M. Bhattacharya

Hamiltonian chaos in a coupled BEC-optomechanical-cavity system

We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.

Optomechanical trapping and cooling of partially reflective mirrors

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.

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.

Optomechanical control of atoms and molecules

We briefly review some of our recent and ongoing work on nanoscale optomechanics, an emerging area at the confluence of atomic, condensed matter and gravitational wave physics. A central tenet of optomechanics is the laser cooling of a moving mirror, typically an end mirror of a Fabry-Perot resonator, to a point near its quantum-mechanical ground state of vibration. Following a general introduction we discuss how the motion of such a macroscopic quantum oscillator can be squeezed, and then show how the placement of a ferroelectric tip on the oscillator allows the coherent manipulation and control of the center-of-mass motion of ultracold polar molecules.

Classical dynamics of the optomechanical modes of a Bose-Einstein condensate in a ring cavity

We consider a cavity optomechanical system consisting of a Bose-Einstein condensate (BEC) interacting with two counterpropagating traveling-wave modes in an optical ring cavity. In contrast to the more familiar case where the condensate is driven by the standing-wave field of a high-Q Fabry-Perot cavity we find that both symmetric and antisymmetric collective density side modes of the BEC are mechanically excited by the light field. In the semiclassical, mean-field limit where the light field and the zero-momentum mode of the condensate are treated classically the system is found to exhibit a rich multistable behavior, including the appearance of isolated branches of solutions (isolas). We also present examples of the dynamics of the system as input parameters such as the frequency of the driving lasers are varied.

Optomechanical trapping and cooling of partially transparent mirrors

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.

Quantum Control of Ultracold AMO Systems by Nanomechanical Resonators

Laser-cooled nanomechanical oscillators are promising new tools to manipulate and control ultracold atomic and molecular samples. As an illustration, we show how they can be exploited to entangle and squeeze a lattice of dipolar molecules.

Activation Energies and Temperature Dependent Frequency Factors in Thermoluminescence Recorded with Hyperbolic Heating Scheme

A method has been developed for the evaluation of activation energy of thermoluminescence peak recorded with hyperbolic heating scheme by taking into account temperature dependent frequency factor. We have arrived at a number of expressions of activation energy involving the peak temperature and/or temperatures corresponding to the two points of inflection of the peak. It has been observed that the temperature dependence of frequency factor might lead to an error of the order of 10% in the determination of activation energy.