Building a 3.5 m prototype interferometer for the Q & A vacuum birefringence experiment and high precision ellipsometry

We have built and tested a 3.5 m high-finesse Fabry-Perot prototype inteferometer with a precision ellipsometer for the QED test and axion search (Q & A) experiment. We use X-pendulum-double-pendulum suspension designs and automatic control schemes developed by the gravitational-wave detection community. Verdet constant and Cotton-Mouton constant of the air are measured as a test. Double modulation with polarization modulation 100 Hz and magnetic-field modulation 0.05 Hz gives 10^{-7} rad phase noise for a 44-minute integration.Comment: This draft has been presented in the 5th Edoardo Amaldi Conference on Gravitational Wave

Effect of Spin-Orbit Interaction in Spin-Triplet Superconductor: Structure of d{\bf d}-vector and Anomalous 17^{17}O-NQR Relaxation in Sr2_2RuO4_4

Supposing the spin-triplet superconducting state of Sr$_2$RuO$_4$, the spin-orbit (SO) coupling associated with relative motion in Cooper pairs is calculated by extending the method for the dipole-dipole coupling given by Leggett in the superfluid $^{3}$He. It is shown that the SO coupling works only in the equal-spin pairing (ESP) state to make the pair angular momentum $\hbar{\vec L}$ and the pair spin angular momentum ${\rm i}{\vec d}\times{\vec d}^{*}$ parallel with each other. The SO coupling gives rise to the internal Josephson effect in a chiral ESP state as in superfluid A-phase of $^3$He with a help of an additional anisotropy arising from SO coupling of atomic origin which works to direct the {\bf d}-vector into $ab$-plane. This resolves the problem of the anomalous relaxation of $^{17}$O-NQR and the structure of {\bf d}-vector in Sr$_2$RuO$_4$.Comment: Accepted for publication in J. Phys. Soc. Jpn. vol.79 (2010), No.2 (February issue); 18 pages, 2 figure

Improved Simulation of the Mass Charging for ASTROD I

The electrostatic charging of the test mass in ASTROD I (Astrodynamical Space Test of Relativity using Optical Devices I) mission can affect the quality of the science data as a result of spurious Coulomb and Lorentz forces. To estimate the size of the resultant disturbances, credible predictions of charging rates and the charging noise are required. Using the GEANT4 software toolkit, we present a detailed Monte Carlo simulation of the ASTROD I test mass charging due to exposure of the spacecraft to galactic cosmic-ray (GCR) protons and alpha particles (3He, 4He) in the space environment. A positive charging rate of 33.3 e+/s at solar minimum is obtained. This figure reduces by 50% at solar maximum. Based on this charging rate and factoring in the contribution of minor cosmic-ray components, we calculate the acceleration noise and stiffness associated with charging. We conclude that the acceleration noise arising from Coulomb and Lorentz effects are well below the ASTROD I acceleration noise limit at 0.1 mHz both at solar minimum and maximum. The coherent Fourier components due to charging are investigated, it needs to be studied carefully in order to ensure that these do not compromise the quality of science data in the ASTROD I mission.Comment: 20 pages, 14 figures, submitted to International Journal of Modern Physics

A theory of new type of heavy-electron superconductivity in PrOs_4Sb_12: quadrupolar-fluctuation mediated odd-parity pairings

It is shown that unconventional nature of superconducting state of PrOs_4Sb_12, a Pr-based heavy electron compound with the filled-Skutterudite structure, can be explained in a unified way by taking into account the structure of the crystalline-electric-field (CEF) level, the shape of the Fermi surface determined by the band structure calculation, and a picture of the quasiparticles in f$^{2}$-configuration with magnetically singlet CEF ground state. Possible types of pairing are narrowed down by consulting recent experimental results. In particular, the chiral "p"-wave states such as p_x+ip_y is favoured under the magnetic field due to the orbital Zeeman effect, while the "p"-wave states with two-fold symmetery such as p_x can be stabilized by a feedback effect without the magnetic field. It is also discussed that the double superconducting transition without the magnetic field is possible due to the spin-orbit coupling of the "triplet" Cooper pairs in the chiral state.Comment: 12 pages, 2 figures, submitted to J. Phys.: Condens. Matter Lette

Spin-fluctuation exchange study of superconductivity in two- and three-dimensional single-band Hubbard models

In order to identify the most favorable situation for superconductivity in the repulsive single-band Hubbard model, we have studied instabilities for d-wave pairing mediated by antiferromagnetic spin fluctuations and p-pairing mediated by ferromagnetic fluctuations with the fluctuation exchange approximation in both two dimensions and three dimensions. By systematically varying the band filling and band structure we have shown that (i) d-pairing is stronger in two dimensions than in three dimensions, and (ii) p-pairing is much weaker than the d-pairing.Comment: RevTex, 5 figures in Postscript, to be published in Phys. Rev.

