Demonstration of the trapped-ion quantum CCD computer architecture.

The trapped-ion quantum charge-coupled device (QCCD) proposal1,2 lays out a blueprint for a universal quantum computer that uses mobile ions as qubits. Analogous to a charge-coupled device (CCD) camera, which stores and processes imaging information as movable electrical charges in coupled pixels, a QCCD computer stores quantum information in the internal state of electrically charged ions that are transported between different processing zones using dynamic electric fields. The promise of the QCCD architecture is to maintain the low error rates demonstrated in small trapped-ion experiments3-5 by limiting the quantum interactions to multiple small ion crystals, then physically splitting and rearranging the constituent ions of these crystals into new crystals, where further interactions occur. This approach leverages transport timescales that are fast relative to the coherence times of the qubits, the insensitivity of the qubit states of the ion to the electric fields used for transport, and the low crosstalk afforded by spatially separated crystals. However, engineering a machine capable of executing these operations across multiple interaction zones with low error introduces many difficulties, which have slowed progress in scaling this architecture to larger qubit numbers. Here we use a cryogenic surface trap to integrate all necessary elements of the QCCD architecture-a scalable trap design, parallel interaction zones and fast ion transport-into a programmable trapped-ion quantum computer that has a system performance consistent with the low error rates achieved in the individual ion crystals. We apply this approach to realize a teleported CNOT gate using mid-circuit measurement6, negligible crosstalk error and a quantum volume7 of 26 = 64. These results demonstrate that the QCCD architecture provides a viable path towards high-performance quantum computers.

Non-thermalization in trapped atomic ion spin chains.

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'.

Ultrafast creation of large Schrödinger cat states of an atom.

Mesoscopic quantum superpositions, or Schrödinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and maintenance of such states relies upon a balance between efficient external coherent control of the system and sufficient isolation from the environment. Here we create a variety of cat states of a single trapped atom's motion in a harmonic oscillator using ultrafast laser pulses. These pulses produce high fidelity impulsive forces that separate the atom into widely separated positions, without restrictions that typically limit the speed of the interaction or the size and complexity of the resulting motional superposition. This allows us to quickly generate and measure cat states larger than previously achieved in a harmonic oscillator, and create complex multi-component superposition states in atoms.Generation of mesoscopic quantum superpositions requires both reliable coherent control and isolation from the environment. Here, the authors succeed in creating a variety of cat states of a single trapped atom, mapping spin superpositions into spatial superpositions using ultrafast laser pulses.

Active stabilization of ion trap radiofrequency potentials.

We actively stabilize the harmonic oscillation frequency of a laser-cooled atomic ion confined in a radiofrequency (rf) Paul trap by sampling and rectifying the high voltage rf applied to the trap electrodes. We are able to stabilize the 1 MHz atomic oscillation frequency to be better than 10 Hz or 10 ppm. This represents a suppression of ambient noise on the rf circuit by 34 dB. This technique could impact the sensitivity of ion trap mass spectrometry and the fidelity of quantum operations in ion trap quantum information applications.

Sensing Atomic Motion from the Zero Point to Room Temperature with Ultrafast Atom Interferometry.

We sense the motion of a trapped atomic ion using a sequence of state-dependent ultrafast momentum kicks. We use this atom interferometer to characterize a nearly pure quantum state with n=1 phonon and accurately measure thermal states ranging from near the zero-point energy to n[over ¯]~10^{4}, with the possibility of extending at least 100 times higher in energy. The complete energy range of this method spans from the ground state to far outside of the Lamb-Dicke regime, where atomic motion is greater than the optical wavelength. Apart from thermometry, these interferometric techniques are useful for characterizing ultrafast entangling gates between multiple trapped ions.

Ultrafast spin-motion entanglement and interferometry with a single atom.

We report entanglement of a single atom's hyperfine spin state with its motional state in a time scale of less than 3 ns. We engineer a short train of intense laser pulses to impart a spin-dependent momentum transfer of ± 2 hk. Using pairs of momentum kicks, we create an atomic interferometer and demonstrate collapse and revival of spin coherence as the motional wave packet is split and recombined. The revival after a pair of kicks occurs only when the second kick is delayed by an integer multiple of the harmonic trap period, a signature of entanglement and disentanglement of the spin with the motion. Such quantum control opens a new regime of ultrafast entanglement in atomic qubits.

Anisotropic polarizability of ultracold polar 40K87Rb molecules.

We report the measurement of the anisotropic ac polarizability of ultracold polar (40)K(87)Rb molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a "magic" angle between the laser polarization and the quantization axis is found where the polarizability of the |N=0,m(N)=0> and the |N=1,m(N)=0> states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the coherence time. This paves the way for precise spectroscopic measurements and coherent manipulations of rotational states as a tool in the creation and probing of novel quantum many-body states of polar molecules.

