Nitzan Akerman

Hybrid quantum systems combining neutral atoms and trapped ions offer the prospect of integrating the scalability of atom arrays with the high-fidelity control available in trapped-ion platforms. Here we propose and analyze a quantum interface between individually trapped neutral atoms and a trapped-ion crystal. In our scheme, a neutral 88Sr atom trapped in optical tweezers interacts with a small 88Sr+ ion crystal, and by exciting the atom to a Rydberg state, the atom-ion polarization interaction is strongly enhanced, resulting in a state-dependent modification of the ions' collective motional modes. We show that this shift enables conditional control of a MS gate, allowing the neutral atom to act as a control qubit for an entangling operation between two ions. We investigate the feasibility of the scheme by analyzing Rydberg trapping in the combined optical tweezers and Paul trap potentials, identifying negative-polarizability Rydberg states as particularly favorable for stable confinement. We further evaluate the relevant trapping conditions, Rydberg lifetimes, and coherence requirements, and show that the proposed interface is compatible with realistic experimental parameters. These results establish a practical route toward deterministic atom-ion hybrid quantum gates and quantum interfaces.

High-fidelity quantum gates require precise classical control signals, yet the analog hardware delivering these signals introduces nonlinear distortions that degrade gate performance. We demonstrate digital predistortion of an acousto-optic modulator used to generate multi-tone entangling-gate waveforms in a trapped-ion processor based on $^{88}$Sr$^+$. By measuring and inverting the static nonlinear amplitude response of the modulator, we apply a feed-forward correction that extends its linear operating range and suppresses spurious intermodulation products. Spectral analysis of the gate beam shows 3--5 dB suppression of the dominant intermodulation tones, approximately doubling the usable diffraction efficiency at a $10^{-3}$ estimated gate-error threshold. Direct two-qubit Bell-state fidelity measurements confirm that predistortion consistently improves entangling-gate performance. The calibrate-and-invert methodology is device and platform agnostic, applicable to any nonlinear element in the classical control chain of a quantum processor.

We propose an entanglement protocol where ions illuminated by optical tweezers serve as control qubits. We experimentally demonstrate this proposal with a controlled M$ø$lmer-S$ø$rensen operation on a three-ion chain, analogous to the canonical Toffoli gate. Our demonstration features cases in which the control qubit was in one of its logical basis states, and not in their superposition, due to dephasing by tweezer beam intensity fluctuations. Finally, we discuss how our protocol generalizes to a broad class of unitary operations and larger qubit systems, enabling a single-pulse implementation of $n$-controlled unitaries.

We report on signatures of classical chaos in ultracold collisions between a trapped ion and a free atom. Using numerical simulations, we show that the scattering dynamics can be highly sensitive to initial conditions for various mass ratios and trapping frequencies, indicating the onset of chaos. We quantify this chaotic dynamics by calculating its fractal dimension. We show that for a trapped $^{88}$Sr$^+$ ion and a free $^{87}$Rb atom chaotic dynamic appears under experimentally relevant conditions, and find its characteristic energy scale. The observation of classical chaos in atom-trapped-ion collisions suggests that signatures of quantum chaos might appear, for example, through a Wigner-Dyson distribution of collisional resonances.

The Mpemba effect is a counter-intuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e. due to interference effects. We experimentally demonstrate our findings on a single $^{88}\text{Sr}^+$ trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.

Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity and degree of local control. In principle there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice there are two main issues associated with long trapped-ion crystals, that stem from the 'softening' of their modes of motion, upon scaling up: high heating rates of the ions' motion, and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here we propose a holistic, scalable architecture for quantum computing with large ion-crystals that overcomes these issues. Our method relies on dynamically-operated optical potentials, that instantaneously segment the ion-crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion-crystal, and also enables efficient mid-circuit measurements. We study the implementation of large-scale parallel multi-qubit entangling gates that operate simultaneously on all cells, and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations.

Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in carrying out accurate simulations over long evolution times. Here we experimentally demonstrate a method for quantum simulations on a small-scale trapped ions-based quantum simulator. Our method enables quantum simulations of programmable spin-Hamiltonians, using only simple global fields, driving all qubits homogeneously and simultaneously. We measure the evolution of a quantum Ising ring and accurately reconstruct the Hamiltonian parameters, showcasing an accurate and high-fidelity simulation. Our method enables a significant reduction in the required control and depth of quantum simulations, thus generating longer evolution times with higher accuracy.

Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, $N$, in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as $N^2$, the gate duration scales as $N$, leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path towards scaling up quantum computers based on ion-crystals with hundreds of qubits.

Pairs of free particles cannot form bound states in elastic collision due to momentum and energy conservation. In many ultracold experiments, however, the particles collide in the presence of an external trapping potential which can couple the center-of-mass and relative motions and assist the formation of bound-states. Here, we report on observation of weakly bound molecular states formed between one ultracold $^{87}$Rb atom and a single trapped $^{88}$Sr$^+$ ion in the presence of a linear Paul trap. We show that bound states can form efficiently in binary collisions, and enhance the rate of inelastic processes. By observing electronic spin-exchange rate, we study the dependence of these bound states on the collision energy and magnetic field and extract the average molecular binding energy $E_{\textrm{bind}}=0.7(1)$ mK$\cdot k_B$ and the mean lifetime of the molecule $τ=0.5(1)\,μ$s, with good agreement with molecular-dynamics simulations. Our simulations predict a highly unusual power-law distribution of molecular lifetimes with a mean that is dominated by extreme, long-lived, events. The dependence of the molecular properties on the trapping parameters opens new avenues to study and control ultracold collisions.

High fidelity single and multi-qubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single qubit operations including resonant $π$ rotations and off-resonant sideband transitions . We further analyze the effect of fast phase noise on the Molmer-Sorensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spin-like qubits are coupled by a common bosonic field. Our analysis can help in guiding the deign of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.

Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.

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 potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation. Of these, platforms with universal quantum control can experimentally access a wide range of physical properties. However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high fidelity quantum control in a scalable manner is challenging. Here we realized quantum simulations of interacting, time-reversal broken quantum systems in a universal trapped-ion quantum processor. Using a scalable scheme that was recently proposed we implemented time-reversal breaking synthetic gauge fields, shown for the first time in a trapped ion chain, along with unique coupling geometries, potentially extendable to simulation of multi dimensional systems. Our high fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current, and to observe dynamics of a time-reversal broken system with nontrivial interactions. Our results open a path towards simulation of time-reversal broken many-body systems with a wide range of features and coupling geometries.

Quantum computers are expected to achieve a significant speed-up over classical computers in solving a range of computational problems. Chains of ions held in a linear Paul trap are a promising platform for constructing such quantum computers, due to their long coherence times and high quality of control. Here we report on the construction of a small, five-qubit, universal quantum computer using $^{88}\text{Sr}^{+}$ ions in an RF trap. All basic operations, including initialization, quantum logic operations, and readout, are performed with high fidelity. Selective two-qubit and single-qubit gates, implemented using a narrow linewidth laser, comprise a universal gate set, allowing realization of any unitary on the quantum register. We review the main experimental tools, and describe in detail unique aspects of the computer: the use of robust entangling gates and the development of a quantum coherent feedback system through EMCCD camera acquisition. The latter is necessary for carrying out quantum error correction protocols in future experiments.

The cross section of a given process fundamentally quantifies the probability for that given process to occur. In the quantum regime of low energies, the cross section can vary strongly with collision energy due to quantum effects. Here, we report on a method to directly measure the atom-ion collisional cross section in the energy range of 0.2-12 mK$\cdot$ k$_B$, by shuttling ultracold atoms trapped in an optical-lattice across a radio-frequency trapped ion. In this method, the average number of atom-ion collisions per experiment is below one such that the energy resolution is not limited by the broad (power-law) steady-state atom-ion energy distribution. Here, we estimate that the energy resolution is below 200 $μ$K$\cdot$k$_B$, limited by drifts in the ion's excess micromotion compensation and can be reduced to the 10's $μ$K$\cdot$k$_B$ regime. This resolution is one order-of-magnitude better than previous experiments measuring cold atom-ion collisional cross section energy dependence. We used our method to measure the energy dependence of the inelastic collision cross sections of a non-adiabatic Electronic-Excitation-Exchange (EEE) and Spin-Orbit Change (SOC) processes. We found that in the measured energy range, the EEE and SOC cross sections statistically agree with the classical Langevin cross section. This method allows for measuring the cross sections of various inelastic processes and opens up possibilities to search for atom-ion quantum signatures such as shape-resonances.