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update

Josephson Current between Triplet and Singlet Superconductors

The Josephson effect between triplet and singlet superconductors is studied. Josephson current can flow between triplet and singlet superconductors due to the spin-orbit coupling in the spin-triplet superconductor but it is finite only when triplet superconductor has $L_z=-S_z=\pm 1$, where $L_z$ and $S_z$ are the perpendicular components of orbital angular momentum and spin angular momentum of the triplet Cooper pairs, respectively. The recently observed temperature and orientational dependence of the critical current through a Josephson junction between UPt$_3$ and Nb is investigated by considering a non-unitary triplet state.Comment: 4 pages, no figure

Parity-sensitive measurements based on ferromagnet/superconductor tunneling junctions

A method to identify the parity of unconventional superconductors is proposed based on tunneling spectroscopy. For a model of calculation, we adopt a ferromagnet/superconductor (F/S) junction of which tunneling current is spin polarized. The tunneling conductance spectra are shown to be quite sensitive to the direction of the magnetization axis in the ferromagnet only when the superconductor has odd parity. Therefore, it is possible to distinguish the parity of the superconductor by measuring the tunneling spectroscopy in F/S junctions.Comment: 4 pages, 5 figure. To appear in J. Phys. Soc. Jp

Ellipsometry noise spectrum, suspension transfer function measurement and closed-loop control of the suspension system in the Q & A experiment

The Q & A experiment, aiming at the detection of vacuum birefringence predicted by quantum electrodynamics, consists mainly of a suspended 3.5 m Fabry-Perot cavity, a rotating permanent dipole magnet and an ellipsometer. The 2.3 T magnet can rotate up to 10 rev/s, introducing an ellipticity signal at twice the rotation frequency. The X-pendulum gives a good isolation ratio for seismic noise above its main resonant frequency 0.3 Hz. At present, the ellipsometry noise decreases with frequency, from 1*10^{-5} rad Hz^{-1/2} at 5 Hz, 2*10^{-6} rad Hz^{-1/2} at 20 Hz to 5*10^{-7} rad Hz^{-1/2} at 40 Hz. The shape of the noise spectrum indicates possible improvement can be made by further reducing the movement between the cavity mirrors. From the preliminary result of yaw motion alignment control, it can be seen that some peaks due to yaw motion of the cavity mirror was suppressed. In this paper, we first give a schematic view of the Q & A experiment, and then present the measurement of transfer function of the compound X-pendulum-double pendulum suspension. A closed-loop control was carried out to verify the validity of the measured transfer functions. The ellipsometry noise spectra with and without yaw alignment control and the newest improvement is presented.Comment: 7 pages, 5 figures, presented in 6th Edoardo Amaldi Conference on Gravitational Waves, June 2005, Okinawa Japan and submitted to Journal of Physics: Conference Series. Some modifications are made according to the referee's comments: mainly to explain the relation between the displacement of cavity mirror and the ellipticity noise spectru

ASTROD, ASTROD I and their gravitational-wave sensitivities

ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) is a mission concept with three spacecraft -- one near L1/L2 point, one with an inner solar orbit and one with an outer solar orbit, ranging coherently with one another using lasers to test relativistic gravity, to measure the solar system and to detect gravitational waves. ASTROD I with one spacecraft ranging optically with ground stations is the first step toward the ASTROD mission. In this paper, we present the ASTROD I payload and accelerometer requirements, discuss the gravitational-wave sensitivities for ASTROD and ASTROD I, and compare them with LISA and radio-wave PDoppler-tracking of spacecraft.Comment: presented to the 5th Edoardo Amaldi Conference (July 6-11, 2003) and submitted to Classical and Quantum Gravit