Dipolar collisions of polar molecules in the quantum regime.

Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range and spatially anisotropic. This is in stark contrast to the much studied dilute gases of ultracold atoms, which have isotropic and extremely short-range (or 'contact') interactions. Furthermore, the large electric dipole moment of polar molecules can be tuned using an external electric field; this has a range of applications such as the control of ultracold chemical reactions, the design of a platform for quantum information processing and the realization of novel quantum many-body systems. Despite intense experimental efforts aimed at observing the influence of dipoles on ultracold molecules, only recently have sufficiently high densities been achieved. Here we report the experimental observation of dipolar collisions in an ultracold molecular gas prepared close to quantum degeneracy. For modest values of an applied electric field, we observe a pronounced increase in the loss rate of fermionic potassium-rubidium molecules due to ultracold chemical reactions. We find that the loss rate has a steep power-law dependence on the induced electric dipole moment, and we show that this dependence can be understood in a relatively simple model based on quantum threshold laws for the scattering of fermionic polar molecules. In addition, we directly observe the spatial anisotropy of the dipolar interaction through measurements of the thermodynamics of the dipolar gas. These results demonstrate how the long-range dipolar interaction can be used for electric-field control of chemical reaction rates in an ultracold gas of polar molecules. Furthermore, the large loss rates in an applied electric field suggest that creating a long-lived ensemble of ultracold polar molecules may require confinement in a two-dimensional trap geometry to suppress the influence of the attractive, 'head-to-tail', dipolar interactions.

Controlling the hyperfine state of rovibronic ground-state polar molecules.

We report the preparation of a rovibronic ground-state molecular quantum gas in a single hyperfine state and, in particular, the absolute lowest quantum state. This addresses the last internal degree of freedom remaining after the recent production of a near quantum degenerate gas of molecules in their rovibronic ground state, and provides a crucial step towards full control over molecular quantum gases. We demonstrate a scheme that is general for bialkali polar molecules and allows the preparation of molecules in a single hyperfine state or in an arbitrary coherent superposition of hyperfine states. The scheme relies on electric-dipole, two-photon microwave transitions through rotationally excited states and makes use of electric nuclear quadrupole interactions to transfer molecular population between different hyperfine states.

Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules.

How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single partial-wave scattering, and quantum threshold laws provide a clear understanding of the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near-quantum-degenerate gas of polar 40K87Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules were prepared in a single quantum state at a temperature of a few hundred nanokelvin, we observed p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a short-range chemical reaction with a probability near unity. When these molecules were prepared in two different internal states or when molecules and atoms were brought together, the reaction rates were enhanced by a factor of 10 to 100 as a result of s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.

Ultracold polar molecules near quantum degeneracy.

We report the creation and characterization of a near quantum-degenerate gas of polar 40K-87Rb molecules in their absolute rovibrational ground state. Starting from weakly bound heteronuclear KRb Feshbach molecules, we implement precise control of the molecular electronic, vibrational, and rotational degrees of freedom with phase-coherent laser fields. In particular, we coherently transfer these weakly bound molecules across a 125 THz frequency gap in a single step into the absolute rovibrational ground state of the electronic ground potential. Phase coherence between lasers involved in the transfer process is ensured by referencing the lasers to two single components of a phase-stabilized optical frequency comb. Using these methods, we prepare a dense gas of 4 x 10(4) polar molecules at a temperature below 400 nK. This fermionic molecular ensemble is close to quantum degeneracy and can be characterized by a degeneracy parameter of T/T(F) = 3. We have measured the molecular polarizability in an optical dipole trap where the trap lifetime gives clues to interesting decay mechanisms. Given the large measured dipole moment of the KRb molecules of 0.5 Debye, the study of quantum degenerate molecular gases interacting via strong dipolar interactions is now within experimental reach. PACS numbers: 37.10.Mn, 37.10.Pq.

A high phase-space-density gas of polar molecules.

A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing. We report on the creation of an ultracold dense gas of potassium-rubidium (40K87Rb) polar molecules. Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential. The polar molecular gas has a peak density of 10(12) per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin. The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0.052(2) Debye (1 Debye = 3.336 x 10(-30) coulomb-meters) for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state.

Testing nonclassical theories of electromagnetism with ion interferometry.

We discuss using a tabletop ion interferometer to search for deviations from Coulomb's inverse-square law. Such deviations would result from nonclassical effects such as a nonzero photon rest mass. We discuss the theory behind the proposed measurement, explain which fundamental, experimentally controllable parameters are the relevant figures of merit, and calculate the expected performance of such a device in terms of these parameters. The sensitivity to deviations in the exponent of the inverse-square law is predicted to be a few times 10(-22), an improvement by 5 orders of magnitude over current experiments. It could measure a nonzero photon rest mass smaller than 9 x 10(-50) grams, nearly 100 times smaller than current laboratory experiments.