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Hou J, Zhu J, Ma R, Xue B, Zhu Y, Lin J, Jiang X, Zheng Y, Chen X, Cheng Y, Ge L, Wan W. Enhanced Frequency Conversion in Parity-Time Symmetry Line. PHYSICAL REVIEW LETTERS 2024; 132:256902. [PMID: 38996261 DOI: 10.1103/physrevlett.132.256902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Accepted: 05/09/2024] [Indexed: 07/14/2024]
Abstract
Non-Hermitian degeneracies reveal intriguing and nontrivial behaviors in open physical systems. Examples like parity-time (PT) symmetry breaking, topological encircling chirality, and enhanced sensing near an exceptional point (EP) are often associated with the abrupt nature of the phase transition around these degeneracies. Here we experimentally observe a cavity-enhanced second-harmonic frequency (SHG) conversion on a PT symmetry line, i.e., a set consisting of open-ended isofrequency or isoloss lines, both terminated at EPs on the Riemann surface in parameter space. The enhancement factor can reach as high as 300, depending on the crossing point whether in the symmetry or the broken phase of the PT line. Moreover, such enhancement of SHG enables sensitive distance sensing with a nanometer resolution. Our works may pave the way for practical applications in sensing, frequency conversion, and coherent wave control.
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Affiliation(s)
- Jiankun Hou
- State Key Laboratory of Advanced Optical Communication Systems and Networks, University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | | | - Ruixin Ma
- State Key Laboratory of Advanced Optical Communication Systems and Networks, University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Boyi Xue
- State Key Laboratory of Advanced Optical Communication Systems and Networks, University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yicheng Zhu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | | | - Xiaoshun Jiang
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Science and School of Physics, Nanjing University, Nanjing 210093, China
| | | | | | - Ya Cheng
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Science and School of Physics, Nanjing University, Nanjing 210093, China
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Zou F, Du L, Li Y, Dong H. Amplifying Frequency Up-Converted Infrared Signals with a Molecular Optomechanical Cavity. PHYSICAL REVIEW LETTERS 2024; 132:153602. [PMID: 38682999 DOI: 10.1103/physrevlett.132.153602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Revised: 01/17/2024] [Accepted: 03/19/2024] [Indexed: 05/01/2024]
Abstract
Frequency up-conversion, enabled by molecular optomechanical coupling, has recently emerged as a promising approach for converting infrared signals into the visible range through quantum coherent conversion of signals. However, detecting these converted signals poses a significant challenge due to their inherently weak signal intensity. In this work, we propose an amplification mechanism capable of enhancing the signal intensity by a factor of 1000 or more for the frequency up-converted infrared signal in a molecular optomechanical system. The mechanism takes advantage of the strong coupling enhancement with molecular collective mode and the Stokes sideband pump. This work demonstrates a feasible approach for up-converting infrared signals to the visible range.
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Affiliation(s)
- Fen Zou
- Center for Theoretical Physics & School of Physics and Optoelectronic Engineering, Hainan University, Haikou 570228, China
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Lei Du
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
| | - Yong Li
- Center for Theoretical Physics & School of Physics and Optoelectronic Engineering, Hainan University, Haikou 570228, China
| | - Hui Dong
- Graduate School of China Academy of Engineering Physics, Beijing 100193, China
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3
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Zhou YR, Zhang QF, Liu FF, Han YH, Gao YP, Fan L, Zhang R, Cao C. Controllable nonreciprocal phonon laser in a hybrid photonic molecule based on directional quantum squeezing. OPTICS EXPRESS 2024; 32:2786-2803. [PMID: 38297799 DOI: 10.1364/oe.512280] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 01/01/2024] [Indexed: 02/02/2024]
Abstract
Here, a scheme for a controllable nonreciprocal phonon laser is proposed in a hybrid photonic molecule system consisting of a whispering-gallery mode (WGM) optomechanical resonator and a χ(2)-nonlinear WGM resonator, by directionally quantum squeezing one of two coupled resonator modes. The directional quantum squeezing results in a chiral photon interaction between the resonators and a frequency shift of the squeezed resonator mode with respect to the unsqueezed bare mode. We show that the directional quantum squeezing can modify the effective optomechanical coupling in the optomechanical resonator, and analyze the impacts of driving direction and squeezing extent on the phonon laser action in detail. Our analytical and numerical results indicate that the controllable nonreciprocal phonon laser action can be effectively realized in this system. The proposed scheme uses an all-optical and chip-compatible approach without spinning resonators, which may be more beneficial for integrating and packaging of the system on a chip. Our proposal may provide a new route to realize integratable phonon devices for on-chip nonreciprocal phonon manipulations, which may be used in chiral quantum acoustics, topological phononics, and acoustical information processing.
