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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 midcircuit measurements. We study the implementation of large-scale parallel multiqubit 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.

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 realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor. Using a recently proposed, scalable scheme, we implement 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 multidimensional 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 toward 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}Sr^{+} ions in a radio-frequency (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-line-width 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 electron-multiplying CCD camera acquisition. The latter is necessary for carrying out quantum error-correction protocols in future experiments.

Chemical reactions with ultracold atoms and ions are explored so far with the atom–ion interactions. Here the authors discuss spin-exchange process and show that the spin state of an ensemble of neutral Rb atoms can be used to control the final spin of an imbedded Sr+ ion in the collisions.

In recent years, arrays of atomic ions in a linear radio-frequency 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.

Experiments in which ultra-cold neutral atoms and charged ions are overlapped, constitute a new field in atomic and molecular physics, with applications ranging from studying out-of-equilibrium dynamics to simulating quantum many-body systems. The holy grail of ion-neutral systems is reaching the quantum low-energy scattering regime, known as the s-wave scattering. However, in most atom–ion systems, there is a fundamental limit that prohibits reaching this regime. This limit arises from the time-dependent trapping potential of the ion, the Paul trap, which sets a lower collision energy limit which is higher than the s-wave energy. 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.

The original version of this Article contained an error in the third sentence of the first paragraph of the ‘Spin polarizing the Sr+ ion with ultracold atoms’ section of the Results, which incorrectly read ‘The Langevin collision rate is 1.’ The correct version adds ‘kHz’ after ‘1.’ The fifth sentence of this same paragraph originally read as “Although 87Rb has a I = 3/2 nuclear spin and a hyperfine-split ground-state manifold, 88Sr has no nuclear spin and a Zeeman split two-fold ground state”, which is incorrect. The correct version states “88Sr+” instead of “88Sr”. The first sentence of the fourth paragraph of this same section originally read as “As the collisional energies are on the mK energy scale, spin exchange between Sr+ and Rb prepared in the F = 1 state is allowed only as long as it does not require Rb to change its hyperfine state and climb the 330 m hyperfine energy gap”, which is incorrect. The correct version states “330 mK” instead of “330 m”.In the Discussion section, the text was originally incorrectly repeated.This has been corrected in both the PDF and HTML versions of the Article.

Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, partially cancel leading to improved stability and a reduction in the corresponding systematic shifts. We present and analyze two examples of such combinations. The first uses the optical quadrupole transitions in a ${}^{40}$ Ca ^+ – ${}^{174}$ Yb ^+ two-ion system. The second is a superposition of optical quadrupole transitions in one ${}^{88}$ Sr ^+ ion and three ${}^{202}$ Hg ^+ ions. These combinations have reduced susceptibility to external magnetic fields and blackbody radiation.

A unique property of Zeeman effect based manipulation of paramagnetic particle’s motion is the ability to control velocities of both atoms and molecules. In particular the moving magnetic trap decelerator is capable of slowing and eventually trapping mixtures of both cold atoms and cold molecules generated in a supersonic expansion. Here we report the deceleration of molecular oxygen together with metastable argon atoms. The cold mixture with temperature below 1 K is slowed from an initial velocity of 430 m s ^−1 down to 100 m s ^−1 . Our decelerator spans 2.4 m and consists of 480 quadrupole traps. Our results pave the way for the study of sympathetic cooling of molecules by laser cooled atoms.

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 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.

We demonstrate simultaneous deceleration and trapping of a cold atomic and molecular mixture. This is the first step towards studies of cold atom-molecule collisions at low temperatures as well as application of sympathetic cooling. Both atoms and molecules are cooled in a supersonic expansion and are loaded into a moving magnetic trap that brings them to rest via the Zeeman interaction from an initial velocity of 375 m/s. We use a beam seeded with molecular oxygen, and entrain it with lithium atoms by laser ablation prior to deceleration. The deceleration ends with loading of the mixture into a static quadrupole trap, which is generated by two permanent magnets. We estimate 109 trapped O2 molecules and 105 Li atoms with background pressure limited lifetime on the order of 1 sec. With further improvements to lithium entrainment we expect that sympathetic cooling of molecules is within reach. [ABSTRACT FROM AUTHOR]