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arXiv:quant-ph/0511185 · New Journal of Physics

Excitation and entanglement transfer versus spectral gap

Michael J. Hartmann, M. E. Reuter, Martin Bodo Plenio

Published Jun 9, 2006• 70 citations
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Abstract

We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.

DOI
10.1088/1367-2630/8/6/094

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We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.
Condensed matter systems have recently been proposed as quantum channels for short distance communication. One characteristic of these systems is whether they feature a spectral gap between their ground and excited states. In this paper we study the transfer of excitations and entanglement between two ancillas, which are weakly coupled to a one dimensional chain at different sites. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap between their ground and excited states. In particular this gap vanishes at critical points of quantum phase transitions. In this article we study the relation between the transfer speed and quality of such a system and the size of its spectral gap. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 111-D Heisenberg frustrated J1J_1J1​-J2J_2J2​ spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α=J2/J1≈0.241\alpha=J_2/J_1\approx0.241α=J2​/J1​≈0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 888 sites to 161616 sites, and the value of α\alphaα at which the change in entanglement is observed asymptotically tends to a value αc≈0.24116\alpha_c\approx0.24116αc​≈0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 111-D Heisenberg frustrated J1J_1J1​-J2J_2J2​ spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 222-D Heisenberg J1J_1J1​-J2J_2J2​ model and Shastry-Sutherland model and detect quantum phase transitions.
This thesis covers open quantum systems and information transfer in the face of \ndissipation and disorder through numerical simulation. \nIn Chapter 3 we present work on an open quantum system comprising a two-level system, single bosonic mode and dissipative environment; we have included \nthe bosonic mode in the exact system treatment. This model allows us to gain an understanding of an environment’s role in small energy transfer systems. We observe \nhow the two-level system-mode coupling strength and the spectral density form characterising the environment interplay, affecting the system’s coherent behaviour. We \nfind strong coupling and a spectral density resonantly peaked on the two-level system oscillation frequency enhances the system’s coherent oscillatory dynamics. \nChapter 4 focusses on a physically motivated study of chain and ladder spin \ngeometries and their use for entanglement transfer between qubits. We consider a \nnitrogen vacancy centre qubit implementation with nitrogen impurity spin-channels \nand demonstrate how matrix product operator techniques can be used in simulations \nof this physical system. We investigate coupling parameters and environmental decay \nrates with respect to transfer efficiency effects. Then, in turn, we simulate the effects \nof missing channel spins and disorder in the spin-spin coupling. We conclude by \nhighlighting where our considered channel geometries outperform each other. \nThe work in Chapter 5 is an investigation into the feasibility of routing entanglement between distant qubits in 2D spin networks. We no longer consider a physical \nimplementation, but keep in mind the effects of dissipative environments on entanglement transfer systems. Starting with a single sending qubit-ancilla and multiple \naddressable receivers, we show it is possible to target a specific receiver and establish transferred entanglement between it and the sender’s ancilla through eigenstate tunnelling techniques. We proceed to show that eigenstate tunnelling-mediated entanglement transfer can be achieved simultaneously from two senders across one spin network.
Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.
Abstract The transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum information processing. We address the transfer of n > 1 bosonic and fermionic excitations between the edges of a one-dimensional chain modelled by a quadratic hopping Hamiltonian, where the block edges, embodying the sender and the receiver sites, are weakly coupled to the quantum wire. We find that perturbative high-quality transfer is attainable in the weak-coupling limit, for both bosons and fermions, only for certain modular arithmetic equivalence classes of the wire’s length. Finally we apply our findings to the transport of spins and the charging of a many-body quantum battery.