In this paper we propose an experimental scheme to create and probe optomechanical entanglement between a light field and a mechanical oscillator. This is achieved using a bright laser field that resonates inside a cavity and couples to the position and momentum of a moving (micro)mirror.

https://www.univie.ac.at/qfp/publications3/pdffiles/2007-04.pdf

Optomechanical entanglement between a movable mirror and a cavity field

https://absimage.aps.org/image/MAR08/MWS_MAR08-2007-007528.pdf

Towards experimental optomechanical entanglement between a movable mirror and a cavity field.

We propose an immediately realizable scheme showing signatures of multipartite entanglement generated by radiation pressure in a cavity system with a movable mirror. We show how the entanglement involving the inaccessible massive object is unraveled by means of field-field quantum correlations and persists within a wide range of working conditions. Our proposal provides an operative way to infer the quantum behavior of a system that is only partially accessible.

Creating and probing multipartite macroscopic entanglement with light.

We consider the radiative trapping and cooling of a partially reflecting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick dielectric membrane [J. D. Thompson et al., e-print arXiv:0707.1724v2]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar to that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror-coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially reflective mirrors.

Optomechanical trapping and cooling of partially reflective mirrors

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore, it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that the quantum mechanical dynamics of the mirror become easier to observe. These improvements are expected to bring the task of achieving and detecting ground state occupation for the mirror closer to completion.

Trapping and cooling a mirror to its quantum mechanical ground state

In stability analysis of nonlinear systems, the character of the eigenvalues of the Jacobian matrix (i.e., whether the real part is positive, negative, or zero) is needed, while the actual value of the eigenvalue is not required. We present a simple algebraic procedure, based on the Routh-Hurwitz criterion, for determining the character of the eigenvalues without the need for evaluating the eigenvalues explicitly. This procedure is illustrated for a system of nonlinear ordinary differential equations we have studied previously. This procedure is simple enough to be used in computer code, and, more importantly, makes the analysis possible even for those cases where the secular equation cannot be solved.

/pdf/routh-hurwitz-criterion-in-the-examination-of-eigenvalues-of-2ha6ucu8hm.pdf

Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations.

Viscous incompressible fluid flow along a flat plate is modeled. by the Navier-Stokes equations with appropriate boundary conditions. A series solution is assumed and a set of three nonlinear ordinary differential equations is derived by truncating the series. The Reynolds number appears in these three equations as a parameter. These equations are solved by numerical integration. We show that these solutions exhibit qualitatively different behavior for different values of the Reynolds number of the fluid. The various modes include an asymptotic approach to a time-independent state, laminar (periodic) flow, and turbulence. We give several computer-generated pictures of the various modes.

/pdf/nonperiodic-flow-in-the-numerical-integration-of-a-nonlinear-4i6y71o596.pdf

Edmund X. DeJesus

Papers

Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations.

Nonperiodic flow in the numerical integration of a nonlinear differential equation of fluid dynamics