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 simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

The physics of Markovian open quantum systems can be described by quantum master equations. These are dynamical equations, that incorporate the Hamiltonian and jump operators, and generate the system's time evolution. Reconstructing the system's Hamiltonian and and its coupling to the environment from measurements is important both for fundamental research as well as for performance-evaluation of quantum machines. In this paper we introduce a method that reconstructs the dynamical equation of open quantum systems, directly from a set of expectation values of selected observables. We benchmark our technique both by a simulation and experimentally, by measuring the dynamics of a trapped $^{88}\text{Sr}^+$ ion under spontaneous photon scattering.

The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers is still a prominent challenge. Here we propose and investigate multi-qubit entangling gates for trapped-ions. Our gates couple many qubits at once, allowing to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal-modes of motion of the ion chain, which allows to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbour spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.

The holy grail of ion-neutral systems is reaching the s-wave scattering regime. However, most of these systems have a fundamental lower collision energy limit which is higher than this s-wave regime. This limit arises from the time-dependant trapping potential of the ion, the Paul trap. In this work, we studied both theoretically and experimentally, the way the Paul trap parameters affect the energy distribution of an ion that is immersed in a bath of ultra-cold atoms. Heating rates and energy distributions of the ion are calculated for various trap parameters by a molecular dynamics (MD) simulation that takes into account the attractive atom-ion potential. The deviation of the energy distribution from a thermal one is discussed. Using the MD simulation, the heating dynamics for different atom-ion combinations is also investigated. In addition, we performed measurements of the heating rates of a ground-state cooled $\ ^{88}$Sr$^+$ ion that is immersed in an ultra-cold cloud of $\ ^{87}$Rb atoms, over a wide range of trap parameters, and compare our results to the MD simulation. Both the simulation and the experiment reveal no significant change in the heating for different parameters of the trap. However, in the experiment a slightly higher global heating is observed, relative to the simulation.

Atomic isotope shifts (ISs) are the isotope-dependent energy differences in the atomic electron energy levels. These shifts serve an important role in atomic and nuclear physics, and particularly in the latter as signatures of nuclear structure. Recently ISs have been suggested as unique probes of beyond Standard Model (SM) physics, under the condition that they be determined significantly more precisely than current state of the art. In this work we present a simple and robust method for measuring ISs with ions in a Paul trap, by taking advantage of Hilbert subspaces that are insensitive to common-mode noise yet sensitive to the IS. Using this method we evaluate the IS of the $5S_{1/2}\leftrightarrow4D_{5/2}$ transition in $^{86}\text{Sr}^+$ and $^{88}\text{Sr}^+$ with a $1.6\times10^{-11}$ relative uncertainty to be 570,264,063.435(9) Hz. Furthermore, we detect a relative difference of $3.46(23)\times10^{-8}$ between the orbital g-factors of the electrons in the $4D_{5/2}$ level of the two isotopes. Our method is relatively easy to implement and is indifferent to element or isotope, paving the way for future tabletop searches for new physics and posing interesting prospects for testing quantum many-body calculations and for the study of nuclear structure.

We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals, limiting current optical ion clocks to work with a single probe ion. Cancelling this shift at each interrogation cycle of the ion frequency allows the use of $N>1$ ions in clocks, thus reducing the uncertainty in the clock frequency by $\sqrt{N}$ according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensorial shifts, such as the tensor ac stark shift. We experimentally demonstrate our sequence on three and seven $^{88}\mathrm{Sr}^{+}$ ions trapped in a linear Paul trap, using correlation spectroscopy. We show a reduction of the quadrupole shift difference between ions to $\approx20$ mHz's level where other shifts, such as the relativistic 2$^{\mathrm{nd}}$ order Doppler shift, are expected to limit our spectral resolution. In addition, we show that using radio-frequency dynamic decoupling we can also cancel the effect of 1$^{\mathrm{st}}$ order Zeeman shifts.

High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits, however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the celebrated Mølmer-Sørensen gate by using multi-tone drives. We experimentally implemented several of the proposed gates on $^{88}\text{Sr}^{+}$ ions trapped in a linear Paul trap, and verified their resilience.

Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion, trapped in a radio-frequency Paul trap, and prepared in a coherent state of ~200 K and the bath is an ultracold cloud of atoms at μK temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one, to several, collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cooling in only a few collisions. In the other, collisions can both cool and heat the system due to the non-equilibrium dynamics of the atom-ion collisions in the presence of the ion-trap's oscillating electric fields. While the bulk of our observations agree well with a molecular dynamics simulation of hard-sphere (Langevin) collisions, a measurement of the scattering angle distribution reveals forward-scattering (glancing) collisions which are beyond the Langevin model. This work paves the way for further non-equilibrium and collision dynamics studies using the well-controlled atom-ion system.

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of $\sqrt{N}$, with $N$ being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of $\fracπ{2}$, independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to $σ_z$ noise with ions in a Paul trap.

An ensemble of atoms in steady-state, whether in thermal equilibrium or not, has a well defined energy distribution. Since the energy of single atoms within the ensemble cannot be individually measured, energy distributions are typically inferred from statistical averages. Here, we show how to measure the energy of a single atom in a single experimental realization (single-shot). The energy distribution of the atom over many experimental realizations can thus be readily and directly obtained. We apply this method to a single-ion trapped in a linear Paul trap for which energy measurement in a single-shot is applicable from 10 K and above. Our energy measurement agrees within 5% to a different thermometry method which requires extensive averaging. Apart from the total energy, we also show that the motion of the ion in different trap modes can be distinguished. We believe that this method will have profound implications on single particle chemistry and collision experiments.

Experimental realizations of charged ions and neutral atoms in overlapping traps are gaining increasing interest due to their wide research application ranging from chemistry at the quantum level to quantum simulations of solid-state systems. Here, we describe a system in which we overlap a single ground-state cooled ion trapped in a linear Paul trap with a cloud of ultracold atoms such that both constituents are in the $μ$K regime. Excess micromotion (EMM) currently limits atom-ion interaction energy to the mK energy scale and above. We demonstrate spectroscopy methods and compensation techniques which characterize and reduce the ion's parasitic EMM energy to the $μ$K regime even for ion crystals of several ions. We give a substantial review on the non-equilibrium dynamics which governs atom-ion systems. The non-equilibrium dynamics is manifested by a power-law distribution of the ion's energy. We overview the coherent and non-coherent thermometry tools which we used to characterize the ion's energy distribution after single to many atom-ion collisions.

We study the time-dependent fluorescence of an initially hot, multi-level, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multi-level energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in a coherent, thermal and Tsallis energy distributions.

Ultra-cold atom-ion mixtures are gaining increasing interest due to their potential applications in quantum chemistry, quantum computing and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultra-cold atoms. We measured the ion's energy distribution and observed a clear deviation from Maxwell-Boltzmann to a Tsallis characterized by a power-law tail of high energies. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atom-ion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultra-cold regime, we are capable of studying quantum effects by limiting the interaction to the first collision.

We report on the implementation of a high fidelity universal gate-set on optical qubits based on trapped $^{88}$Sr$^+$ ions for the purpose of quantum information processing. All coherent operations were performed using a narrow linewidth diode laser. We employed a master-slave configuration for the laser, where an ultra low expansion glass (ULE) Fabry-Perot cavity is used as a stable reference as well as a spectral filter. We characterized the laser spectrum using the ions with a modified Ramsey sequence which eliminated the affect of the magnetic field noise. We demonstrated high fidelity single qubit gates with individual addressing, based on inhomogeneous micromotion, on a two-ion chain as well as the Mølmer-Sørensen two-qubit entangling gate.

Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin). The magnetic interaction between two electrons can therefore impose a change in their spin orientation. This process, however, was never observed in experiment. The challenge is two-fold. At the atomic scale, where the coupling is relatively large, the magnetic interaction is often overshadowed by the much larger coulomb exchange counterpart. In typical situations where exchange is negligible, magnetic interactions are also very weak and well below ambient magnetic noise. Here we report on the first measurement of the magnetic interaction between two electronic spins. To this end, we used the ground state valence electrons of two $^{88}$Sr$^+$ ions, co-trapped in an electric Paul trap and separated by more than two micrometers. We measured the weak, millihertz scale (alternatively $10^{-18}$ eV or $10^{-14}$ K), magnetic interaction between their electronic spins. This, in the presence of magnetic noise that was six orders of magnitude larger than the respective magnetic fields the electrons apply on each other. Cooperative spin dynamics was kept coherent for 15 s during which spin-entanglement was generated. The sensitivity necessary for this measurement was provided by restricting the spin evolution to a Decoherence-Free Subspace (DFS) which is immune to collective magnetic field noise. Finally, by varying the separation between the two ions, we were able to recover the inverse cubic distance dependence of the interaction. The reported method suggests an alternative route to the search of long-range anomalous spin-spin forces and can be generalized to include Quantum Error Correction codes for other cases of extremely weak signal detection.

