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.
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.
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.
Cavity optomechanics originated from the research of interferometric detection of gravitational waves, and later became a fast-growing area of techniques and approaches ranging from the fields of atomic, molecular, and optical physics to nano-science and condensed matter physics as well. Recently, it focused on the exploration of operating mechanical oscillators deep in the quantum regime, with an interest ranging from quantum-classical interface tests to high-precision quantum metrology. In this paper, recent theoretical work of our group in the field of quantum measurement with cavity optomechanical systems is reviewed. We explore the quantum measurement theory and its applications with several unconventional cavity optomechanical schemes working in the quantum regime. This review covers the basics of quantum noises in the cavity optomechanical setups and the resulting standard quantum limit of precision displacement and force measurement. Three novel quantum measurement proposals based on the hybrid optomechanical system are introduced. First, we describe a quantum back-action insulated weak force sensor. It is realized by forming a quantum-mechanics-free subsystem with two optomechanical oscillators of reversed effective mass. Then we introduce a role-reversed atomic optomechanical system which enables the preparation and the quantum tomography of a variety of non-classical states of atoms. In this system, the cavity field acts as a mechanical oscillator driven by the radiation pressure force from an ultracold atomic field. In the end, we recommend a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain. These proposals demonstrate the possible applications of optomechanical devices in understanding of quantum-classical crossover and in achieving quantum measurement limit.
The A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2 term. The system consists of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2 term that effectively counteracts or even fully eliminates the original A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching but are coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2 term.
A2-robust superradiant phase transition in hybrid qubit-cavity optomechanics
The A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2 term. The system consist of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2 term that effectively counteracts or even fully eliminates the original A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching, but coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2 term.
In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics. In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.
The precision of quantum sensing could be improved by exploiting quantum phase transitions, where the physical quantity tends to diverge when the system approaches the quantum critical point. This critical enhancement phenomenon has been applied to the quantum Rabi model, showing a promising sensing enhancement without the need for complex initial state preparation. In this work, we present a quantum phase transition in the coupling cavity-mechanical oscillator system when the coupling strength crosses a critical point, determined by the effective detuning of the cavity and frequency of the mechanical mode. By utilizing this critical phenomenon, we obtain a prominent enhancement of quantum sensing, such as the position and momentum of the mechanical oscillator. This result provides an alternative method to enhance the quantum sensing of some physical quantities, such as mass, charge, and weak force, in a large mass system.