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Yang J, Lu TX, Peng M, Liu J, Jiao YF, Jing H. Multi-field-driven optomechanical entanglement. OPTICS EXPRESS 2024; 32:785-794. [PMID: 38175098 DOI: 10.1364/oe.509811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 12/08/2023] [Indexed: 01/05/2024]
Abstract
Cavity optomechanical (COM) entanglement, playing an essential role in building quantum networks and enhancing quantum sensors, is usually weak and easily destroyed by noises. As feasible and effective ways to overcome this obstacle, optical or mechanical parametric modulations have been used to improve the quality of quantum squeezing or entanglement in various COM systems. However, the possibility of combining these powerful means to enhance COM entanglement has yet to be explored. Here, we fill this gap by studying a COM system containing an intra-cavity optical parametric amplifier (OPA), driven optically and mechanically. By tuning the relative strength and the frequency mismatch of optical and mechanical driving fields, we find that constructive interference can emerge and significantly improve the strength of COM entanglement and its robustness to thermal noises. This work sheds what we believe to be a new light on preparing and protecting quantum states with multi-field driven COM systems for diverse applications.
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Liao Q, Ao J, Song M, Qiu H. Generation and enhancement of the sum sideband under double radiation pressure. OPTICS EXPRESS 2023; 31:27508-27519. [PMID: 37710824 DOI: 10.1364/oe.494310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 07/24/2023] [Indexed: 09/16/2023]
Abstract
A theoretical scheme to enhance the sum sideband generation (SSG) via double radiation pressure is proposed. In this scheme, both sides of the double-cavity system are driven by red and blue detuned pump lasers and frequency components are generated at the sum sideband through optomechanical nonlinear interaction. The results show that the efficiency of SSG can be improved with orders of magnitude. We further investigate the properties of SSG in resolved and unresolved sideband regimes. The efficiencies of upper sum sideband generation (USSG) and lower sum sideband generation (LSSG) are the equivalent in the unresolved sideband regime when the threshold condition is satisfied. It is worth noting that with the increase of the ratio between the dissipation rate of the cavity field and the decay rate of the mechanical resonator (MR), the amplitude of the LSSG can be superior to that of the USSG. Our scheme may provide a potential application in realizing the measurement of high-precision weak forces and quantum-sensitive sensing.
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Zhang X, Liu Q, Zhang Q, Li Z, Ma Y, Gong Q, Gu Y. Loss-induced Purcell enhancement in PT-broken whispering gallery microcavities. OPTICS LETTERS 2023; 48:4069-4072. [PMID: 37527120 DOI: 10.1364/ol.496276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 06/25/2023] [Indexed: 08/03/2023]
Abstract
Parity-time (PT)-symmetry brings various opportunities for electromagnetic field manipulation and light-matter interaction, such as modification of spontaneous emission. However, previous works mainly focused on the behavior of spontaneous emission at exceptional points or in the PT-symmetry situation. Here, we theoretically demonstrate loss-induced Purcell enhancement in PT-broken whispering gallery microcavities. In the PT-broken phase, one of the supermodes decays slowly thereby playing a leading role in spontaneous emission. As the loss increases, the quality factor of this supermode is higher and the mode volume is smaller, so that the Purcell factors will be larger if the emitter is placed near the lossless cavity. Our findings indicate that loss can enhance the interaction between light and matter, which could be applied to single photon emission, non-Hermitian photonic devices, etc.
