Relativistic Doppler effect in quantum communication

When an electromagnetic signal propagates in vacuo, a polarization detector cannot be rigorously perpendicular to the wave vector because of diffraction effects. The vacuum behaves as a noisy channel, even if the detectors are perfect. The ``noise'' can however be reduced and nearly cancelled by a relative motion of the observer toward the source. The standard definition of a reduced density matrix fails for photon polarization, because the transversality condition behaves like a superselection rule. We can however define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits, and no exactly orthogonal qubit states.Comment: 10 pages LaTe

Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers

We present a theoretical and experimental investigation of the emission characteristics and the flux of photon pairs generated by spontaneous parametric downconversion in quasi-phase matched bulk crystals for the use in quantum communication sources. We show that, by careful design, one can attain well defined modes close to the fundamental mode of optical fibers and obtain high coupling efficiencies also for bulk crystals, these being more easily aligned than crystal waveguides. We distinguish between singles coupling, conditional coincidence, and pair coupling, and show how each of these parameters can be maximized by varying the focusing of the pump mode and the fiber-matched modes using standard optical elements. Specifically we analyze a periodically poled KTP-crystal pumped by a 532 nm laser creating photon pairs at 810 nm and 1550 nm. Numerical calculations lead to coupling efficiencies above 94% at optimal focusing, which is found by the geometrical relation L/z_R to be ~ 1 to 2 for the pump mode and ~ 2 to 3 for the fiber-modes, where L is the crystal length and z_R is the Rayleigh-range of the mode-profile. These results are independent on L. By showing that the single-mode bandwidth decreases as 1/L, we can therefore design the source to produce and couple narrow bandwidth photon pairs well into the fibers. Smaller bandwidth means both less chromatic dispersion for long propagation distances in fibers, and that telecom Bragg gratings can be utilized to compensate for broadened photon packets--a vital problem for time-multiplexed qubits. Longer crystals also yield an increase in fiber photon flux proportional to sqrt{L}, and so, assuming correct focusing, we can only see advantages using long crystals.Comment: 19 pages, 15 figures, ReVTeX4, minor revisio

A Third Hot White Dwarf Companion Detected by Kepler

We have found a system listed in the Kepler Binary Catalog (3.273 day period; Prsa et al. 2010) that we have determined is comprised of a low-mass, thermally-bloated, hot white dwarf orbiting an A star of about 2.3 solar masses. In this work we designate the object, KIC 10657664, simply as KHWD3. We use the transit depth of ~0.66%, the eclipse depth of ~1.9%, and regular smooth periodic variations at the orbital frequency and twice the orbital frequency to analyze the system parameters. The smooth periodic variations are identified with the classical ellipsoidal light variation and illumination effects, and the newly utilized Doppler boosting effect. Given the measured values of R/a and inclination angle of the binary, both the ELV and DB effects are mostly sensitive to the mass ratio, q = M_2/M_1, of the binary. The two effects yield values of q which are somewhat inconsistent - presumably due to unidentified systematic effects - but which nonetheless provide a quite useful set of possibilities for the mass of the white dwarf (either 0.18 +/- 0.03 M_Sun or 0.37 +/- 0.08 M_Sun). All of the other system parameters are determined fairly robustly. In particular, we show that the white dwarf has a radius of 0.15 +/- 0.01 R_Sun which is extremely bloated over the radius it would have as a fully degenerate object, and an effective temperature T_eff = 14,100 +/- 350 K. Binary evolution scenarios and models for this system are discussed. We suggest that the progenitor binary was comprised of a primary of mass ~2.2 M_Sun (the progenitor of the current hot white dwarf) and a secondary of mass ~1.4 M_Sun (the progenitor of the current A star in the system). We compare this new system with three other white dwarfs in binaries that likely were formed via stable Roche-lobe overflow (KOI-74, KOI-81, and Regulus).Comment: Accepted for publication in Ap

The theory of heating of the quantum ground state of trapped ions

Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.Comment: 9 pages, 2 figure

Bayesian Methods for Exoplanet Science

Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources. Combining repeated observations of periodic events, simultaneous observations with multiple telescopes, different observation techniques, and existing information from theory and prior research can help to disentangle the systematics from the planetary signals, and offers synergistic advantages over analysing observations separately. Bayesian inference provides a self-consistent statistical framework that addresses both the necessity for complex systematics models, and the need to combine prior information and heterogeneous observations. This chapter offers a brief introduction to Bayesian inference in the context of exoplanet research, with focus on time series analysis, and finishes with an overview of a set of freely available programming libraries.Comment: Invited revie