We propose a simple method to spectrally resolve single-spins in a cold atomic system, thus realizing single-spin addressing. This scheme uses a dressing field with a spatially-dependent coupling to the atoms. We realize this scheme experimentally using a linear chain of trapped ions that are separated by $\sim3$ $μ$m, dressed by a laser field that is resonant with the micromotion sideband of a narrow optical transition.

A qubit can be used as a sensitive spectrum analyzer of its environment. Here we show how the problem of spectral analysis of noise induced by a strongly coupled environment can be solved for discrete spectra. Our analytical model shows non-linear signal dependence on noise power, as well as possible frequency mixing, both are inherent to quantum evolution. This model enabled us to use a single trapped ion as a sensitive probe for strong, non-Gaussian, discrete magnetic field noise. To overcome ambiguities arising from the non-linear character of strong noise, we develop a three step noise characterization scheme: peak identification, magnitude identification and fine-tuning. Finally, we compare experimentally equidistant versus Uhrig pulse schemes for spectral analysis. The method is readily available to any quantum probe which can be coherently manipulated.

The process of quantum measurement has been a long standing source of debate. A measurement is postulated to collapse a wavefunction onto one of the states of a predetermined set - the measurement basis. This basis origin is not specified within quantum mechanics. According to the theory of decohernce, a measurement basis is singled out by the nature of coupling of a quantum system to its environment. Here we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion due to spontaneous photon scattering. Using quantum process tomography we visualize the projection of all spin directions, onto this basis, as a photon is scattered. These basis spin states are found to be aligned with the scattered photon propagation direction. In accordance with decohernce theory, they are subjected to a minimal increase in entropy due to the photon scattering, while, orthogonal states become fully mixed and their entropy is maximally increased. Moreover, we show that detection of the scattered photon polarization measures the spin state of the ion, in the emerging basis, with high fidelity. Lastly, we show that while photon scattering entangles all superpositions of pointer states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings show that photon scattering by atomic spin superpositions fulfils all the requirements from a quantum measurement process.

Spontaneous photon scattering by an atomic qubit is a notable example of environment-induced error and is a fundamental limit to the fidelity of quantum operations. In the scattering process the qubit loses its distinctive and coherent character owing to its entanglement with the photon. Using a single trapped ion we show that by utilizing the information carried by the photon we are able to coherently reverse this process and correct for the scattering error. We further used quantum process tomography to characterize the photon-scattering error and its correction scheme and demonstrate a correction fidelity greater than 85% whenever a photon was measured.

We report on the construction and characterization of an apparatus for quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the $S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions' external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar n=0.05$ and a heating rate of $\dot{\bar n}=0.016$ ms$^{-1}$ is measured.

We demonstrate high-fidelity Zeeman qubit state detection in a single trapped 88 Sr+ ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error-threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.

We report on the implementation of a quantum analog to the classical lock-in amplifier. All the lock-in operations: modulation, detection and mixing, are performed via the application of non-commuting quantum operators on the electronic spin state of a single trapped Sr+ ion. We significantly increase its sensitivity to external fields while extending phase coherence by three orders of magnitude, to more than one second. With this technique we measure magnetic fields with sensitivity of 25 pT/sqrt(Hz) and light shifts with an uncertainty below 140 mHz after 1320 seconds of averaging. These sensitivities are limited by quantum projection noise and, to our knowledge, are more than two orders of magnitude better than with other single-spin probe technologies. In fact, our reported sensitivity is sufficient for the measurement of parity non-conservation, as well as the detection of the magnetic field of a single electronic-spin one micrometer from an ion-detector with nanometer resolution. As a first application we perform light shift spectroscopy of a narrow optical quadruple transition. Finally, we emphasize that the quantum lock-in technique is generic and can potentially enhance the sensitivity of any quantum sensor.

We study the steady state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser-cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate a unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the cooling laser parameters. Our observations open a way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.