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Han Y, Meng C, Pan H, Qian J, Rao Z, Zhu L, Gui Y, Hu CM, An Z. Bound chiral magnonic polariton states for ideal microwave isolation. SCIENCE ADVANCES 2023; 9:eadg4730. [PMID: 37418518 DOI: 10.1126/sciadv.adg4730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Accepted: 06/05/2023] [Indexed: 07/09/2023]
Abstract
Bound states in the continuum (BICs) present a unique solution for eliminating radiation loss. So far, most reported BICs are observed in transmission spectra, with only a few exceptions being in reflection spectra. The correlation between reflection BICs (r-BICs) and transmission BICs (t-BICs) remains unclear. Here, we report the presence of both r-BICs and t-BICs in a three-mode cavity magnonics. We develop a generalized framework of non-Hermitian scattering Hamiltonians to explain the observed bidirectional r-BICs and unidirectional t-BICs. In addition, we find the emergence of an ideal isolation point in the complex frequency plane, where the isolation direction can be switched by fine frequency detuning, thanks to chiral symmetry protection. Our results demonstrate the potential of cavity magnonics and also extend the conventional BICs theory through the application of a more generalized effective Hamiltonians theory. This work offers an alternative idea for designing functional devices in general wave optics.
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Affiliation(s)
- Youcai Han
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Changhao Meng
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Hong Pan
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Jie Qian
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Zejin Rao
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Liping Zhu
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
| | - Yongsheng Gui
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - Can-Ming Hu
- Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
| | - Zhenghua An
- State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, Shanghai, 200232, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai 201210, China
- Yiwu Research Institute of Fudan University, Chengbei Road, Yiwu City, 322000 Zhejiang, China
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Li Z, Li C, Xu G, Chen W, Xiong Z, Jing H, Ho JS, Qiu CW. Synergetic positivity of loss and noise in nonlinear non-Hermitian resonators. SCIENCE ADVANCES 2023; 9:eadi0562. [PMID: 37406112 DOI: 10.1126/sciadv.adi0562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 06/01/2023] [Indexed: 07/07/2023]
Abstract
Loss and noise are usually undesirable in electronics and optics, which are generally mitigated by separate ways in the cost of bulkiness and complexity. Recent studies of non-Hermitian systems have shown a positive role of loss in various loss-induced counterintuitive phenomena, while noise still remains a fundamental challenge in non-Hermitian systems particularly for sensing and lasing. Here, we simultaneously reverse the detrimental loss and noise and reveal their coordinated positive role in nonlinear non-Hermitian resonators. This synergetic effect leads to the amplified spectrum intensity with suppressed spectrum fluctuations after adding both loss and noise. We reveal the underlying mechanism of nonlinearity-induced bistability engineered by loss in the non-Hermitian resonators and noise-loss enhanced coherence of eigenfrequency hopping driven by temporal modulation of detuning. Our findings enrich counterintuitive non-Hermitian physics and lead to a general recipe to overcome loss and noise from electronics to photonics with applications from sensing to communication.
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Affiliation(s)
- Zhipeng Li
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Chenhui Li
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Guoqiang Xu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Weijin Chen
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Ze Xiong
- Wireless and Smart Bioelectronics Lab, School of Biomedical Engineering, ShanghaiTech University, Shanghai 201210, China
| | - Hui Jing
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - John S Ho
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
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Li T, Gao Z, Xia K. Nonlinear-dissipation-induced nonreciprocal exceptional points. OPTICS EXPRESS 2021; 29:17613-17627. [PMID: 34154301 DOI: 10.1364/oe.426474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 05/16/2021] [Indexed: 06/13/2023]
Abstract
Exceptional points (EPs) have revealed a lot of fundamental physics and promise many important applications. The effect of system nonlinearity on the property of EPs is yet to be well studied. Here, we propose an optical system with nonlinear dissipation to achieve a nonreciprocal EP. Our system consists of a linear whispering-gallery-mode microresonator (WGMR) coupling to a WGMR with nonlinear dissipation. In our system, the condition of EP appearance is dependent on the field intensity in the nonlinear WGMR. Due to the chirality of intracavity field intensity, the EPs and the transmission of the system can be nonreciprocal. Our work may pave the way to exploit nonreciprocal EP for optical information processing.
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Gupta SK, Zou Y, Zhu XY, Lu MH, Zhang LJ, Liu XP, Chen YF. Parity-Time Symmetry in Non-Hermitian Complex Optical Media. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1903639. [PMID: 31830340 DOI: 10.1002/adma.201903639] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2019] [Revised: 09/25/2019] [Indexed: 06/10/2023]
Abstract
The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.
