Abstract. A working free-space quantum key distribution (QKD) system has been developed and tested over an outdoor optical path of ∼ 1 km at Los Alamos National Laboratory under nighttime conditions. Results show that QKD can provide secure real-time key distribution between parties who have a need to communicate secretly. Finally, we examine the feasibility of surface to satellite QKD.Quantum cryptography was introduced in the mid1980s [1] as a new method for generating the shared, secret random number sequences, known as cryptographic keys, that are used in crypto-systems to provide communications security. The appeal of quantum cryptography is that its security is based on laws of nature, in contrast to existing methods of key distribution that derive their security from the perceived intractability of certain problems in number theory, or from the physical security of the distribution process.Since the introduction of quantum cryptography, several groups have demonstrated quantum communications [2,3] and quantum key distribution [4-9] over multikilometer distances of optical fiber. Free-space QKD (over an optical path of ∼ 30 cm) was first introduced in 1991 [12], and recent advances have led to demonstrations of QKD over free-space indoor optical paths of 205 m [10], and outdoor optical paths of 75 m [11]. These demonstrations increase the utility of QKD by extending it to line-of-site laser communications systems. Indeed there are certain key distribution problems in this category for which free-space QKD would have definite practical advantages (for example, it is impractical to send a courier to a satellite). We are developing such QKD, and here we report our results of free-space QKD over outdoor optical paths of up to 950 m under nighttime conditions. The success of QKD over free-space optical paths depends on the transmission and detection of singlephotons against a high background through a turbulent medium. Although this problem is difficult, a combination of sub-nanosecond timing, narrow filters [13,14], spatial filtering [10] and adaptive optics [15] can render the transmission and detection problems tractable. Furthermore, the essentially non-birefringent nature of the atmosphere at optical wavelengths allows the faithful transmission of the single-photon polarization states used in the free-space QKD protocol.A QKD procedure starts with the sender, "Alice," gen-

No abstract

No abstract

Two preliminary determinations of the Newtonian constant of gravitation have been performed at Los Alamos National Laboratory employing low-Q torsion pendulums and using the time-of-swing method.Recently, Kuroda has predicted that such determinations have an upward bias inversely proportional to the oscillation Q, and our results support this conjecture. If this conjecture is correct, our best value for the constant is ͑6.6740 6 0.0007͒ 3 10 211 m 3 kg 21 s 22 .Interest in the value of the Newtonian gravitational constant, G, has increased recently with the publication of several disparate results [1][2][3][4]. This discrepancy, as much as 50 standard deviations, is an error unheard of in the measurement of any other of the fundamental constants. A torsion pendulum instrument has been assembled at Los Alamos National Laboratory which determines G by the method of Heyl, also called the time-of-swing method, and preliminary results of this effort are reported herein. Kuroda has shown [5] that popular models of anelasticity predict a bias in these determinations where the damping of the pendulum is caused by losses in the suspension fiber, and this upward fractional bias should be 1͞pQ. Two determinations were carried out employing systems which differ in Q by a factor of 2, and the disagreement of their results is consistent with that predicted by Kuroda.In a time-of-swing, or Heyl-type, measurement, the oscillation frequency of a torsion pendulum is perturbed by the presence of source masses. In their absence, the free oscillation frequency, squared, is related to the moment of inertia, I, and fiber torsion constantThe interaction potential energy of the pendulum and source masses, U g ͑w͒, contributes a "gravitational torsion constant,"where w is the angle between the axis of the pendulum and that of the source masses. Therefore, the frequency of small oscillations of the pendulum isThe gravitational torsion constant is at a maximum when the pendulum is in line with the source masses (w 0, or "near" position), and at a minimum when it is perpendicular (w p͞2, or "far" position). It is proportional to G, and is calculable from the geometry and densities of the pendulum and masses, so the gravitational constant is given bywhere k g K g ͞G, and D͑v 2 ͒ is the difference of the square of the frequencies recorded at the two orientations.The above derivation assumes that k g remains the same at each orientation, but this assumption has been called into question recently. Interest in gravitational wave detectors has spurred research into the anelastic properties of suspension materials at low frequencies, and one model of anelasticity has been shown [6-8] to predict accurately the behavior of several different materials. This model treats a physical spring as a perfectly elastic spring in parallel with a continuous number of Maxwell units, characterized by a spectrum of relaxation times. The model predicts that the torsion constant is a function of oscillation frequency. Kuroda [5] has shown that, for a Heyl-type measu...

Hamiltonian Lie-Poisson structures of the three-wave equations associated with the Lie algebras su(3) and su(2, 1) are derived and shown to be compatible. Poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated. These results can be applied to applications of nonlinear-waves in, for instance, nonlinear optics. Some of the general structures presented in the latter part of this paper are implicit in the literature; our purpose is to put the three-wave interaction in the modern setting of geometric mechanics and to explore some new things, such as explicit geometric phase formulas, as well as some old things, such as integrability, in this context.