A. Safavi-Naini

Tightly-focused laser beams, or optical tweezers, are essential for analogue and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which breaks down at the focus of optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how non-paraxial effects will manifest in the next-generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole $^2$S$_{1/2}\rightarrow$ $^2$D$_{5/2}$ transition in $^{40}$Ca$^+$. Longitudinal field components in the beam center cause spatially-dependent Rabi frequencies and AC Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where non-paraxial effects should be taken into account for high-precision quantum control. Finally, we highlight that non-paraxial effects are potentially more severe in the case of neutral atom and molecule addressing.

We consider the quantum simulation of quadratic spin-phonon coupling in a crystal of trapped ions. The coupling is implemented using tightly focused optical tweezers on each ion that change the local trapping potential in a state-dependent way. By encoding spins in the internal states of the ions and adding a tunneling term via Mølmer-Sørensen-type interactions, we calculate the emergence of mobile bipolarons driven by the zero-point energy of the ion crystal phonons. We show that thermal occupation may pin the bipolarons for ion crystals at finite temperature. Our scheme can be used to study and illustrate the emergence of mobile bipolarons as a function of temperature.

This paper presents a routine to align an optical tweezer on a single trapped ion and use the ion as a probe to characterize the tweezer. We find a smallest tweezer waist of $2.3(2)\,μ$m, which is in agreement with the theoretical minimal attainable waist of $2.5(2)\,μ$m in our setup. We characterize the spatial dependence of the tweezer Rabi frequency which is suppressed by a factor of 19(3) in the immediate surrounding of the ion. We investigate the effects of optical forces and coherent population trapping on the ion. Finally, we show that the challenges posed by these forces can be overcome, and that the number of tweezers can be easily scaled up to reach several ions by using a spatial light modulator.

We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state dependent forces generated by this effect live on the plane perpendicular to the direction of propagation of the laser beams opening new ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground state cooling of the ions and does not rely on the Lamb-Dicke approximation, although the waist of the tightly focused beam needs to be comparable with its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be performed on both ground state and magnetic field insensitive clock state qubits without the need for counter-propagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular pointing errors $<30$ nm in the tweezers reduce the gate fidelity from $\mathcal F\gtrsim 0.99998$ to $\gtrsim 0.999$.

We theoretically investigate the trap-assisted formation of complexes in atom-ion collisions and their impact on the stability of the trapped ion. The time-dependent potential of the Paul trap facilitates the formation of temporary complexes by reducing the energy of the atom, which gets temporarily stuck in the atom-ion potential. As a result, those complexes significantly impact termolecular reactions leading to molecular ion formation via three-body recombination. We find that complex formation is more pronounced in systems with heavy atoms, but the mass has no influence on the lifetime of the transient state. Instead, the complex formation rate strongly depends on the amplitude of the ion's micromotion. We also show that complex formation persists even in the case of a time-independent harmonic trap. In this case, we find higher formation rates and longer lifetimes than the Paul trap, indicating that the atom-ion complex plays an essential role in atom-ion mixtures in optical traps.

We measure chemical reactions between a single trapped $^{174}$Yb$^+$ ion immersed in an ultracold bath of $^6$Li atoms containing trace amounts of Li$_2$ dimers. This produces LiYb$^+$ molecular ions that we detect via mass spectrometry. We explain the reaction rates by modelling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, with a detection sensitivity below molecule densities of $10^{14}\,\mathrm{m}^{-3}$, we provide a new method to detect low-density molecular gases.

For exploration of quantum effects with hybrid atom-ion systems, reaching ultracold temperatures is the major limiting factor. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom-ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion's groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into quantum chemistry and precision spectroscopy.

We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.

The ability to harness the dynamics of quantum information and entanglement is necessary for the development of quantum technologies and the study of complex quantum systems. On the theoretical side the dynamics of quantum information is a topic that is helping us unify and confront common problems in otherwise disparate fields in physics, such as quantum statistical mechanics and cosmology. On the experimental side the impressive developments on the manipulation of neutral atoms and trapped ions are providing new capabilities to probe their quantum dynamics. Here, we overview and discuss progress in characterizing and understanding the dynamics of quantum entanglement and information scrambling in quantum many-body systems. The level of control attainable over both the internal and external degrees of freedom of individual particles in these systems provides great insight into the intrinsic connection between entanglement and thermodynamics, bounds on information transport and computational complexity of interacting systems. In turn this understanding should enable the realization of quantum technologies.

