Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0208144 · Physical Review Letters

Decoherence-Free Generation of Many-Particle Entanglement by Adiabatic Ground-State Transitions

Razmik G. Unanyan, Michael Fleischhauer

Published Apr 2, 2003• 105 citations
arXivHTMLPDF

Abstract

We discuss a decoherence insensitive method to create many-particle entanglement in a spin system with controllable collective interactions and propose an implementation in an ion trap. An adiabatic change of parameters allows a transfer from separable to a large variety of entangled eigenstates. We show that the Hamiltonian can have a supersymmetry permitting an explicit construction of the ground state at all times. Of particular interest is a transition in a nondegenerate ground state with a finite energy gap since here the influence of collective as well as individual decoherence mechanisms is substantially reduced. A lower bound for the energy gap is given.

DOI
10.1103/physrevlett.90.133601

Related papers

Noise-resistant entanglement of strongly interacting spin systems

Ana María Rey, Liang Jiang, Michael Fleischhauer +2 more

We propose and analyze a scheme that makes use of interactions between spins to protect certain correlated many-body states from decoherence. The method exploits the finite energy gap of properly designed Hamiltonians to generate a manifold insensitive to local noise fluctuations. We apply the scheme to achieve decoherence-resistant generation of many particle GHZ states and show that it can improve the sensitivity in precision spectroscopy with trapped ions. Finally we also show that cold atoms in optical lattices interacting via short range interactions can be utilized to engineer the required long range interactions for a robust generation of entangled states.

arXiv:cond-mat/0703108•Mar 5, 2007•1 citation

Many-particle entanglement in the gaped antiferromagnetic Lipkin model

Razmik G. Unanyan, C. Ionescu, Michael Fleischhauer

Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin-$1∕2$ particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter $\ensuremath{\gamma}$, from a separable $(\ensuremath{\gamma}=\ensuremath{\infty})$ to a maximally entangled state $(\ensuremath{\gamma}=0)$. From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point $\ensuremath{\gamma}=0$: While at $\ensuremath{\gamma}=0$ the entanglement grows logarithmically with the system size with no upper bound, it saturates for $\ensuremath{\gamma}\ensuremath{\ne}0$ at a level only depending on $\ensuremath{\gamma}$.

Physical Review A•Aug 18, 2005•31 citations

Many-body protected entanglement generation in interacting spin systems

Ana María Rey, Liang Jiang, Michael Fleischhauer +2 more

We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.

arXiv:0706.3378•Physical Review A•May 5, 2008•56 citations

Entanglement generation by adiabatic navigation in the space of symmetric multiparticle states

Razmik G. Unanyan, Michael Fleischhauer, Nikolay V. Vitanov +1 more

We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states.One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.

arXiv:quant-ph/0205118•Physical Review A•Oct 1, 2002•32 citations

Adiabatic quantum simulation with a segmented ion trap: Application to long-distance entanglement in quantum spin systems

Stefano Zippilli, M. Johanning, S. M. Giampaolo +2 more

We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states.

arXiv:1304.0261•Physical Review A•Apr 10, 2014•25 citations

Bi-partite and global entanglement in a many-particle system with collective spin coupling

Razmik G. Unanyan, C. Ionescu, Michael Fleischhauer

Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter $γ$ from a separable ($γ=\infty $) to a maximally entangled many-particle state ($γ=0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point $γ=0$. For $% γ=0$ the entanglement grows logarithmically with the system size with no upper bound, for $γ\neq 0$ it saturates at a level only depending on $γ$. For finite systems with total spin $J=N/2$ the scaling behavior changes at $γ=γ_{\mathrm{crit}}=1/J$.

arXiv:quant-ph/0412164•Dec 21, 2004•1 citation
We discuss a decoherence insensitive method to create many-particle entanglement in a spin system with controllable collective interactions and propose an implementation in an ion trap. An adiabatic change of parameters allows a transfer from separable to a large variety of entangled eigenstates. We show that the Hamiltonian can have a supersymmetry permitting an explicit construction of the ground state at all times. Of particular interest is a transition in a nondegenerate ground state with a finite energy gap since here the influence of collective as well as individual decoherence mechanisms is substantially reduced. A lower bound for the energy gap is given.
We propose and analyze a scheme that makes use of interactions between spins to protect certain correlated many-body states from decoherence. The method exploits the finite energy gap of properly designed Hamiltonians to generate a manifold insensitive to local noise fluctuations. We apply the scheme to achieve decoherence-resistant generation of many particle GHZ states and show that it can improve the sensitivity in precision spectroscopy with trapped ions. Finally we also show that cold atoms in optical lattices interacting via short range interactions can be utilized to engineer the required long range interactions for a robust generation of entangled states.
Bipartite and global entanglement are analyzed for the ground state of a system of NNN spin-1∕21∕21∕2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter $\ensuremath{\gamma}$, from a separable $(\ensuremath{\gamma}=\ensuremath{\infty})$ to a maximally entangled state $(\ensuremath{\gamma}=0)$. From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point $\ensuremath{\gamma}=0$: While at $\ensuremath{\gamma}=0$ the entanglement grows logarithmically with the system size with no upper bound, it saturates for $\ensuremath{\gamma}\ensuremath{\ne}0$ at a level only depending on $\ensuremath{\gamma}$.
We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.
We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states.One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.
We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states.
Bipartite and global entanglement are analyzed for the ground state of a system of NNN spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter γγγ from a separable ($γ=\infty )toamaximallyentangledmany−particlestate() to a maximally entangled many-particle state ()toamaximallyentangledmany−particlestate(γ=0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point γ=0γ=0γ=0. For % γ=0 the entanglement grows logarithmically with the system size with no upper bound, for γ≠0γ\neq 0γ=0 it saturates at a level only depending on γγγ. For finite systems with total spin J=N/2J=N/2J=N/2 the scaling behavior changes at γ=γcrit=1/Jγ=γ_{\mathrm{crit}}=1/Jγ=γcrit​=1/J.