Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate unexpected quantum phenomena in few-body systems. A pair of ions interacting in such traps exchange vibrational quanta through the Coulomb interaction. This linear interaction can be anharmonically modulated by an elementary coupling to the internal two-level structure of one of the ions. Driven by thermal energy in the passively coupled oscillators, which are themselves coupled to the internal ground states of the ions, the nonlinear interaction autonomously and unconditionally generates entanglement between the mechanical modes of the ions. We examine this counter-intuitive thermally induced entanglement for several experimentally feasible model systems and propose parameter regimes where state-of-the-art trapped ion systems can produce such phenomena. In addition, we demonstrate a multiqubit enhancement of such thermally induced entanglements.
Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate unexpected quantum phenomena in few-body systems. A pair of ions interacting in such traps exchange vibrational quanta through the Coulomb interaction. This linear interaction can be anharmonically modulated by an elementary coupling to the internal two-level structure of one of the ions. Driven by thermal energy in the passively coupled oscillators, which are themselves coupled to the internal ground states of the ions, the nonlinear interaction autonomously and unconditionally generates entanglement between the mechanical modes of the ions. We examine this counter-intuitive thermally induced entanglement for several experimentally feasible model systems and propose parameter regimes where state-of-the-art trapped ion systems can produce such phenomena. In addition, we demonstrate a multiqubit enhancement of such thermally induced entanglements.
The quantum simulation of complex many body systems holds promise for understanding the origin of emergent properties of strongly correlated systems, such as high-Tc superconductors and spin liquids. Cold atomic systems provide an almost ideal platform for quantum simulation due to their excellent quantum coherence, initialization and readout properties, and their ability to support several forms of interactions. In this thesis, I present experiments on the quantum simulation of long range Ising models in the presence of transverse magnetic fields with a chain of up to sixteen ultracold 171-Yb+ ions trapped in a linear radio frequency Paul trap. Two hyperfine levels in each of the 171-Yb+ ions serve as the spin-1/2 systems. We detect the spin states of the individual ions by observing state-dependent fluorescence with single site resolution, and can directly measure any possible spin correlation function. The spin-spin interactions are engineered by applying dipole forces from precisely tuned lasers whose beatnotes induce stimulated Raman transitions that couple virtually to collective phonon modes of the ion motion. The Ising couplings are controlled, both in sign and strength with respect to the effective transverse field, and adiabatically manipulated to study various aspects of this spin model, such as the emergence of a quantum phase transition in the ground state and spin frustration due to competing antiferromagnetic interactions. Spin frustration often gives rise to a massive degeneracy in the ground state, which can lead to entanglement in the spin system. We detect and characterize this frustration induced entanglement in a system of three spins, demonstrating the first direct experimental connection between frustration and entanglement. With larger numbers of spins we also vary the range of the antiferromagnetic couplings through appropriate laser tunings and observe that longer range interactions reduce the excitation energy and thereby frustrate the ground state order. This system can potentially be scaled up to study a wide range of fully connected spin networks with a few dozens of spins, where the underlying theory becomes intractable on a classical computer.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
Single trapped ions trapped in Paul traps correspond to ideal candidates for realization of extremely accurate optical atomic clocks and practical studies of the light–atom interactions and nonlinear mechanical dynamics. These systems benefit from both, the superb isolation of the ion from surrounding environment and excellent control of its external and internal\ndegrees of freedom, at the same time, which makes them exquisite platforms for experimental studies and applications of light matter interaction at its most fundamental level. The exceptional degree of control of single or few ion's state enabled in past decade number of major advancements in the applications from the fields of experimental quantum information\nprocessing and frequency metrology, including recent realization of scalable Shor's\nalgorithm, fractional uncertainties of the frequency measurements close to 10-18 level, or simulations of complex quantum many-body effects. These results, together with the rapid advancements in the production of low-noise segmented micro-traps, promise prompt access to long-desired regimes of quantum optomechanics and further development and applications\nof optical atomic clocks.
Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
Laser-cooled and trapped ions can crystallize and feature discrete solitons that are nonlinear, topologically protected configurations of the Coulomb crystal. Such solitons, as their continuum counterparts, can move within the crystal, while their discreteness leads to the existence of a gap-separated, spatially localized motional mode of oscillation above the spectrum. Suggesting that these unique properties of discrete solitons can be used for generating entanglement between different sites of the crystal, we study a detailed proposal in the context of state-of-the-art experimental techniques. We analyze the interaction of periodically driven planar ion crystals with optical forces, revealing the effects of micromotion in radio-frequency traps inherent to such structures, as opposed to linear ion chains. The proposed method requires Doppler cooling of the crystal and sideband cooling of the soliton's localized modes alone. Since the gap separation of the latter is nearly independent of the crystal size, this approach could be particularly useful for producing entanglement and studying system-environment interactions in large, two- and possibly three-dimensional systems.
While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.