We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a 2-D array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.

Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena. Here, we demonstrate that a family of fidelity out-of-time-order correlators (FOTOCs), recently measured in a trapped-ion quantum simulator via time reversal of the many-body dynamics followed by a fidelity measurement, can serve as a unifying diagnostic tool that elucidates the intrinsic connection between fast scrambling, volume law entanglement, ergodicity, quantum chaos, and the associated butterfly effect in the semiclassical dynamics of the system. We demonstrate the utility of FOTOCs by computing them in the Dicke model, an iconic model in quantum optics, recently implemented in atomic and trapped-ion setups. This model describes the coupling of a large spin to an oscillator and features rich behaviors, including a quantum phase transition and chaos. Here, we show that FOTOCs provide a direct measure of the spin-phonon Renyi entropy and quantum thermalization. Moreover, we connect the FOTOCs to the variance of simple operators, allowing us to observe fast scrambling in the parameter regime where the system's classical trajectories are chaotic, and to explicitly relate the quantum and classical Lyapunov exponents in a truly quantum many-body system. Our results open a path for the experimental use of FOTOCs to quantify fast scrambling, determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant/ferromagnetic and a normal/paramagnetic phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in the presence of an external transverse field to engineer a quantum simulator of the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom which are encoded by two hyperfine states in each ion and the center of mass motional mode of the crystal, respectively. The Dicke model features a quantum critical point separating two distinct phases: the superradiant (ferromagnetic) and normal (paramagnetic) phases. We experimentally explore protocols that aim to adiabatically prepare the superradiant ground state, a spin-boson cat state with macroscopic phonon occupation, which is well-suited for enhanced metrology and quantum information processing. We start in the normal phase, with all spins aligned along a large transverse field and ramp down the field across the critical point following various protocols. We measure the spin observables, both experimentally and in our simulations to characterize the state of the system at the end of the ramp. We find that under current operating conditions an optimally designed ramp is not sufficient to achieve significant fidelity with the superradiant ground state. However, our theoretical investigation shows that slight modifications of experimental parameters, together with modest reductions in decoherence rates and thermal noise can increase the cat-state fidelity to $\sim 75\%$ for $N \sim 20$ spins. Our results open a path for the use of large ensembles of trapped ions as powerful quantum sensors and quantum computers.

An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase space methods such as the Truncated Wigner Approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [Schachenmayer, PRX 5, 011022 (2015)]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations [Pucci, PRB 93, 174302 (2016)] to our coupled spin-boson model. This allows in principle to study how systematically adding higher order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for arbitrary number of bosonic modes.

The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from the trap-electrode surfaces. In this work, we investigate the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by density functional theory, based on detailed scanning probe microscopy, how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values.

Electric field noise is a hinderance to the assembly of large scale quantum computers based on entangled trapped ions. Apart from ubiquitous technical noise sources, experimental studies of trapped ion heating have revealed additional limiting contributions to this noise, originating from atomic processes on the electrode surfaces. In a recent work [A. Safavi-Naini et al., Phys. Rev. A 84, 023412 (2011)] we described a microscopic model for this excess electric field noise, which points a way towards a more systematic understanding of surface adsorbates as progenitors of electric field jitter noise. Here, we address the impact of surface monolayer contamination on adsorbate induced noise processes. By using exact numerical calculations for H and N atomic monolayers on an Au(111) surface representing opposite extremes of physisorption and chemisorption, we show that an additional monolayer can significantly affect the noise power spectrum and either enhance or suppress the resulting heating rates.

Motional heating of ions in micro-fabricated traps is a challenge hindering experimental realization of large-scale quantum processing devices. Recently a series of measurements of the heating rates in surface-electrode ion traps characterized their frequency, distance, and temperature dependencies, but our understanding of the microscopic origin of this noise is still vague. In this work we develop a theoretical model for the electric field noise which is associated with a random distribution of adsorbed atoms on the trap electrode surface. By using first principle calculations of the fluctuating dipole moments of the adsorbed atoms we evaluate the distance, frequency and temperature dependence of the resulting electric field fluctuation spectrum.Our theory calculates the noise spectrum beyond the standard scenario of two-level fluctuators, by incorporating all the relevant vibrational states. The $1/f$ noise is shown to commence at roughly the frequency of the fundamental phonon transition rate and the $d^{-4}$ dependence with distance of the ion from the electrode surface is established.