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Chaos An Interdisciplinary Journal of Nonlinear Science

Phase-controlled and chaos-assisted or -suppressed quantum entanglement for a spin-orbit coupled Bose-Einstein condensate

Chao Kong, Xiaobing Luo, Hao Chen, Yunrong Luo, Wenhua Hai

Published Oct 1, 2019• 11 citations
Publisher

Abstract

It has been demonstrated that the presence of chaos may lead to greater entanglement generation for some physical systems. Here, we find different effects of chaos on the spin-motion entanglement for a two-frequency driven Bose-Einstein condensate with spin-orbit coupling. We analytically and numerically demonstrate that classical chaos can assist or suppress entanglement generation, depending on the initial phase differences between two motional states, which can be manipulated by using the known phase-engineering method. The results could be significant in engineering nonlinear dynamics for quantum information processing with many-body entanglement.

DOI
10.1063/1.5118873

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We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.

arXiv:2005.08532•Physical Review A•Aug 18, 2020•13 citations
It has been demonstrated that the presence of chaos may lead to greater entanglement generation for some physical systems. Here, we find different effects of chaos on the spin-motion entanglement for a two-frequency driven Bose-Einstein condensate with spin-orbit coupling. We analytically and numerically demonstrate that classical chaos can assist or suppress entanglement generation, depending on the initial phase differences between two motional states, which can be manipulated by using the known phase-engineering method. The results could be significant in engineering nonlinear dynamics for quantum information processing with many-body entanglement.
We study the spatially chaoticity-dependent spin-motion entanglement of a spin-orbit (SO) coupled Bose-Einstein condensate with a source of ultracold atoms held in an optical superlattice. In the case of phase synchronization, we analytically demonstrate that (a) the SO coupling (SOC) leads to the generation of spin-motion entanglement; (b) the area of the high-chaoticity parameter region inversely relates to the SOC strength which renormalizes the chemical potential; and (c) the high-chaoticity is associated with the lower chemical potential and the larger ratio of the short-lattice depth to the longer-lattice depth. Then, we numerically generate the Poincaré sections to pinpoint that the chaos probability is enhanced with the decrease in the SOC strength and/or the spin-dependent current components. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. For an appropriate lattice depth ratio, the complete stop of one of (or both) the current components is related to the full chaoticity. The results mean that the weak SOC and/or the small current components can enhance the chaoticity. Based on the insensitivity of chaos probability to initial conditions, we propose a feasible scheme to manipulate the ensemble of chaotic spin-motion entangled states, which may be useful in coherent atom optics with chaotic atom transport.
In this paper, we have investigated the stability and population oscillations in a spin–orbit coupled Bose–Einstein condensate. For the time-independent system parameters, the stability of the steady-state solutions was analyzed with the linear stability theorem. For the asymmetric case, we demonstrated that a larger relative energy can enhance macroscopic quantum self-trapping. A larger relative energy or a stronger population transfer strength can assist or suppress the tunneling rate, depending on the initial population. Finally, the chaotic parameter regions and the chaotic atomic tunneling between two periodically driven Bose–Einstein condensates have been investigated. The results reveal that chaos can notably enhance the tunneling rate. The results could be significant in the quantum transport of the spin–orbit coupled cold-atom system.
Abstract We study the spin-field and the spin-spin entanglement in the ground state of a spin-orbit coupled Bose–Einstein condensate. It is found that the spin-field and the spin-spin entanglement can be induced by the spin-orbit coupling. By mapping the system to the Dicke-like model, the system exhibits a quantum phase transition from a normal (spin balanced) phase to superradiant (spin polarized) phase. The Dicke-like phase transition can be captured by the spin-field and the spin-spin entanglement arising from the spin-orbit coupling. The spin-field and the spin-spin entanglement increase as the Raman coupling increases in the superradiant phase, while they decrease with the Raman coupling increasing in the normal phase. We also consider the effect of a finite detuning on these entanglement show that the presence of the detuning suppresses the spin-field and the spin-spin entanglement.
Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
This dissertation sets out to examine some fundamental open questions in quantum physics regarding quantum-classical correspondence in regular versus chaotic systems. Specifically, we study these questions using approaches in quantum information science in an experimentally realized textbook model of quantum chaos - the quantum kicked top (QKT). \n \nThe effect of classical chaos on the generation of entanglement in spin systems has been a field of active research for a couple of decades. Whether high entanglement in these systems is a hallmark of chaos or not remains a widely debated topic. We explain the connection between entanglement and chaos in spin systems and resolve previous conflicting results. The previous studies have mostly drawn conclusions from numerical work on a few initial states in regular versus chaotic regions. We instead focus on stable and unstable periodic orbits because chaos emerges around unstable periodic orbits. We first propose a new set of criteria for determining whether quantum evolution will correspond to the classical trajectory in a localized manner at stable periodic orbits in periodically driven systems. These criteria can be used to calculate the quantum numbers that will lead to quantum-classical correspondence even in a deep quantum regime, and thus to quantify the well-known Bohr correspondence principle. Next, we analytically show a direct connection between entanglement generation and a measure of delocalization of a quantum state in spin systems. More concretely, we describe a method to calculate an upper bound on entanglement generation in any bipartition of spin systems, where the upper bound is a function of trace distance between the evolved state and the most localized classical-like separable states. This method along with our criteria for localized evolution enables us to explain the behaviour of entanglement in both deep quantum and semiclassical regimes for regular as well as chaotic regions. Hence, our analysis resolves the long-standing debates regarding the connection between classical chaos and quantum entanglement in deep quantum and semiclassical regimes. \n \nIn addition to the study of entanglement, we perform the first study of nonlocality, and the effect of chaos on its generation in the QKT. Since nonlocality and entanglement are inequivalent quantum resources, the effect of chaos on nonlocality merits an explicit study. Violations of Bell inequalities in the presence of spacelike separation among the subsystems imply nonlocality - meaning nonlocal correlations between subsystems of the total spin system. We show that the QKT evolution can lead to states that violate multiqubit Bell inequalities and hence provides a deterministic method to prepare nonlocal quantum states. Our numerical results suggest a correlation between delocalized evolution of a pure quantum state and generation of nonlocality in the quantum state. We further demonstrate that dynamical tunnelling - a classically forbidden phenomenon - in the QKT leads to the generation of Greenberger-Horne-Zeilinger (GHZ)-like states for even numbers of qubits. We analytically prove that these states are maximally nonlocal. On the other hand, we numerically show that any reduced state of the QKT obtained by tracing out a subsystem of the total spin system does not violate Bell inequalities. We provide an analytical explanation of the numerical results for 2−2-2−qubit reduced states by formulating and proving two general theorems regarding 2−2-2−qubit Bell inequalities. These theorems imply that any 2−2-2−qubit mixed state having a symmetric extension or symmetric purification cannot violate the Clauser-Horne-Shimony-Holt inequality. This highlights fundamental connections between two important and distinct concepts in quantum information science - Bell inequalities and symmetric extension of quantum states. \n \nApart from providing deeper insights into the fundamental questions of quantum-classical correspondence and new approaches to analyze quantum chaos, the methods developed in this thesis can be used to design quantum systems that can efficiently generate entanglement and nonlocality. Thus, our results could have interesting applications in quantum computing and quantum information science.
We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.