Phonon Cooling by an Optomechanical Heat Pump.

We propose and analyze theoretically a cavity optomechanical analog of a heat pump that uses a polariton fluid to cool mechanical modes coupled to a single precooled phonon mode via external modulation of the substrate of the mechanical resonator. This approach permits us to cool phonon modes of arbitrary frequencies not limited by the cavity-optical field detuning deep into the quantum regime from room temperature.

Macroscopic tunneling of a membrane in an optomechanical double-well potential.

The macroscopic tunneling of an optomechanical membrane is considered. A cavity mode which couples quadratically to the membranes position can create highly tunable adiabatic double-well potentials, which together with the high Q factors of such membranes render the observation of macroscopic tunneling possible. A suitable, pulsed measurement scheme using a linearly coupled mode of the cavity for the verification of the effect is studied.

Quantum optomechanics of a Bose-Einstein antiferromagnet.

We investigate the cavity optomechanical properties of an antiferromagnetic Bose-Einstein condensate, where the role of the mechanical element is played by spin-wave excitations. We show how this system can be described by a single rotor that can be prepared deep in the quantum regime under realizable experimental conditions. This system provides a bottom-up realization of dispersive rotational optomechanics, and opens the door to the direct observation of quantum spin fluctuations.

Optomechanics of a quantum-degenerate Fermi gas.

We explore theoretically the optomechanical interaction between a light field and a mechanical mode of ultracold fermionic atoms inside a Fabry-Pérot cavity. The low-lying phonon mode of the fermionic ensemble is a collective density oscillation associated with particle-hole excitations, and is mathematically analogous to the momentum side-mode excitations of a bosonic condensate. The mechanical motion of the fermionic particle-hole system behaves hence as a "moving mirror." We derive an effective system Hamiltonian that has the form of generic optomechanical systems. We also discuss the experimental consequences the optomechanical coupling in optical bistability and in the noise spectrum of the system.

All-optical optomechanics: an optical spring mirror.

The dominant hurdle to the operation of optomechanical systems in the quantum regime is the coupling of the vibrating element to a thermal reservoir via mechanical supports. Here we propose a scheme that uses an optical spring to replace the mechanical support. We show that the resolved-sideband regime of cooling can be reached in a configuration using a high-reflectivity disk mirror held by an optical tweezer as one of the end mirrors of a Fabry-Perot cavity. We find a final phonon occupation number of the trapped mirror n=0.56 for reasonable parameters, the limit being set by our approximations, and not any fundamental physics. This demonstrates the promise of dielectric disks attached to optical springs for the observation of quantum effects in macroscopic objects.

Generating entangled atom-photon pairs from bose-einstein condensates

We propose using spontaneous Raman scattering from an optically driven Bose-Einstein condensate as a source of atom-photon pairs whose internal states are maximally entangled. Generating entanglement between a particle which is easily transmitted (the photon) and one which is easily trapped and coherently manipulated (an ultracold atom) will prove useful for a variety of quantum-information related applications. We analyze the type of entangled states generated by spontaneous Raman scattering and construct a geometry which results in maximum entanglement.

Eliminating the mean-field shift in two-component bose-einstein condensates

We demonstrate that the nonlinear mean-field shift in a multicomponent Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification can be achieved by engineering the environment of the condensate. We consider the case of a two-component condensate in a quasi-one-dimensional atomic waveguide, achieving modification of the atom-atom interactions by varying the transverse wave functions of the components. Eliminating the density-dependent phase shift represents a promising potential application for multicomponent condensates in atom interferometry and precision measurements.

Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.

Quantum noise in the collective abstraction reaction A + B2-->AB + B.

We demonstrate theoretically that the collective abstraction reaction A + B2-->AB + B can be realized efficiently with degenerate bosonic or fermionic matter waves. We show that this is dominated by quantum fluctuations, which are critical in triggering its initial stages with the appearance of macroscopic nonclassical correlations of the atomic and molecular fields as a result. This study opens up a promising new regime of quantum-degenerate matter-wave chemistry.

Coupling nanomechanical cantilevers to dipolar molecules.

We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.

Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror.

We show theoretically that it is possible to trap and cool the rotational motion of a macroscopic mirror made of a perfectly reflecting spiral phase element using orbital angular momentum transfer from a Laguerre-Gaussian optical field. This technique offers a promising route to the placement of the rotor in its quantum mechanical ground state in the presence of thermal noise. It also opens up the possibility of simultaneously cooling a vibrational mode of the same mirror. Lastly, the proposed design may serve as a sensitive torsional balance in the quantum regime.

Trapping and cooling a mirror to its quantum mechanical ground state.

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.

Fermionic stabilization and density-wave ground state of a polar condensate.

We examine the stability of a trapped dipolar condensate mixed with a single-component fermion gas at T=0. Whereas pure dipolar condensates with a small s-wave interaction are unstable even at small dipole-dipole interaction strength, we find that the admixture of fermions can significantly stabilize them, depending on the strength of the boson-fermion interaction. Within the stable regime we find a region where a ground state is characterized by a density wave along the soft trap direction.

Coherent atom-trimer conversion in a repulsive Bose-Einstein condensate.

We show that the use of a generalized atom-molecule dark state permits the enhanced coherent creation of triatomic molecules in a repulsive atomic Bose-Einstein condensate, with further enhancement being possible in the case of heteronuclear trimers via the constructive interference between two chemical reaction channels.

Number statistics of molecules formed from ultracold atoms.

We calculate the number statistics of a single-mode molecular field excited by photo-association or via a Feshbach resonance from an atomic Bose-Einstein condensate (BEC), a normal atomic Fermi gas, and a Fermi system with pair correlations (BCS state). We find that the molecule formation from a BEC leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, result for short times in a molecular field analog of a classical chaotic light source. The BCS situation is intermediate between the two and goes from producing an incoherent to a coherent molecular field with an increasing gap parameter. This distinct signature of the initial atomic state in the resulting molecular field makes single molecule counting into a powerful diagnostic tool.

Repeated quantum measurements on a single-harmonic oscillator.

Repeated quantum measurements on the intracavity field of a lossless micromaser are discussed. The effect of the associated quantum state reductions is to generate photon statistics bearing little relation to the original ones or to those obtained if no measurement is performed.