Erratum: Entanglement and Tunable Spin-Spin Couplings between Trapped Ions Using Multiple Transverse Modes [Phys. Rev. Lett.<b>103</b>, 120502 (2009).]

Kim, K.; Chang, M.-S.; Islam, Rajibul; Korenblit, S. É.; Duan, Liwei; Monroe, C.

doi:10.1103/physrevlett.105.109901

Cited by 90 publications

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“…States with desired quantum entanglement properties find important applications in quantum information processing, cryptography, and computation [1]. Indeed efforts in this direction can be found in areas as diverse as quantum dots [2], trapped ions [3], and cold atoms [4,5], to name a few. It has also been recognized recently that similar ideas can be used to create exotic many-body states in cold atoms.…”

Section: Introductionmentioning

confidence: 99%

Preparation of two-particle total-hyperfine-spin-singlet states via spin-changing dynamics

2012

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Section: Introductionmentioning

confidence: 99%

Preparation of two-particle total-hyperfine-spin-singlet states via spin-changing dynamics

2012

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“…When N ions are placed in a linear Paul trap [9,10,20] with harmonic trapping potentials, they form a nonuniform (Wigner) lattice, with increasing interparticle spacing as one moves from the center to the edge of the chain. The ions vibrate in all three spatial dimensions about these equilibrium positions [21] with 3N normal modes.…”

Section: Theory a Microscopic Hamiltonianmentioning

confidence: 99%

“…In recent years, there has been significant success in trying to achieve this goal by quantum simulation of desired spin models through analogous cold atom systems [6][7][8]. We focus here on one platform for performing analog quantum computation, the simulation of interacting quantum spins via manipulation of hyperfine states of ions in a linear Paul trap [9][10][11][12][13] although many ideas presented here can be generalized * Electronic address: joseph@physics.georgetown.edu to adiabatic quantum state computation in the two dimensional Penning trap as well [8]. In the Paul trap systems, clock states of the ions (states with no net zcomponent of angular momentum) are the pseudospin states, which can be manipulated independently by a pseudospin-dependent force driven by laser beams.…”

Section: Introductionmentioning

confidence: 99%

“…In the Paul trap systems, clock states of the ions (states with no net zcomponent of angular momentum) are the pseudospin states, which can be manipulated independently by a pseudospin-dependent force driven by laser beams. The lasers couple the pseudospin states to the lattice vibrations of the trapped ions, which leads to effective spinspin interactions when the phonon degrees of freedom are adiabatically eliminated [10,14,15] based on the idea of geometric phase gate [16] or Mølmer-Sørensen gate [17]. Theoretically, the analog ion-trap simulators can be described as nonequilibrium driven quantum systems with both spin and phonon degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

Wang

Freericks

2012

Phys. Rev. A

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Linear Paul traps have been used recently to simulate the transverse field Ising model with longrange spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbation theory and exact numerical integration of the Schrödinger equation in a truncated spin-phonon Hilbert space followed by a tracing out of the phonon degrees of freedom to study this problem. We find that moderate phonon creation often makes the probabilities of different spin states behave differently from the static spin Hamiltonian. In circumstances in which phonon creation is minor, the spin dynamics state probabilities converge to the static spin Hamiltonian prediction at the cost of reducing the spin entanglement. We show how phonon creation can severely impede the observation of kink transitions in frustrated spin systems when the number of ions increases. Many of our results also have implications for quantum simulation in a Penning trap.

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“…We study DQPTs in a trapped-ion quantum simulator, realizing the dynamics of an effective transverse-field Ising Hamiltonian [19][20][21],…”

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Quantum Phase Transitions Go Dynamical

Gurarie

2017

Physics

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The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production. DOI: 10.1103/PhysRevLett.119.080501 Today, the equilibrium properties of quantum matter are theoretically described with great success. Yet, in recent years pioneering experiments have created quantum states beyond this equilibrium paradigm [1,2]. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization [3,4], prethermalization [5,6], particle-antiparticle production in the lattice Schwinger model [7], and light-induced superconductivity [8]. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for concepts that extend important principles such as universality to the nonequilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs) [9], which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this Letter, we directly observe the defining real-time nonanalyticities at DQPTs in a trapped-ion quantum simulator for interacting transverse-field Ising models. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.Statistical mechanics and thermodynamics provide us with an excellent understanding of equilibrium quantum many-body systems. A key concept in this framework is the canonical partition function ZðTÞ ¼ Trðe −H=k B T Þ, with T being the temperature, k B the Boltzmann constant, and H the system Hamiltonian. The partition function encodes thermodynamics via the free-energy density f ¼ −ðk B T=NÞ log ½ZðTÞ , where N denotes the number of degrees of freedom.A phase transition, i.e., a sudden change of macroscopic behavior, is associated with a nonanalytical behavior of f as a function of temperature or another control parameter g such as an external magnetic field. QPTs [10] occur when T is kept at absolute 0, where the system's ground-state properties undergo a nonanalytic change as a function of g [see Fig. 1(a)]. Scenarios where boundary conditions are essential, such as for the Casimir effect, can be studied by boundary partition functions Z B ¼ hψ 0 je −RH jψ 0 i, where jψ 0 i encodes the spatial boundary conditions on two ends of the system at dis...

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Erratum: Entanglement and Tunable Spin-Spin Couplings between Trapped Ions Using Multiple Transverse Modes [Phys. Rev. Lett.103, 120502 (2009).]

Abstract: The authors have found typographical errors on page 2 and page 3. On page 2, Eq. (3) should readOn page 3, right-hand column, the 5th line of the second paragraph should read ''.

Cited by 90 publications

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Preparation of two-particle total-hyperfine-spin-singlet states via spin-changing dynamics

Preparation of two-particle total-hyperfine-spin-singlet states via spin-changing dynamics

Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

Quantum Phase Transitions Go Dynamical

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