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arXiv:1511.09260 · Physical Review A

Entanglement storage by classical fixed points in the two-axis countertwisting model

Dariusz Kajtoch, Krzysztof Pawłowski, Emilia Witkowska

Published Feb 26, 2016• 2 citations
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Abstract

We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in the mean-field phase portrait. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. We also discuss evolution with noise. In some cases the effect of noise turns out to be relatively weak, which is explained by parity conservation.

DOI
10.1103/physreva.93.022331

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We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in the mean-field phase portrait. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. We also discuss evolution with noise. In some cases the effect of noise turns out to be relatively weak, which is explained by parity conservation.
We study the quantum dynamics generated by the two-axis countertwisting Hamiltonian from an initial spin coherent state in a spin-1/21/21/2 ensemble. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of four neutrally stable and two saddle unstable fixed points. The presence of the latter is responsible for a high level of squeezing. The squeezing is accompanied by the appearance of several quantum states of interest in quantum metrology with Heisenberg-limited sensitivity, and we show fidelity functions for some of them. We present exact results for the quantum Fisher information and the squeezing parameter. Although the overall time evolution of both changes strongly with the number of particles, we find that they have regular dynamics for short times. We explain scaling with the system size by using a Gaussian approach.
A scheme for dynamical stabilization of entanglement quantified by the quantum Fisher information is analyzed numerically and analytically for bimodal and spin-1 Bose-Einstein condensates in the context of atomic interferometry. The scheme consists of twisting dynamics followed by a single rotation of a state which limits further evolution around stable center fixed points in the mean-field phase space. The resulting level of entanglement is of the order or larger than at the moment of rotation. It is demonstrated that the readout measurement of parity quantifies the level of entanglement during the entire evolution.
Fisher information is an important concept in estimation theory, which has recently been found closely related with the criteria of the entanglement in quantum information. Under the condition of non-rotating wave approximation, the classical phase space of the Dicke model displays chaotic dynamic properties. This paper studies the quantum Fisher information and the dynamic properties of spin squeezing in the interaction system of light and matter described in the Dicke model. Results reveal that, in the short-time instant state, wherever the initial state is, in a regular region or a chaotic region, the system displays entanglement; but in the long-time stable state, when the initial state is in the regular region, the system entanglement disappears, however, when the initial state is in the chaotic region, the system is always entangled. Compared with the spin-squeezing dynamic properties of the system, Fisher information is found to be able to effectively characterize quantum chaos. On further examination on the dynamic evolvement properties of the density matrix and purity of the system when in the regular and chaotic regions, we find that chaos gives rise to decoherence of the system, showing that quantum information become more sensitive to chaos.
The quantum Fisher information, the quantum analog of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using numerically exact methods applied to a paradigmatic open quantum system, the spin-boson model, we calculate both static and dynamical quantum Fisher information matrix elements with respect to spin-bath couplings and magnetic field strengths. As the spin-bath interaction increases, we first show that the coupling-coupling matrix elements relative to the ground state of the Hamiltonian are linked to the entanglement growth and signal the Berezinskii-Kosterlitz-Thouless quantum phase transition through their nonmonotonic behavior. We also point out that the static quantum Fisher information exhibits a nonperturbative behavior in the zero-coupling limit, which we justify with an analytic argument. Furthermore, we demonstrate that the time-dependent matrix elements can reveal non-Markovian effects as well as the transition from the coherent to incoherent regime at the Toulouse point, remaining robust under pure dephasing noise. Nonmonotonic signatures of the quantum Fisher information matrix reflect changes in quantum resources such as entanglement and coherence, quantify non-Markovian behavior, and enable criticality-enhanced quantum sensing, thereby shedding light on key features of open quantum systems.
We study the effect of noise on the dynamics of the transverse-field Ising model quenched across a quantum critical point. To quantify two-spin correlations, we employ the quantum Fisher information (QFI) and the Wigner-Yanase skew information (WYSI) as measures of quantum coherence. In the noiseless case, in contrast to the dynamics of entanglement in anisotropic XY chains, both QFI and WYSI increase monotonically with the ramp quench time, approaching their adiabatic limits without exhibiting any Kibble-Zurek-type scaling with quench duration. In contrast, when noise is added to the quench protocol, the coherence dynamics change qualitatively: QFI and WYSI both decay exponentially with the timescale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reaches its maximum, scales linearly with the noise variance, featuring the same exponent that determines the optimal annealing time for minimizing defect production in noisy quantum annealing.
We study the effect of dipolar interactions on the level of squeezing in spin-1 Bose-Einstein condensates by using the single mode approximation. We limit our consideration to the SU(2) Lie subalgebra spanned by spin operators. The biaxial nature of dipolar interactions allows for dynamical generation of spin-squeezed states in the system. We analyze the phase portraits in the reduced mean-field space in order to determine positions of unstable fixed points. We calculate numerically the spin squeezing parameter showing that it is possible to reach the strongest squeezing set by the two-axis countertwisting model. We partially explain scaling with the system size by using the Gaussian approach and the frozen spin approximation.