Polarizabilities of the 87Sr Clock Transition

In this paper, we propose an in-depth review of the vector and tensor polarizabilities of the two energy levels of the 87Sr clock transition whose measurement was reported in [P. G. Westergaard et al., Phys. Rev. Lett. 106, 210801 (2011)]. We conduct a theoretical calculation that reproduces the measured coefficients. In addition, we detail the experimental conditions used for their measurement in two Sr optical lattice clocks, and exhibit the quadratic behaviour of the vector and tensor shifts with the depth of the trapping potential and evaluate their impact on the accuracy of the clock

Ultrastable lasers based on vibration insensitive cavities

We present two ultra-stable lasers based on two vibration insensitive cavity designs, one with vertical optical axis geometry, the other horizontal. Ultra-stable cavities are constructed with fused silica mirror substrates, shown to decrease the thermal noise limit, in order to improve the frequency stability over previous designs. Vibration sensitivity components measured are equal to or better than 1.5e-11 per m.s^-2 for each spatial direction, which shows significant improvement over previous studies. We have tested the very low dependence on the position of the cavity support points, in order to establish that our designs eliminate the need for fine tuning to achieve extremely low vibration sensitivity. Relative frequency measurements show that at least one of the stabilized lasers has a stability better than 5.6e-16 at 1 second, which is the best result obtained for this length of cavity.Comment: 8 pages 12 figure

Quantum Interference between a Single-Photon Fock State and a Coherent State

We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.Comment: 9 pages, 6 figure

Continuous variable quantum key distribution with two-mode squeezed states

Quantum key distribution (QKD) enables two remote parties to grow a shared key which they can use for unconditionally secure communication [1]. The applicable distance of a QKD protocol depends on the loss and the excess noise of the connecting quantum channel [2-10]. Several QKD schemes based on coherent states and continuous variable (CV) measurements are resilient to high loss in the channel, but strongly affected by small amounts of channel excess noise [2-6]. Here we propose and experimentally address a CV QKD protocol which uses fragile squeezed states combined with a large coherent modulation to greatly enhance the robustness to channel noise. As a proof of principle we experimentally demonstrate that the resulting QKD protocol can tolerate more noise than the benchmark set by the ideal CV coherent state protocol. Our scheme represents a very promising avenue for extending the distance for which secure communication is possible.Comment: 8 pages, 5 figure

The Space Optical Clocks Project: Development of high-performance transportable and breadboard optical clocks and advanced subsystems

The use of ultra-precise optical clocks in space ("master clocks") will allow for a range of new applications in the fields of fundamental physics (tests of Einstein's theory of General Relativity, time and frequency metrology by means of the comparison of distant terrestrial clocks), geophysics (mapping of the gravitational potential of Earth), and astronomy (providing local oscillators for radio ranging and interferometry in space). Within the ELIPS-3 program of ESA, the "Space Optical Clocks" (SOC) project aims to install and to operate an optical lattice clock on the ISS towards the end of this decade, as a natural follow-on to the ACES mission, improving its performance by at least one order of magnitude. The payload is planned to include an optical lattice clock, as well as a frequency comb, a microwave link, and an optical link for comparisons of the ISS clock with ground clocks located in several countries and continents. Undertaking a necessary step towards optical clocks in space, the EU-FP7-SPACE-2010-1 project no. 263500 (SOC2) (2011-2015) aims at two "engineering confidence", accurate transportable lattice optical clock demonstrators having relative frequency instability below 1\times10^-15 at 1 s integration time and relative inaccuracy below 5\times10^-17. This goal performance is about 2 and 1 orders better in instability and inaccuracy, respectively, than today's best transportable clocks. The devices will be based on trapped neutral ytterbium and strontium atoms. One device will be a breadboard. The two systems will be validated in laboratory environments and their performance will be established by comparison with laboratory optical clocks and primary frequency standards. In this paper we present the project and the results achieved during the first year.Comment: Contribution to European Frequency and Time Forum 2012, Gothenburg, Swede

A clock network for geodesy and fundamental science

Leveraging the unrivaled performance of optical clocks in applications in fundamental physics beyond the standard model, in geo-sciences, and in astronomy requires comparing the frequency of distant optical clocks truthfully. Meeting this requirement, we report on the first comparison and agreement of fully independent optical clocks separated by 700 km being only limited by the uncertainties of the clocks themselves. This is achieved by a phase-coherent optical frequency transfer via a 1415 km long telecom fiber link that enables substantially better precision than classical means of frequency transfer. The fractional precision in comparing the optical clocks of three parts in $10^{17}$ was reached after only 1000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than with any other existing frequency transfer method. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.Comment: 14 pages, 3 figures, 1 tabl

Continuous Variable Quantum Cryptography using Two-Way Quantum Communication

Quantum cryptography has been recently extended to continuous variable systems, e.g., the bosonic modes of the electromagnetic field. In particular, several cryptographic protocols have been proposed and experimentally implemented using bosonic modes with Gaussian statistics. Such protocols have shown the possibility of reaching very high secret-key rates, even in the presence of strong losses in the quantum communication channel. Despite this robustness to loss, their security can be affected by more general attacks where extra Gaussian noise is introduced by the eavesdropper. In this general scenario we show a "hardware solution" for enhancing the security thresholds of these protocols. This is possible by extending them to a two-way quantum communication where subsequent uses of the quantum channel are suitably combined. In the resulting two-way schemes, one of the honest parties assists the secret encoding of the other with the chance of a non-trivial superadditive enhancement of the security thresholds. Such results enable the extension of quantum cryptography to more complex quantum communications.Comment: 12 pages, 7 figures, REVTe

High-rate quantum cryptography in untrusted networks

We extend the field of continuous-variable quantum cryptography to a network formulation where two honest parties connect to an untrusted relay by insecure quantum links. To generate secret correlations, they transmit coherent states to the relay where a continuous-variable Bell detection is performed and the outcome broadcast. Even though the detection could be fully corrupted and the links subject to optimal coherent attacks, the honest parties can still extract a secret key, achieving high rates when the relay is proximal to one party, as typical in public networks with access points or proxy servers. Our theory is confirmed by an experiment generating key-rates which are orders of magnitude higher than those achievable with discrete-variable protocols. Thus, using the cheapest possible quantum resources, we experimentally show the possibility of high-rate quantum key distribution in network topologies where direct links are missing between end-users and intermediate relays cannot be trusted.Comment: Theory and Experiment. Main article (6 pages) plus Supplementary Information (additional 13 pages

Geodesy and metrology with a transportable optical clock

partially_open24openGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, DavideGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, David