Unusual entanglement dynamics in the quantum kicked top

Presenting Author: Arjendu Pattanayak, Carleton College
Contributing Author(s): Sudheesh Srivastava

We study the quantum kicked top in the experimentally accessible regime of a few qubits \(N \in \{2, 8\}\). We focus on the entanglement dynamics \(|\psi(t)>\) of intial spin coherent states on the \((J_x,J_y,J_z)\) sphere. We demonstrate that the quantum behavior at a given location can correlate with, or anti-correlate with, or be decorrelated with the limiting \(N \to \infty\) classical phase-space behavior. Globally, quantum spectra and eigenfunctions visualized via expansion coefficients in the Hilbert space of the \(J_z\) operator are shown to be periodic in \(K\) whence the quantum dynamics are (quasi-)periodic in time \(T\) and nonlinear kick strength \(K\), unlike the classical dynamics although decoherence distinguishes between different \(K\) regimes. Further, there are patterns in the quantum dynamics that repeat as a function of \(N\). We explore novel oscillations where |\(\psi>\) moves between two maximally entangled (GHZ-like) configurations \((|\chi_+>, |\chi_->)\) which occur for \(N=4,8\) in our system. We show that linear combinations of the \(\chi\) states relax to different final entangled states for a decoherent Kraus map of weighted sum of Floquet operators. Thus quantum entanglement for a classically chaotic system can depend on initial conditions (but not as for the classical system) and can yield final high entanglement even for states 'thermalized' under decoherence. We connect to the classical phase-space dynamics via the Husimi projections of these \(\chi\) states.

(Session 9c : Monday from 5:15pm - 5:45pm)


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