Session C8: Quantum Simulation

Simulating a Quantum Phase Transition with a Surface Electrode Ion Trap

The Rabi model describes the interaction of a two-level atom with a quantized electromagnetic field. The model is predicted to have a quantum phase transition (QPT) between a normal and superradiant phase depending on the strength of the interaction. A recent proposal describes how the QPT can be simulated using a trapped ion where the quantized modes of motion simulate the electromagnetic field \footnote{Puebla, R., Hwang, M. J., Casanova, J., \& Plenio, M. B., \textbf{arXiv} 1607.03781, (2016)}. The simulation is controlled by an external laser that drives transitions coupling the internal state of the ion to its motion. For this simulation it is critical that the carrier transition, which only changes the internal state, is suppressed. We have demonstrated that the relative coupling strength of ion-motion sidebands to the carrier can be controlled by positioning the ion in a standing wave beam \footnote{Burkhardt, K. A., Vittorini, G., Merrill, J. T., Brown, K. R., \& Amini, J. M., \textbf{Phys. Rev. A} 92(6), 061402, (2015)}. Here we present our results on optimizing the suppression of the carrier and our progress towards simulating the QPT.   

Development of a Phonon Toolbox on a Surface Electrode Trap

We report on our current experimental progress towards using a surface electrode trap for quantum simulation with $\text{Yb}^+$ ions. Currently, we are developing a toolbox for creating, manipulating and reading out phonon occupations in all normal modes of a three ion chain. Using shuttling, composite pulse sequences, and state distillation, we prepare given phonon number-states in these modes and show that these states preserve spin-motion coherence. The prepared state is read out either through a single sideband operation or through a STIRAP process. The sideband operation gives a binary measurement of phonon(s) vs. no phonon occupation; the STIRAP process is sensitive to the number-state occupation. We also engineer coherent couplings between normal modes through optical dipole forces, manipulating the prepared state to sample interacting Bosonic modes.   

Phonon Effects on Trapped Ion Quantum Simulators

Trapped ion quantum simulators are beginning to scale in size further than the ability of classical computers to efficiently benchmark results. Nevertheless, if one examines a ferromagnetic coupling between spins, with an all-to-all coupling in a transverse field Ising model, then the system has extra symmetry, which allows simulators with 100s of spins to be described with a classical computer. Here, we examine the laser-driven coupling betweena center-of-mass (COM) phonon and the spins, which produces such an all-to-all coupling for the effective spin model, when one is detuned to the blue of the COM mode.We examine the full time dependence for different ramping profiles of the transverse field including a shortcut to adiabaticity called the bang-bang protocol. Our results show that keeping track of real phonon creation and the resultant phonon-spin entanglement, actually helps the system to be described by a static Ising model. But, this comes at a price. While the probabilities for the final state to be in the ground state improve over what is seen in a time-dependent spin system, the spin entanglement in the ground state is suppressed, when the phonons are not explicitly measured.   

Engineering effective 2D Hamiltonians from 1D ion chains

The lattice geometry in 2D systems affords one the ability to study a rich variety of physical phenomena -- from quantum transport and localization, topological insulators and the Haldane model and in topological quantum computation. Ion traps have emerged as the preeminent platform for quantum simulation, where it would be desirable to simulate several of these 2D Hamiltonian models. The long-ranged Coulomb mediated spin-spin interactions in an ion trap make this possible in conventional radio-frequency ion traps where the ions are often arranged in a linear geometry. In this work, we describe a method for the Floquet engineering of 2D nearest neighbor Hamiltonian models from a linear chain of ions. Each cycle of the periodically driven dynamics consists of a calibrated evolution under a flip-flop type spin interaction and laser AC Stark shift assisted field gradient. We show that experimental implementations scale efficiently with system size, and discuss a range of 2D models that can be simulated.   

Quantum Information with 2-D Ion-Trap Arrays

Laboratory efforts on trapped-ion quantum information are currently focused on two distinct trap architectures -- segmented linear traps and 2D trap arrays. In 2D-ion-trap-arrays, each ion is located in its own individually-controllable trapping well, so that interactions between selected ions can be tuned and different array patterns can be fabricated. These features are likely to be useful for a variety of applications in both quantum simulation and computing. Recently we demonstrated quantum entanglement between two ions in separate trapping wells, and now we are working to extend to larger numbers of ions in micro-fabricated surface-electrode traps beginning with confinement in triangular geometries. This talk is an update on progress.   

