Test of Causal Nonlinear Quantum Mechanics by Ramsey Interferometry with a Trapped Ion.

Quantum mechanics requires the time evolution of the wave function to be linear. While this feature has been associated with the preservation of causality, a consistent causal nonlinear theory was recently developed. Interestingly, this theory is unavoidably sensitive to the full physical spread of the wave function, rendering existing experimental tests for nonlinearities inapplicable. Here, using well-controlled motional superpositions of a trapped ion, we set a stringent limit of 5.4×10^{-12} on the magnitude of the unitless scaling factor ε[over ˜]_{γ} for the predicted causal nonlinear perturbation.

Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor.

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 µm. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Trapped Electrons and Ions as Particle Detectors.

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As illustrations, we suggest some applications in particle physics. We outline a nondestructive time-of-flight measurement capable of sub-eV energy resolution for slowly moving, collimated particles. We also show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges ≪e. Our calculations may also be useful in the characterization of noise in quantum computers coming from backgrounds of charged particles.

Improved Test of Local Lorentz Invariance from a Deterministic Preparation of Entangled States.

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.

Realization of Translational Symmetry in Trapped Cold Ion Rings.

We crystallize up to 15 ^{40}Ca^{+} ions in a ring with a microfabricated silicon surface Paul trap. Delocalization of the Doppler laser-cooled ions shows that the translational symmetry of the ion ring is preserved at millikelvin temperatures. By characterizing the collective motion of the ion crystals, we identify homogeneous electric fields as the dominant symmetry-breaking mechanism at this energy scale. With increasing ion numbers, such detrimental effects are reduced. We predict that, with only a ten-ion ring, uncompensated homogeneous fields will not break the translational symmetry of the rotational ground state. This experiment opens a door towards studying quantum many-body physics with translational symmetry at the single-particle level.

Coherent all-optical control of ultracold atoms arrays in permanent magnetic traps.

We propose a hybrid architecture for quantum information processing based on magnetically trapped ultracold atoms coupled via optical fields. The ultracold atoms, which can be either Bose-Einstein condensates or ensembles, are trapped in permanent magnetic traps and are placed in microcavities, connected by silica based waveguides on an atom chip structure. At each trapping center, the ultracold atoms form spin coherent states, serving as a quantum memory. An all-optical scheme is used to initialize, measure and perform a universal set of quantum gates on the single and two spin-coherent states where entanglement can be generated addressably between spatially separated trapped ultracold atoms. This allows for universal quantum operations on the spin coherent state quantum memories. We give detailed derivations of the composite cavity system mediated by a silica waveguide as well as the control scheme. Estimates for the necessary experimental conditions for a working hybrid device are given.

Precision measurement method for branching fractions of excited P(1/2) states applied to 40Ca+.

We present a method for measuring branching fractions for the decay of J=1/2 atomic energy levels to lower-lying states based on time-resolved recording of the atom's fluorescence during a series of population transfers. We apply this method to measure the branching fractions for the decay of the 4²P(1/2) state of 40Ca+ to the 4²S(1/2) and 3²D(3/2) states to be 0.935 65(7) and 0.064 35(7), respectively. The measurement scheme requires that at least one of the lower-lying states be long lived. The method is insensitive to fluctuations in laser light intensity and magnetic field and is readily applicable to various atomic species due to its simplicity. Our result distinguishes well among existing state-of-the-art theoretical models of Ca+.

Surface trap with dc-tunable ion-electrode distance.

We describe the design, fabrication, and operation of a novel surface-electrode Paul trap that produces a radio-frequency-null along the axis perpendicular to the trap surface. This arrangement enables control of the vertical trapping potential and consequentially the ion-electrode distance via dc-electrodes only. We demonstrate the confinement of single 40Ca+ ions at heights between 50 µm and 300 µm above planar copper-coated aluminum electrodes. Laser-cooling and coherent operations are performed on both the planar and vertical motional modes. This architecture provides a platform for precision electric-field noise detection and trapping of vertical ion strings without excess micromotion and may have applications for scalable quantum computers with surface ion traps.

Realization of the Cirac-Zoller controlled-NOT quantum gate.

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac-Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac-Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.

Control and measurement of three-qubit entangled states.

We report the deterministic creation of maximally entangled three-qubit states-specifically the Greenberger-Horne-Zeilinger (GHZ) state and the W state-with a trapped-ion quantum computer. We read out one of the qubits selectively and show how GHZ and W states are affected by this local measurement. Additionally, we demonstrate conditional operations controlled by the results from reading out one qubit. Tripartite entanglement is deterministically transformed into bipartite entanglement by local operations only. These operations are the measurement of one qubit of a GHZ state in a rotated basis and, conditioned on this measurement result, the application of single-qubit rotations.

New determination of the electron's mass.

A new independent value for the electron's mass in units of the atomic mass unit is presented, m(e) = 0.000 548 579 909 2(4) u. The value is obtained from our recent measurement of the g factor of the electron in (12)C(5+) in combination with the most recent quantum electrodynamical (QED) predictions. In the QED corrections, terms of order alpha(2) were included by a perturbation expansion in Zalpha. Our total precision is three times better than that of the accepted value for the electron's mass.

Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer.

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.