Quantum Key Distribution over Probabilistic Quantum Repeaters

A feasible route towards implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413 (2001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters, by accounting for the DLCZ self-purification property, in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases of with and without a repeater node. We find the cross-over distance beyond which the repeater system outperforms the non-repeater one. That provides us with the optimum inter-node distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance.Comment: 12 pages, 6 figures; Fig. 5(a) is replace

Cavity sideband cooling of a single trapped ion

We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped 88Sr+ ion in the resolved sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the moderate coupling between the ion and the cavity, are consistent with a simple model [Phys. Rev. A 64, 033405] without any free parameters, validating the rate equation model for cavity cooling.Comment: 5 pages, 4 figure

Quantum interface between an electrical circuit and a single atom

We show how to bridge the divide between atomic systems and electronic devices by engineering a coupling between the motion of a single ion and the quantized electric field of a resonant circuit. Our method can be used to couple the internal state of an ion to the quantized circuit with the same speed as the internal-state coupling between two ions. All the well-known quantum information protocols linking ion internal and motional states can be converted to protocols between circuit photons and ion internal states. Our results enable quantum interfaces between solid state qubits, atomic qubits, and light, and lay the groundwork for a direct quantum connection between electrical and atomic metrology standards.Comment: Supplemental material available on reques

Relating Green's Functions in Axial and Lorentz Gauges using Finite Field-Dependent BRS Transformations

We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial gauge can be written as a series in terms of those in Lorentz gauges. Our method also applies to operator Green's functions. We show that this process involves another set of related FFBRS transfomations that is derivable from infinitesimal FBRS. We suggest possible applications.Comment: 20 pages, LaTex, Section 4 expanded, typos corrected; last 2 references modified; (this) revised version to appear in J. Math. Phy

Ion traps fabricated in a CMOS foundry

We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This is the first demonstration of scalable quantum computing hardware, in any modality, utilizing a commercial CMOS process, and it opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays.Comment: 4 pages, 3 figure

Cryogenic Ion Trapping Systems with Surface-Electrode Traps

We present two simple cryogenic RF ion trap systems in which cryogenic temperatures and ultra high vacuum pressures can be reached in as little as 12 hours. The ion traps are operated either in a liquid helium bath cryostat or in a low vibration closed cycle cryostat. The fast turn around time and availability of buffer gas cooling made the systems ideal for testing surface-electrode ion traps. The vibration amplitude of the closed cycled cryostat was found to be below 106 nm. We evaluated the systems by loading surface-electrode ion traps with $^{88}$Sr$^+$ ions using laser ablation, which is compatible with the cryogenic environment. Using Doppler cooling we observed small ion crystals in which optically resolved ions have a trapped lifetime over 2500 minutes.Comment: 10 pages, 13 EPS figure

Superconducting microfabricated ion traps

We fabricate superconducting ion traps with niobium and niobium nitride and trap single 88Sr ions at cryogenic temperatures. The superconducting transition is verified and characterized by measuring the resistance and critical current using a 4-wire measurement on the trap structure, and observing change in the rf reflection. The lowest observed heating rate is 2.1(3) quanta/sec at 800 kHz at 6 K and shows no significant change across the superconducting transition, suggesting that anomalous heating is primarily caused by noise sources on the surface. This demonstration of superconducting ion traps opens up possibilities for integrating trapped ions and molecular ions with superconducting devices.Comment: 3 pages, 2 figure

Sympathetic Cooling of Mixed Species Two-Ion Crystals for Precision Spectroscopy

Sympathetic cooling of trapped ions has become an indispensable tool for quantum information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalisation dynamics after a background gas collision for the Al+/Ca+ crystal for different cooling laser configurations.Comment: Made Graphics black & white print compatible, clarified abstract and summar

Suppression of Heating Rates in Cryogenic Surface-Electrode Ion Traps

Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100 um ion-electrode distances. We characterize heating rates in cryogenically cooled surface-electrode traps, with characteristic sizes in 75 um to 150 um range. Upon cooling to 6 K, the measured rates are suppressed by 7 orders of magnitude, two orders of magnitude below previously published data of similarly sized traps operated at room temperature. The observed noise depends strongly on fabrication process, which suggests further improvements are possible.Comment: 4 pages, 4 figure