generated via indirect interaction, the entanglement reaches its maximum value.
We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s1 and s2, in a constant magnetic field. Two different situations are considered:(a) s1 ->\\infty, s2 = 1/2 and (b) s1 = s2 ->\\infty, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.