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Affiliation(s)
- Samit Kumar Gupta
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Yi Zou
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Xue-Yi Zhu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Ming-Hui Lu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Li-Jian Zhang
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Xiao-Ping Liu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Yan-Feng Chen
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
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Du L, Chen YT, Wu JH, Li Y. Nonreciprocal interference and coherent photon routing in a three-port optomechanical system. OPTICS EXPRESS 2020; 28:3647-3659. [PMID: 32122029 DOI: 10.1364/oe.379990] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Accepted: 01/17/2020] [Indexed: 06/10/2023]
Abstract
We study the interference between different weak signals in a three-port optomechanical system, which is achieved by coupling three cavity modes to the same mechanical mode. If one cavity serves as a control port and is perturbed continuously by a control signal, nonreciprocal interference can be observed when another signal is injected upon different target ports. In particular, we exhibit frequency-independent perfect blockade induced by the completely destructive interference over the full frequency domain. Moreover, coherent photon routing can be realized by perturbing all ports simultaneously, with which the synthetic signal only outputs from the desired port. We also reveal that the routing scheme can be extended to more-port optomechanical systems. The results in this paper may have potential applications for controlling light transport and quantum information processing.
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Qin GQ, Yang H, Mao X, Wen JW, Wang M, Ruan D, Long GL. Manipulation of optomechanically induced transparency and absorption by indirectly coupling to an auxiliary cavity mode. OPTICS EXPRESS 2020; 28:580-592. [PMID: 32118983 DOI: 10.1364/oe.381760] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 12/09/2019] [Indexed: 06/10/2023]
Abstract
We theoretically study the optomechanically induced transparency (OMIT) and absorption (OMIA) phenomena in a single microcavity optomechanical system, assisted by an indirectly coupled auxiliary cavity mode. We show that the interference effect between the two optical modes plays an important role and can be used to control the multiple-pathway induced destructive or constructive interference effect. The three-pathway interference could induce an absorption dip within the transparent window in the red sideband driving regime, while we can switch back and forth between OMIT and OMIA with the four-pathway interference. The conversion between the transparency peak and absorption dip can be achieved by tuning the relative amplitude and phase of the multiple light paths interference. Our system proposes a new platform to realize multiple pathways induced transparency and absorption in a single microcavity and a feasible way for realizing all-optical information processing.
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Jiang C, Cui Y, Zhai Z, Yu H, Li X, Chen G. Phase-controlled amplification and slow light in a hybrid optomechanical system. OPTICS EXPRESS 2019; 27:30473-30485. [PMID: 31684295 DOI: 10.1364/oe.27.030473] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 09/19/2019] [Indexed: 06/10/2023]
Abstract
We theoretically investigate the transmission and group delay of a probe field incident on a hybrid optomechanical system, which consists of a mechanical resonator simultaneously coupled to an optical cavity and a two-level system (qubit). The cavity field is driven by a strong red-detuned control field, and a weak coherent mechanical driving field is applied to the mechanical resonator. With the assistance of additional mechanical driving field, it is shown that double optomechanically induced transparency can be switched into absorption due to destructive interference or amplification because of constructive interference, which depends on the phase difference of the applied fields. We study in detail how to control the probe transmission by tuning the parameters of the optical and mechanical driving fields. Furthermore, we find that the group delay of the transmitted probe field can be prolonged by the tuning the amplitude and phase of the mechanical driving field.
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Wang XY, Si LG, Lu XH, Wu Y. Generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions. OPTICS EXPRESS 2019; 27:29297-29308. [PMID: 31684666 DOI: 10.1364/oe.27.029297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 09/13/2019] [Indexed: 06/10/2023]
Abstract
We investigate theoretically the generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions. It is shown that the generation of frequency components at the sum sideband stems from the nonlinear optomechanical interactions via two-phonon processes in the quadratically coupled optomechanical system, while an optical parametric amplifier (OPA) inside the system can considerably improve the sum sideband generation (SSG). The dependence of SSG on the system parameters, including the power of the control field, the frequency detuning of the probe fields and the nonlinear gain of OPA are analyzed in detail. Our analytic calculation indicates that the SSG can be obtained even under weak driven fields and greatly enhanced via meeting the matching conditions. The effect of SSG may have potential applications for achieving measurement of electric charge (or other weak forces) with higher precision and on-chip manipulation of light propagation.
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