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The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic…
While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show…
A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range…
The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. As this method is reversible and state selective it effectively implements a…
The trapped-ion system has been a leading platform for practical quantum computation and quantum simulation since the first scheme of a quantum gate was proposed by Cirac and Zoller in 1995. Quantum gates with trapped ions have shown the…
Quantum systems inside high-Q cavities offer an excellent testbed for the control of emergent symmetries induced by light and their interplay with quantum matter. Recently several developments in cavity experiments with neutral atoms and…
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focussing on long- and short-range Ising-type Hamiltonians, we introduce schemes…
Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model…
Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled…
We propose an analog quantum simulator that uses ion traps to realize the many-body electron-electron Coulomb interaction of an electron gas. This proposal maps a system that is difficult to solve and control to an experimentally-feasible…
Quantum computers have the potential to efficiently simulate the dynamics of many interacting quantum particles, a classically intractable task of central importance to fields ranging from chemistry to high-energy physics. However,…
In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such…
We study the quantum phase transition in a spin chain with variable Ising interaction and position-dependent coupling to a resonator field. Such a complicated model, usually not present in natural physical systems, can be simulated by an…
Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors, and are therefore a major target of research in modern physics. Quantum simulators can…
In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions…
Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented.…
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eingenstates naturally protected against local sources of decoherence. This Hamiltonian involves long range coupling between particles and provides a…