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Register a new userQuantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
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We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources. The proposed scheme can be relevant in a variety of fields as condensed-matter or high-energy physics, where quantum simulations may solve problems intractable for classical computers.
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We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies itself a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a system of trapped ions, and find that the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster than the regimes currently explored in experiments. We propose a scheme to test the bounds by measuring retarded correlation functions via the crystal fluorescence.
A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable.
We discuss the simulation of non-perturbative cavity-QED effects using systems of trapped ions. Specifically, we address the implementation of extended Dicke models with both collective dipole-field and direct dipole-dipole interactions, which represent a minimal set of models for describing light-matter interactions in the ultrastrong and deep-strong coupling regime. We show that this approach can be used in state-of-the-art trapped ion setups to investigate excitation spectra or the transition between sub- and superradiant ground states, which are currently not accessible in any other physical system. Our analysis also reveals the intrinsic difficulty of accessing this non-perturbative regime with larger numbers of dipoles, which makes the simulation of many-dipole cavity QED a particularly challenging test case for future quantum simulation platforms.
The generating functional of a self-interacting scalar quantum field theory (QFT), which contains all the relevant information about real-time dynamics and scattering experiments, can be mapped onto a collection of multipartite-entangled two-level sensors via an interferometric protocol that exploits a specific set of source functions. Although one typically focuses on impulsive delta-like sources, as these give direct access to $n$-point Feynman propagators, we show in this work that using always-on harmonic sources can simplify substantially the sensing protocol. In a specific regime, the effective real-time dynamics of the quantum sensors can be described by a quantum Ising model with long-range couplings, the range and strength of which contains all the relevant information about the renormalisation of the QFT, which can now be extracted in the absence of multi-partite entanglement. We present a detailed analysis of how this sensing protocol can be relevant to characterise the long-wavelength QFT that describes quantised sound waves of trapped-ion crystals in the vicinity of a structural phase transition, opening a new route to characterise the associated renormalisation of sound.
We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.
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