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arXiv:2006.06342 · Physical Review A

Spin squeezing and concurrence under Lee-Yang dephasing channels

Yuguo Su, Hongbin Liang, Xiaoguang Wang

Published Nov 30, 2020• 9 citations
arXivHTMLPDF

Abstract

The Lee-Yang zeros are one-to-one mapped to zeros in the coherence of a probe spin coupled to a many-body system. Here, we propose two different types of Lee-Yang dephasing channels, where the partition functions vanish at Lee-Yang zeros, and study the spin squeezing under them. Under the first type of channels where probes are coupled to their own bath, we find that the performance of spin squeezing is improved and its maximum only depends on the initial state. Moreover, the centers of all the concurrence vanishing domains are corresponding to the Lee-Yang zeros. Under the second type of the channel where probes are coupled to one bath together, the performance of spin squeezing is not improved, however, the concurrence shares almost the same properties under both channels. These results provide experimental possibilities in many-body physics and give an alternative perspective on the relationship between the entanglement and spin squeezing in probes-bath systems.

DOI
10.1103/physreva.102.052423

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The Lee-Yang zeros are one-to-one mapped to zeros in the coherence of a probe spin coupled to a many-body system. Here, we propose two different types of Lee-Yang dephasing channels, where the partition functions vanish at Lee-Yang zeros, and study the spin squeezing under them. Under the first type of channels where probes are coupled to their own bath, we find that the performance of spin squeezing is improved and its maximum only depends on the initial state. Moreover, the centers of all the concurrence vanishing domains are corresponding to the Lee-Yang zeros. Under the second type of the channel where probes are coupled to one bath together, the performance of spin squeezing is not improved, however, the concurrence shares almost the same properties under both channels. These results provide experimental possibilities in many-body physics and give an alternative perspective on the relationship between the entanglement and spin squeezing in probes-bath systems.
Abstract We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109 , 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms.
Recently in the paper by Peng X. et al. , Phys. Rev. Lett. , 114 (2015) 010601, the experimental observation of the Lee-Yang zeros of an Ising-type spin-(1/2) bath, by measuring the coherence of a probe spin, was reported. We generalize this problem to the case of an arbitrary high-spin bath. Namely, we consider the evolution of a probe arbitrary spin which interacts with a bath composed by N arbitrary spins. As a result, the connection between the observed values of the probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is found. We apply these results to some models, namely, a triangle spin cluster, the Ising model with a long-range interaction and the 1D Ising model with nearest-neighbor interaction. Also we propose the implementation of these models on real physical systems.
Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their thermodynamics. Notwithstanding their fundamental importance, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that they would occur only at complex values of physical parameters, which are generally regarded as unphysical. Here we report the first observation of Lee-Yang zeros, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath. The quantum evolution of the probe spin introduces a complex phase factor and therefore effectively realizes an imaginary magnetic field. From the measured Lee-Yang zeros, we reconstructed the free energy of the spin bath and determined its phase transition temperature. This experiment opens up new opportunities of studying thermodynamics in the complex plane.
We study the Yang-Lee theory in quantum phase transitions from the perspective of quantum entanglement in one-dimensional many-body systems. We primarily focus on the distribution of Yang-Lee zeros and its associated Yang-Lee edge singularity of two prototypical models: the Su-Schrieffer-Heeger model and the XXZ spin chain. By taking the zero-temperature limit, we show how the Yang-Lee zeros approach the quantum phase transition points on the complex plane of parameters. To characterize the edge singularity induced by Yang-Lee zeros in a quantum phase transition, we introduce the entanglement entropy of the ground state to show that the edges of Yang-Lee zeros lead to the ground-state entanglement transition. We further show that our results are also applicable to the general noninteracting parity-time-symmetric Hamiltonians.
Phase transitions are not usually seen in the time domain. Here, we report on the finding of critical times at which a physical observable, in the thermodynamic limit, becomes nonanalytic as a function of time. We find that the coherence of a probe spin coupled to a many-body system vanishes at times in one-to-one correspondence to the Lee-Yang zeros of the partition function of the many-body system. In the thermodynamic limit, the Lee-Yang zeros form a continuum cut in the complex plane of fugacity and the probe spin coherence presents sudden death and birth at the critical times corresponding to the Yang-Lee singularities. These results provide new experimental possibilities in many-body physics.
In order to witness multipartite correlations beyond pairwise entanglement, spin-squeezing parameters are analytically calculated for a spin ensemble in a collective initial state under three different decoherence channels. It is shown that, in analogy to pairwise entanglement, the spin squeezing described by different parameters can suddenly become zero at different vanishing times. This finding shows the general occurrence of sudden vanishing phenomena of quantum correlations in many-body systems, which here is referred to as spin-squeezing sudden death (SSSD). It is shown that the SSSD usually occurs due to decoherence and that SSSD never occurs for some initial states in the amplitude-damping channel. We also analytically obtain the vanishing times of spin squeezing.