Abstract
The optomechanics shows a great potential in quantum control and precise measurement due to appropriate mechanical control. Here we theoretically study the quantum phase transition in a hybrid atom-optomechanical cavity with an external force. Our study shows, in the thermodynamic limit, the critical value of quantum phase transition between the normal phase and super-radiant phase can be controlled and modified by the external force via the tunable frequency of optomechanics, then a force dependent quantum phase transition can be achieved in our system. Moreover, this force dependent quantum phase transition can be employed to detect the external force variation. In addition, our numerical simulations illustrate the sensitivity of the external force measurement can be improved by the squeezing properties of the quantum phase transition.
Highlights
Transition in the HybridOptomechanical cavity works as an ideal platform to study the quantum properties of macroscopic mechanical systems
The critical value of the quantum phase transition (QPT) between the normal phase and the super-radiant phase can be shifted by adjusting the external force, which can modify the frequency of the optomechanical cavity via its effective length
As the critical value for Dicke Hamiltonian is determined by the frequencies of single mode cavity field and atomic ensemble [58], the tunable effective frequency of the optomechanicial cavity (5) reminds us that it is possible to modify the critical value with the external force, and achieve a force dependent QPT between normal phase and superradiant phase
Summary
Optomechanical cavity works as an ideal platform to study the quantum properties of macroscopic mechanical systems. With the increase of the atom-cavity coupling, the Dicke model undergoes a quantum phase transition (QPT) from the normal phase to the super-radiant one [27,28]. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations In this scheme, we illustrate it is possible to control the critical value of QPT in a hybrid atom-optomechanical system via an external force. The critical value of the QPT between the normal phase and the super-radiant phase can be shifted by adjusting the external force, which can modify the frequency of the optomechanical cavity via its effective length. Our work focuses on the tunability of critical value of the QPT from normal phase to super-radiant phase without dissipations, and squeezing properties are considered to realize the precision measurement. The squeezing properties in super-radiant phase ensures the force measurement in the hybrid atom-optomechanical system is out of reach for the traditional optomechanics without squeezing properties [10,23,24], and paves a way to enhance the sensitivity with the squeezing properties of QPT
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