Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals.

Fully controllable ultracold atomic systems are creating opportunities for quantum sensing, yet demonstrating a quantum advantage in useful applications by harnessing entanglement remains a challenging task. Here, we realize a many-body quantum-enhanced sensor to detect displacements and electric fields using a crystal of ~150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high- mechanical oscillator, and the collective electronic spin serves as the measurement device.

Broadening of the drumhead-mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap.

Two-dimensional crystals of ions stored in Penning traps are a leading platform for quantum simulation and sensing experiments. For small amplitudes, the out-of-plane motion of such crystals can be described by a discrete set of normal modes called the drumhead modes, which can be used to implement a range of quantum information protocols. However, experimental observations of crystals with Doppler-cooled and even near-ground-state-cooled drumhead modes reveal an unresolved drumhead-mode spectrum.

Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals.

Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode.

Generating Greenberger-Horne-Zeilinger states with squeezing and postselection.

Many quantum state preparation methods rely on a combination of dissipative quantum state initialization followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement, and postselection, generates highly entangled multipartite states, which we refer to as (PS) states.

Author Correction: Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Quantum amplification of mechanical oscillator motion.

Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations.

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model.

Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect).

Near Ground-State Cooling of Two-Dimensional Trapped-Ion Crystals with More than 100 Ions.

We experimentally study electromagnetically induced transparency cooling of the drumhead modes of planar two-dimensional arrays with up to N≈190 Be^{+} ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all N drumhead modes. Quantitative measurements for the center-of-mass mode show near ground-state cooling with motional quantum numbers of n[over ¯]=0.

Trapped Ion Quantum Information Processing with Squeezed Phonons.

Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion-by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation.

Stroboscopic approach to trapped-ion quantum information processing with squeezed phonons.

In trapped-ion quantum information processing, interactions between spins (qubits) are mediated by collective modes of motion of an ion crystal. While there are many different experimental strategies to design such interactions, they all face both technical and fundamental limitations to the achievable coherent interaction strength. In general, obtaining strong interactions and fast gates is an ongoing challenge.

Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition.

We use a self-assembled two-dimensional Coulomb crystal of ∼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.

Amplitude Sensing below the Zero-Point Fluctuations with a Two-Dimensional Trapped-Ion Mechanical Oscillator.

We present a technique to measure the amplitude of a center-of-mass (c.m.) motion of a two-dimensional ion crystal of ∼100 ions.

Quantum spin dynamics and entanglement generation with hundreds of trapped ions.

Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of (9)Be(+) ions in a Penning trap.

Spectroscopy and thermometry of drumhead modes in a mesoscopic trapped-ion crystal using entanglement.

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a ~400 μm-diameter planar crystal of several hundred 9Be(+) ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the 9Be(+) valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing (~20 μm).

Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins.

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems.

Phase-coherent detection of an optical dipole force by Doppler velocimetry.

We report phase-coherent Doppler detection of optical dipole forces using large ion crystals in a Penning trap. The technique is based on laser Doppler velocimetry using a cycling transition in 9Be+ near 313 nm and the center-of-mass (COM) ion motional mode. The optical dipole force is tuned to excite the COM mode, and measurements of photon arrival times synchronized with the excitation potential show oscillations with a period commensurate with the COM motional frequency.

Decoherence due to elastic Rayleigh scattering.

We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal.

Ultrasensitive detection of force and displacement using trapped ions.

The ability to detect extremely small forces and nanoscale displacements is vital for disciplines such as precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 aN Hz(-1/2) (refs 6,7) through coupling of nanomechanical resonators to a variety of physical readout systems. Here, we demonstrate that crystals of trapped atomic ions behave as nanoscale mechanical oscillators and may form the core of exquisitely sensitive force and displacement detectors.

Optimized noise filtration through dynamical decoupling.

Recent studies have shown that applying a sequence of Hahn spin-echo pulses to a qubit system at judiciously chosen intervals can, in certain noise environments, greatly improve the suppression of phase errors compared to traditional dynamical decoupling approaches. By enforcing a simple analytical condition, we obtain sets of dynamical decoupling sequences that are designed for optimized noise filtration, but are independent of the noise spectrum up to a single scaling factor set by the coherence time of the system. These sequences are tested in a model qubit system, ;{9}Be;{+} ions in a Penning trap.

Entangled mechanical oscillators.

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the 'Schrödinger's cat' thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature.

Optimized dynamical decoupling in a model quantum memory.

Any quantum system, such as those used in quantum information or magnetic resonance, is subject to random phase errors that can dramatically affect the fidelity of a desired quantum operation or measurement. In the context of quantum information, quantum error correction techniques have been developed to correct these errors, but resource requirements are extraordinary. The realization of a physically tractable quantum information system will therefore be facilitated if qubit (quantum bit) error rates are far below the so-called fault-tolerance error threshold, predicted to be of the order of 10(-3)-10(-6).

Microfabricated surface-electrode ion trap for scalable quantum information processing.

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations.

Rapid heating of a strongly coupled plasma near the solid-liquid phase transition.

Between 10(4) and 10(6) 9Be+ ions were trapped in a Penning trap and laser cooled to approximately 1 mK, where they formed a crystalline plasma. We measured the ion temperature as a function of time after turning off the laser cooling and observed a rapid temperature increase as the plasma underwent the solid-liquid phase transition at T approximately 10 mK (Gamma approximately 170). We present evidence that this rapid heating is due to a sudden release of energy from weakly cooled degrees of freedom involving the cyclotron motion of trapped impurity ions.

Laser-generated waves and wakes in rotating ion crystals.

Locally excited plasma waves are generated in a Coulomb crystal by "pushing" with radiation pressure on a rotating cloud of laser-cooled 9Be+ ions. The waves form a stationary wake that is directly imaged through the dependence of the ion fluorescence on Doppler shifts, and theoretical calculations in a slab geometry are shown to accurately reproduce these images. The technique demonstrates a new method of exciting and studying waves in cold ion clouds.