Aranya B. Bhattacherjee

Achieving the quantum ground state of a mechanical oscillator using a Bose–Einstein condensate with back-action and cold damping feedback schemes

We present a detailed study to show the possibility of approaching the quantum ground state of a hybrid optomechanical quantum device formed by a Bose–Einstein condensate (BEC) confined inside a high-finesse optical cavity with an oscillatory end mirror. Cooling is achieved using two experimentally realizable schemes: back-action cooling and cold damping quantum feedback cooling. In both the schemes, we found that increasing the two-body atom–atom interaction brings the mechanical oscillator to its quantum ground state. It has been observed that back-action cooling is more effective in the good cavity limit, while the cold damping cooling scheme is more relevant in the bad cavity limit. It is also shown that in the cold damping scheme, the device is more efficient in the presence of a BEC than in the absence of a BEC.

Dynamical Casimir effect in superradiant light scattering by Bose?Einstein condensate in an optomechanical cavity

We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose–Einstein condensate in an optomechanical cavity.The system is studied using both classical and quantized mirror motions.The cavity frequency is harmonically modulated in time for both the cases.The main quantity of interest is the number of intracavity scattered photons.The system has been investigated under the weak and strong modulations.It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion.Also,initially,the amplitude of scattered photons is high for lower modulation amplitude than higher modulation amplitude.We also found that the behavior of the plots are similar under strong and weak modulations for the quantized mirror motion.

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.

Quantum dynamics of two-optical modes and a single mechanical mode optomechanical system: Selective energy exchange

Abstract We study the quantum dynamics of an optomechanical setup comprising two optical modes and one mechanical mode. We show that the same system can undergo a dynamical phase transition analogous to Dicke–Hepp–Lieb superradiant type phase transition. We found that the coupling between the momentum quadratures of the two optical fields gives rise to a new dynamical critical point. We show that selective energy exchange between any two modes is possible by coherent control of the coupling parameters. In addition we also demonstrate the occurrence of normal mode splitting (NMS) in the mechanical displacement spectrum.

Selective entanglement in a two-mode optomechanical system

We analyze an optomechanical system formed by a mechanical mode and the two optical modes of an optomechanical cavity for the realization of a strongly quantum correlated three-mode system. We show that the steady state of the system shows three possible bipartite continuous variable (CV) entanglements in an experimentally accessible parameter regime, which are robust against temperature. We further show that selective entanglement between the mechanical mode and any of the two optical modes is also possible by the proper choice of the system parameters. Such a two-mode optomechanical system can be used for the realization of CV quantum information interfaces and networks.

Measuring finite-range phase coherence in an optical lattice using Talbot interferometry

One of the important goals of present research is to control and manipulate coherence in a broad variety of systems, such as semiconductor spintronics, biological photosynthetic systems, superconducting qubits and complex atomic networks. Over the past decades, interferometry of atoms and molecules has proven to be a powerful tool to explore coherence. Here we demonstrate a near-field interferometer based on the Talbot effect, which allows us to measure finite-range phase coherence of ultracold atoms in an optical lattice. We apply this interferometer to study the build-up of phase coherence after a quantum quench of a Bose–Einstein condensate residing in a one-dimensional optical lattice. Our technique of measuring finite-range phase coherence is generic, easy to adopt and can be applied in practically all lattice experiments without further modifications.

Effect of optomechanical coupling on squeezed-spin states

We investigate the effect of optomechanical coupling on the squeezed-spin states for a Bose-Einstein Condensate embedded within the lossless optomechanical cavity for the three special cases of initial states of cavity field, namely, a coherent state, a squeezed vacuum state and a squeezed state. We show that the radiation pressure or pondermotive force acting on the cavity end mirror plays a significant role in producing the atomic-squeezed states by producing squeezed states of the cavity field which is then transferred to the condensate. We further show that the maximum spin-squeezing along the x-direction is obtained in the presence of optomechanical coupling for the initial cavity field prepared in the amplitude squeezed state, whereas, squeezing along the y-direction reaches a maximum value in the absence of optomechanical coupling for the initial coherent cavity field. We also study the additional effect of nonlinear atomic interaction on spin-squeezing.

Optomechanical Entanglement Between an Ion and an Optical Cavity Field

I study an optomechanical system in which the mechanical motion of a single trapped ion is coupled to a cavity field for the realization of a strongly quantum correlated two-mode system. I show that for large pump intensities the steady state photon number exhibits bistable behaviour. I further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the ion motion which indicates a coherent energy exchange. I also find that in the parameter regime where NMS exists, the steady state of the system shows continuous variable entanglement. Such a two-mode optomechanical system can be used for the realization of continuous variable quantum information interfaces and networks.

Influence of periodically modulated cavity field on the generation of atomic-squeezed states

We investigate the influence of periodically time-modulated cavity frequency on the generation of atomic squeezed states for a collection of N two-level atoms confined in a non-stationary cavity with a moving mirror. We show that the two-photon character of the field generated from the vacuum state of field plays a significant role in producing the atomic or spin squeezed states. We further show that the maximum amount of persistent atomic squeezing is obtained for the initial cavity field prepared in the vacuum state.

Non-equilibrium Dynamics of an Optomechanical Dicke Model

Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.