Weak Value in Wave Function of Detector

A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.Comment: 3 pages, no figures, Published in Journal of the Physical Society of Japa

Realization of a Measurement of a Weak Value

We present the first realization of a measurement of a weak value, a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This weak measurement is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects

Realization of a Measurement of a Weak Value

We present the first realization of a measurement of a weak value, a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This weak measurement is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matte

Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment

Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a particular final measurement result. I show that weak values arise naturally in quantum optics, as weak measurements occur whenever an open system is monitored (as by a photodetector). I use quantum trajectory theory to derive a generalization of AAV's formula to include (a) mixed initial conditions, (b) nonunitary evolution, (c) a generalized (non-projective) final measurement, and (d) a non-back-action-evading weak measurement. I apply this theory to the recent Stony-Brook cavity QED experiment demonstrating wave-particle duality [G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, and H.J. Carmichael, Phys. Rev. Lett. {85}, 3149 (2000)]. I show that the ``fractional'' correlation function measured in that experiment can be recast as a weak value in a form as simple as that introduced by AAV.Comment: 6 pages, no figures. To be published in Phys. Rev.

Dicluster Stopping in a Degenerate Electron Gas

In this paper we report on our theoretical studies of various aspects of the correlated stopping power of two point-like ions (a dicluster) moving in close but variable vicinity of each other in some metallic target materials the latter being modelled by a degenerate electron gas with appropriate densities. Within the linear response theory we have made a comprehensive investigation of correlated stopping power, vicinage function and related quantities for a diproton cluster in two metallic targets, aluminum and copper, and present detailed and comparative results for three approximations to the electron gas dielectric function, namely the plasmon-pole approximation without and with dispersion as well as with the random phase approximation. The results are also compared, wherever applicable, with those for an individual projectile.Comment: 29 figures, LaTe

Magneto-optical Trapping of Cadmium

We report the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0-1P1 transition at 229 nm in this two-electron atom and also photoionizes atoms directly from the 1P1 state. This photoionization overwhelms the other loss mechanisms and allows a direct measurement of the photoionization cross section, which we measure to be 2(1)x10^(-16)cm^(2) from the 1P1 state. When combined with nearby laser-cooled and trapped Cd^(+) ions, this apparatus could facilitate studies in ultracold interactions between atoms and ions.Comment: 8 pages, 11 figure

Quadratic electronic response of a two-dimensional electron gas

The electronic response of a two-dimensional (2D) electron system represents a key quantity in discussing one-electron properties of electrons in semiconductor heterojunctions, on the surface of liquid helium and in copper-oxide planes of high-temperature superconductors. We here report an evaluation of the wave-vector and frequency dependent dynamical quadratic density-response function of a 2D electron gas (2DEG), within a self-consistent field approximation. We use this result to find the $Z_1^3$ correction to the stopping power of a 2DEG for charged particles moving at a fixed distance from the plane of the 2D sheet, $Z_1$ being the projectile charge. We reproduce, in the high-density limit, previous full nonlinear calculations of the stopping power of a 2DEG for slow antiprotons, and we go further to calculate the $Z_1^3$ correction to the stopping power of a 2DEG for a wide range of projectile velocities. Our results indicate that linear response calculations are, for all projectile velocities, less reliable in two dimensions than in three dimensions.Comment: 17 pages, 5 figures, to appear in Phys. Rev.

Observation of Velocity-Tuned Multiphoton Doppleron Resonances in Laser-Cooled Atoms

An atomic beam of Li was transversely cooled using an intense standing-wave radiation field. A dramatic change in the transverse velocity distribution was observed. Structure in the resulting velocity distribution was found to be due to velocity-tuned multiphoton Doppleron resonances. The force due to seven-photon resonances is clearly resolved in the data. The data are in good agreement with theoretical predictions