Two-Brane Randall-Sundrum Model in AdS_5 and dS_5

Two flat Randall - Sundrum three-branes are analyzed, at fixed mutual distance, in the case where each brane contains an ideal isotropic fluid. Both fluids are to begin with assumed to obey the equation of state p=(\gamma -1)\rho, where \gamma is a constant. Thereafter, we impose the condition that there is zero energy flux from the branes into the bulk, and assume that the tension on either brane is zero. It then follows that constant values of the fluid energies at the branes are obtained only if the value of \gamma is equal to zero (i.e., a `vacuum' fluid). The fluids on the branes are related: if one brane is a dS_4 brane (the effective four-dimensional constant being positive), then the other brane is dS_4 also, and if the fluid energy density on one brane is positive, the energy density on the other brane is larger in magnitude but negative. This is a non-acceptable result, which sheds some light on how far it is possible to give a physical interpretation of the two-brane scenario. Also, we discuss the graviton localization problem in the two-brane setting, generalizing prior works.Comment: 12 pages, no figures; revised discussion in section III on negative energy densitie

Proposal for entangling remote micromechanical oscillators via optical measurements

We propose an experiment to create and verify entanglement between remote mechanical objects by use of an optomechanical interferometer. Two optical cavities, each coupled to a separate mechanical oscillator, are coherently driven such that the oscillators are laser cooled to the quantum regime. The entanglement is induced by optical measurement and comes about by combining the output from the two cavities to erase which-path information. It can be verified through measurements of degrees of second-order coherence of the optical output field. The experiment is feasible in the regime of weak optomechanical coupling. Realistic parameters for the membrane-in-the-middle geometry suggest entangled state lifetimes on the order of milliseconds.Comment: 4 pages, 2 figures + supplementary material (7 pages, 2 figs). Updates in v2: New Eq. (7) and Fig. 1 - results unchanged. Added supplementary material with various details. Updates in v3: Minor changes, journal ref. adde

Cooling in the single-photon strong-coupling regime of cavity optomechanics

In this paper we discuss how red-sideband cooling is modified in the single-photon strong-coupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. Using Fermi's Golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolved-sideband limit we find multiple-phonon cooling resonances for strong single-photon coupling that lead to non-thermal steady states including the possibility of phonon anti-bunching. Our study generalizes the standard linear cooling theory.Comment: 4 pages, 3 figure

Single-photon Optomechanics

Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady-states of the mechanical oscillator when multi-photon transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.Comment: 4 pages, 4 figure

Quantum state purity versus average phonon number for characterization of mechanical oscillators in cavity optomechanics

Quantum oscillators in Gaussian states are often characterized by average occupation numbers that refer to a basis of eigenstates of the non-interacting oscillator. We argue that quantum state purity is a more appropriate characteristic of such states, which can be applied to oscillators of any dimensionality. For a one-dimensional oscillator, the state purity is directly related to a thermal occupation number defined with respect to the basis in which the oscillator's quantum state is diagonal. Thus, it naturally introduces a more versatile definition of an average occupation number. We study optomechanical sideband cooling of one- and two-dimensional mechanical oscillators in particular, and derive exact analytical expressions for the maximal mechanical state purity achievable in the quantum backaction limit. In the case of a one-dimensional oscillator, we show that the thermal occupation number related to purity can be well approximated by the average phonon number in the weak-coupling regime, but that the two differ in the regime of ultrastrong optomechanical coupling or in cases where the oscillator's resonance frequency is strongly renormalized.Comment: 11 pages, 4 figure

Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.Comment: 15 pages, 16 figure

Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

Theoretical studies of a planar tunnel junction between two superconductors with antisymmetric spin-orbit coupling are presented. The half-space Green's function for such a superconductor is determined. This is then used to derive expressions for the dissipative current and the Josephson current of the junction. Numerical results are presented in the case of the Rashba spin-orbit coupling, relevant to the much studied compound CePt$_3$Si. Current-voltage diagrams, differential conductance and the critical Josephson current are presented for different crystallographic orientations and different weights of singlet and triplet components of the pairing state. The main conclusion is that Josephson junctions with different crystallographic orientations may provide a direct connection between unconventional pairing in superconductors of this kind and the absence of inversion symmetry in the crystal.Comment: 16 pages, 10 figure

Cooling and squeezing via quadratic optomechanical coupling

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.Comment: 4 pages, 3 figure

Observability of radiation pressure shot noise in optomechanical systems

We present a theoretical study of an experiment designed to detect radiation pressure shot noise in an optomechanical system. Our model consists of a coherently driven optical cavity mode that is coupled to a mechanical oscillator. We examine the cross-correlation between two quadratures of the output field from the cavity. We determine under which circumstances radiation pressure shot noise can be detected by a measurement of this cross-correlation. This is done in the general case of nonzero detuning between the frequency of the drive and the cavity resonance frequency. We study the qualitative features of the different contributions to the cross-correlator and provide quantitative figures of merit for the relative importance of the radiation pressure shot noise contribution to other contributions. We also propose a modified setup of this experiment relevant to the "membrane-in-the-middle" geometry, which potentially can avoid the problems of static bistability and classical noise in the drive.Comment: 12 pages + 4 page appendix, 10 figure

Detecting Majorana Bound States by Nanomechanics

We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states.Comment: 6 pages, 4 figure