F. Schmidt-Kaler

Deterministic quantum teleportation with atoms

Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

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.

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.

Quantum State Engineering on an Optical Transition and Decoherence in a Paul Trap

A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.

Coupling a single atomic quantum bit to a high finesse optical cavity.

The quadrupole S(1/2)-D(5/2) optical transition of a single trapped Ca+ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ions response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ions vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer precision.

Light interference from single atoms and their mirror images

A single atom emitting single photons is a fundamental source of light. But the characteristics of this light depend strongly on the environment of the atom. For example, if an atom is placed between two mirrors, both the total rate and the spectral composition of the spontaneous emission can be modified. Such effects have been observed using various systems: molecules deposited on mirrors, dye molecules in an optical cavity, an atom beam traversing a two-mirror optical resonator, single atoms traversing a microwave cavity and a single trapped electron. A related and equally fundamental phenomenon is the optical interaction between two atoms of the same kind when their separation is comparable to their emission wavelength. In this situation, light emitted by one atom may be reabsorbed by the other, leading to cooperative processes in the emission. Here we observe these phenomena with high visibility by using one or two single atom(s), a collimating lens and a mirror, and by recording the individual photons scattered by the atom(s). Our experiments highlight the intimate connection between one-atom and two-atom effects, and allow their continuous observation using the same apparatus.

A single atom heat engine

Making a teeny tiny engine Steam locomotives, cars, and the drinking bird toy all convert heat into useful work as it cycles between two reservoirs at different temperatures. Usually, the working substance where the heat-work conversion occurs is a liquid or a gas, consisting of many molecules. Roβnagel et al. have made a working substance of a single calcium ion in a tapered ion trap. A laser-cooling beam plays the part of a cold reservoir for the calcium ion, and in turn, electric field noise acts as a hot reservoir. Science, this issue p. 325 A calcium ion held in a tapered trap is used as the working substance of a tiny thermodynamic engine. Heat engines convert thermal energy into mechanical work and generally involve a large number of particles. We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we were able to determine the thermodynamic cycles for various temperature differences of the reservoirs. We then used these cycles to evaluate the power P and efficiency η of the engine, obtaining values up to P = 3.4 × 10–22 joules per second and η = 0.28%, consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the limit of single atoms.

Experimental Demonstration of Ground State Laser Cooling with Electromagnetically Induced Transparency

Ground state laser cooling of a single trapped Ca(+)on is achieved with a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency. Using the Zeeman structure of the S(1/2) to P(1/2) dipole transition we achieve up to 90% ground state probability. The new method is robust, easy to implement, and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.

Controlling Fast Transport of Cold Trapped Ions

We realize fast transport of ions in a segmented microstructured Paul trap. The ion is shuttled over a distance of more than 10(4) times its ground state wave function size during only five motional cycles of the trap (280 μm in 3.6 μs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.

Single-Ion Heat Engine at Maximum Power

O. Abah, J. Roßnagel, G. Jacob, S. Deffner, 3 F. Schmidt-Kaler, K. Singer, and E. Lutz 4 Department of Physics, University of Augsburg, D-86159 Augsburg, Germany Institut für Quantenphysik, Universität Mainz, 55128 Mainz, Germany Department of Chemistry and Biochemistry and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA Dahlem Center for Complex Quantum Systems, FU Berlin, D-14195 Berlin, Germany