Five Kepler target stars that show multiple transiting exoplanet candidates

We present and discuss five candidate exoplanetary systems identified with the Kepler spacecraft. These five systems show transits from multiple exoplanet candidates. Should these objects prove to be planetary in nature, then these five systems open new opportunities for the field of exoplanets and provide new insights into the formation and dynamical evolution of planetary systems. We discuss the methods used to identify multiple transiting objects from the Kepler photometry as well as the false-positive rejection methods that have been applied to these data. One system shows transits from three distinct objects while the remaining four systems show transits from two objects. Three systems have planet candidates that are near mean motion commensurabilities---two near 2:1 and one just outside 5:2. We discuss the implications that multitransiting systems have on the distribution of orbital inclinations in planetary systems, and hence their dynamical histories; as well as their likely masses and chemical compositions. A Monte Carlo study indicates that, with additional data, most of these systems should exhibit detectable transit timing variations (TTV) due to gravitational interactions---though none are apparent in these data. We also discuss new challenges that arise in TTV analyses due to the presence of more than two planets in a system.Comment: Accepted to Ap

Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for Kepler-9, and validation of Kepler-9d, a super-Earth-size planet in a multiple system

Light curves from the Kepler Mission contain valuable information on the nature of the phenomena producing the transit-like signals. To assist in exploring the possibility that they are due to an astrophysical false positive, we describe a procedure (BLENDER) to model the photometry in terms of a "blend" rather than a planet orbiting a star. A blend may consist of a background or foreground eclipsing binary (or star-planet pair) whose eclipses are attenuated by the light of the candidate and possibly other stars within the photometric aperture. We apply BLENDER to the case of Kepler-9, a target harboring two previously confirmed Saturn-size planets (Kepler-9b and Kepler-9c) showing transit timing variations, and an additional shallower signal with a 1.59-day period suggesting the presence of a super-Earth-size planet. Using BLENDER together with constraints from other follow-up observations we are able to rule out all blends for the two deeper signals, and provide independent validation of their planetary nature. For the shallower signal we rule out a large fraction of the false positives that might mimic the transits. The false alarm rate for remaining blends depends in part (and inversely) on the unknown frequency of small-size planets. Based on several realistic estimates of this frequency we conclude with very high confidence that this small signal is due to a super-Earth-size planet (Kepler-9d) in a multiple system, rather than a false positive. The radius is determined to be 1.64 (+0.19/-0.14) R(Earth), and current spectroscopic observations are as yet insufficient to establish its mass.Comment: 20 pages in emulateapj format, including 8 tables and 16 figures. To appear in ApJ, 1 January 2010. Accepted versio

Berkeley Supernova Ia Program I: Observations, Data Reduction, and Spectroscopic Sample of 582 Low-Redshift Type Ia Supernovae

In this first paper in a series we present 1298 low-redshift (z\leq0.2) optical spectra of 582 Type Ia supernovae (SNe Ia) observed from 1989 through 2008 as part of the Berkeley SN Ia Program (BSNIP). 584 spectra of 199 SNe Ia have well-calibrated light curves with measured distance moduli, and many of the spectra have been corrected for host-galaxy contamination. Most of the data were obtained using the Kast double spectrograph mounted on the Shane 3 m telescope at Lick Observatory and have a typical wavelength range of 3300-10,400 Ang., roughly twice as wide as spectra from most previously published datasets. We present our observing and reduction procedures, and we describe the resulting SN Database (SNDB), which will be an online, public, searchable database containing all of our fully reduced spectra and companion photometry. In addition, we discuss our spectral classification scheme (using the SuperNova IDentification code, SNID; Blondin & Tonry 2007), utilising our newly constructed set of SNID spectral templates. These templates allow us to accurately classify our entire dataset, and by doing so we are able to reclassify a handful of objects as bona fide SNe Ia and a few other objects as members of some of the peculiar SN Ia subtypes. In fact, our dataset includes spectra of nearly 90 spectroscopically peculiar SNe Ia. We also present spectroscopic host-galaxy redshifts of some SNe Ia where these values were previously unknown. [Abridged]Comment: 34 pages, 11 figures, 11 tables, revised version, re-submitted to MNRAS. Spectra will be released in January 2013. The SN Database homepage (http://hercules.berkeley.edu/database/index_public.html) contains the full tables, plots of all spectra, and our new SNID template

The Transit Light Curve Project. XIII. Sixteen Transits of the Super-Earth GJ 1214b

We present optical photometry of 16 transits of the super-Earth GJ 1214b, allowing us to refine the system parameters and search for additional planets via transit timing. Starspot-crossing events are detected in two light curves, and the star is found to be variable by a few percent. Hence, in our analysis, special attention is given to systematic errors that result from star spots. The planet-to-star radius ratio is 0.11610+/-0.00048, subject to a possible upward bias by a few percent due to the unknown spot coverage. Even assuming this bias to be negligible, the mean density of planet can be either 3.03+/-0.50 g cm^{-3} or 1.89+/-0.33 g cm^{-3}, depending on whether the stellar radius is estimated from evolutionary models or from an empirical mass-luminosity relation combined with the light curve parameters. One possible resolution is that the orbit is eccentric (e approximately equal to 0.14), which would favor the higher density, and hence a much thinner atmosphere for the planet. The transit times were found to be periodic within about 15s, ruling out the existence of any other super-Earths with periods within a factor-of-two of the known planet.Comment: Accepted in Ap