Quantum absorption refrigerator with trapped ions

We report on an experimental realization of a quantum absorption refrigerator in a system of the three trapped $^{171}\mathrm{Yb}^+$ ions. The normal modes of motion are coupled by a trilinear Hamiltonian $a^{\dagger}bc + h.c.$ and represent ``hot", ``work" and ``cold" bodies of the refrigerator. We investigate the equilibrium properties of the refrigerator, and demonstrate the absorption refrigeration effect with the modes being prepared in thermal states. We also investigate the coherent dynamics and steady state properties of such a system away from equilibrium operation. We compare the cooling capabilities of thermal versus squeezed thermal states prepared in the work mode as a quantum resource for cooling. Finally, we exploit the coherent dynamics of the system and demonstrate single-shot cooling in the refrigerator. By stopping the evolution in the right moment, we show a significant advantage in cooling as compared to both the steady state and equilibrium performance.   

Sympathetic Cooling of Quantum Simulators

We discuss the possibility of maximizing the cooling of a quantum simulator by controlling the system-environment coupling such that the system is driven into the ground state. We make use of various analytical tools such as effective operator formalism \footnote{F. Reiter et al, \textbf{Phys. Rev. A 85, 032111} 161, 1500} and the quantum master equations to exactly solve the model of an Ising spin chain consisting of N particles coupled to a radiation field. We maximize the cooling by finding the dependence of the effective rate of transitions of the various excited states into the ground state. We show that by adding a single dissipative qubit, we already get quite substantial cooling rates.   

Steady-state spin synchronization through the collective motion of trapped ions

Ultranarrow-linewidth atoms coupled to a lossy optical cavity mode synchronize, i.e. develop correlations, and exhibit steady-state superradiance when continuously repumped. This type of system displays rich collective physics and promises metrological applications. These features inspire us to investigate if a model inspired from cavity superradiance can generate analogous spin synchronization in a different platform that is one of the most robust and controllable experimental testbeds currently available: ion-trap systems. We design a system with a primary and secondary species of ions that share a common set of normal modes of vibration. In analogy to the lossy optical mode, we propose to use a lossy normal mode, obtained by sympathetic cooling with the secondary species of ions, to mediate spin synchronization in the primary species of ions. Our numerical study shows that spin-spin correlations develop, leading to a macroscopic collective spin in steady-state. We propose an experimental method based on Ramsey interferometry to detect signatures of this collective spin; we predict that correlations prolong the visibility of Ramsey fringes, and that population statistics at the end of the Ramsey sequence can be used to directly infer spin-spin correlations.   

Experimental measurement of correlation functions in trapped ions

We measure the time-correlation functions of spins and phonons of a system that evolves under a Hamiltonian of Jaynes-Cumming model or Dirac equation with trapped 171Yb$+$ ions. The algorithm proposed in Ref. [1] requires only one ancilla qubit to obtain the time correlations of the observables in the system. In the experiment, conditional gates depending on the state of the ancilla, spin-dependent force and spin-independent force have been performed. We measure the spin-spin time-correlations in spin system and the spin-phonon time-correlation in bosonic field. According to the linear response theory, the time-correlations can be used to characterize relevant physical magnitude such as magnetic susceptibility. This scheme can be extended to a system including n-time spins and phonons correlations. [1] J. S. Pedernales, et al., Phys. Rev. Lett. 113, 020505 (2014).   

Performance Characterization of a Scalable Trapped Ion Based Quantum Computer

The rapid progress towards a scalable platform for atomic ion based quantum computing has resulted in a need for a careful characterization of the initial performance of basic qubit functions. This work characterizes the error rate for state readout, measurement crosstalk, and single qubit gates for a $^{171}$Yb$^+$ qubit in a surface trap. Photons scattered from the qubit are coupled into a multimode fiber using a high numerical aperture lens (0.6 NA) and directed towards a superconducting nanowire single photon detector (SNSPD). State dependent fluorescence is used to determine the state of the qubit, with an average state detection time of 12.3 $\mu$s and $6.9(5) \times 10^{-4}$ detection error. To characterize measurement crosstalk between two qubits, a measurement is performed on one qubit using a focused detection beam, and the coherence of a second qubit is measured as a function of the distance between the two. Gate set tomography is used for the characterization of global single qubit gates driven by a microwave field ($5.(6) \times 10^{-4}$ R$_x$($\frac{\pi}{2}$) error). Individual single qubit gates and two qubit gates driven by Raman transitions will be performed and characterized with tightly focused beams steered across the qubits by tilting MEMS mirrors.