Photon-Assisted Quantum Phase Transitions in a Cavity Optomechanical System with Two Nonlinear Mechanical Modes
Deng-Kui Jiang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
College of Mathematics and Science, Hunan University of Arts and Science, Changde, 450002 China
Search for more papers by this authorRui Zhang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Search for more papers by this authorYing Liu
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Search for more papers by this authorCorresponding Author
Le-Man Kuang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Synergetic Innovation Academy for Quantum Science and Technology, Zhengzhou University of Light Industry, Zhengzhou, 450002 China
E-mail: [email protected]
Search for more papers by this authorDeng-Kui Jiang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
College of Mathematics and Science, Hunan University of Arts and Science, Changde, 450002 China
Search for more papers by this authorRui Zhang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Search for more papers by this authorYing Liu
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Search for more papers by this authorCorresponding Author
Le-Man Kuang
Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University, Changsha, 410081 China
Synergetic Innovation Academy for Quantum Science and Technology, Zhengzhou University of Light Industry, Zhengzhou, 450002 China
E-mail: [email protected]
Search for more papers by this authorAbstract
Photon-assisted quantum phase transitions (QPTs) are studied in a cavity optomechanical system that consists of one optical cavity and two nonlinear mechanical resonators and explore ground-state properties of quantum phases. It is indicated that the cavity mode can induce effective two-phonon tunneling interaction between two mechanical resonators. It is found that QPTs between the localization phase (LP) and delocalization phase (DP) of phonons can happen through tuning the phonon tunneling interaction. It is shown that the photon-assisted QPT is the second order QPT. Ground-state properties of the quantum phases are also investigated. It is indicated that the ground state of the LP is a separable squeezed state while the ground state of the DP is an entangled state. The results open a new way to engineer quantum phases and QPTs in macroscopic mechanical systems and can benefit a wide range of criticality-enhanced quantum sensing applications.
Conflict of Interest
The authors declare no conflict of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
- 1S. Sachdev, Quantum phase transitions, 2nd ed., Cambridge University Press, Cambridge, England 2011.
10.1017/CBO9780511973765 Google Scholar
- 2S. L. Sondhi, S. M. Girvin, J. P. Carini, D. Shahar, Rev. Mod. Phys. 1997, 69, 315.
- 3M. Vojta, Rep. Prog. Phys. 2003, 66, 2069.
- 4D. V. Shopova, D. I. Uzunov, Phys. Rep. 2003, 379, 1.
- 5A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 2002, 416, 608.
- 6C. Emary, T. Brandes, Phys. Rev. Lett. 2003, 90, 044101.
- 7N. Lambert, C. Emary, T. Brandes, Phys. Rev. Lett. 2004, 92, 073602.
- 8J. Ma, X. Wang, Phys. Rev. A 2009, 80, 012318.
- 9Q. Ai, T. Shi, G. Long, C. P. Sun, Phys. Rev. A 2008, 78, 022327.
10.1103/PhysRevA.78.022327 Google Scholar
- 10T. L. Wang, L. N. Wu, W. Yang, G. R. Jin, N. Lambert, F. Nori, New J. Phys. 2014, 16, 063039.
- 11X. Y. Lü, G. L. Zhu, L. L. Zheng, Y. Wu, Phys. Rev. A 2018, 97, 033807.
- 12J. F. Huang, Y. Li, J. Q. Liao, L. M. Kuang, C. P. Sun, Phys. Rev. A 2009, 80, 063829.
10.1103/PhysRevA.80.063829 Google Scholar
- 13J. B. Yuan, L. M. Kuang, Phys. Rev. A 2013, 87, 024101.
10.1103/PhysRevA.87.024101 Google Scholar
- 14W. J. Lu, Z. Li, L. M. Kuang, Chin. Phys. Lett. 2018, 35, 116401.
- 15J. B. Yuan, W. J. Lu, Y. J. Song, L. M. Kuang, Sci. Rep. 2017, 7, 7404.
- 16P. Zanardi, M. G. A. Paris, L. Campos Venuti, Phys. Rev. A 2008, 78, 042105.
10.1103/PhysRevA.78.042105 Google Scholar
- 17M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, J. Zakrzewski, Phys. Rev. X 2018, 8, 021022.
- 18S. Fernández-Lorenzo, D. Porras, Phys. Rev. A 2017, 96, 013817.
- 19T. L. Heugel, M. Biondi, O. Zilberberg, R. Chitra, Phys. Rev. Lett. 2019, 123, 173601.
- 20L. Garbe, M. Bina, A. Keller, M. G. A. Paris, S. Felicetti, Phys. Rev. Lett. 2020, 124, 120504.
- 21R. D. Candia, F. Minganti, K. V. Petrovnin, G. S. Paraoanu, S. Felicetti, npj Quantum Inf. 2023, 9, 23.
10.1038/s41534-023-00690-z Google Scholar
- 22K. Gietka, F. Metz, T. Keller, J. Li, Quantum 2021, 5, 489.
- 23Y. Chu, S. Zhang, B. Yu, J. Cai, Phys. Rev. Lett. 2021, 126, 010502.
- 24M. Salado-Mejía, R. Román-Ancheyta, F. Soto-Eguibar, H. M. Moya-Cessa, Quantum Sci. Technol. 2021, 6, 025010.
10.1088/2058-9565/abdca5 Google Scholar
- 25W. Wu, C. Shi, Phys. Rev. A 2021, 104, 022612.
- 26J. Zhang, Y. L. Zhou, Y. Zuo, H. Zhang, P. X. Chen, H. Jing, L. M. Kuang, Adv. Quantum Technol. 2024, 2300350.
10.1002/qute.202300350 Google Scholar
- 27L. Zhou, J. Kong, Z. H. Lan, W. P. Zhang, Phys. Rev. Research 2023, 5, 013087.
- 28R. Salvia, M. Mehboudi, M. Perarnau-Llobet, Phys. Rev. Lett. 2023, 130, 240803.
- 29G. Di Fresco, B. Spagnolo, D. Valenti, A. Carollo, Sci. Post. Phys. 2022, 13, 077.
10.21468/SciPostPhys.13.4.077 Google Scholar
- 30K. Gietka, L. Ruks, T. Busch, Quantum 2022, 6, 700.
10.22331/q-2022-04-27-700 Google Scholar
- 31T. Ilias, D. Yang, S. F. Huelga, M. B. Plenio, PRX Quantum 2022, 3, 010354.
- 32W. T. He, C. W. Lu, Y. X. Yao, H. Y. Zhu, Q. Ai, Front. Phys. 2023, 18, 31304.
10.1007/s11467-023-1278-2 Google Scholar
- 33L. Garbe, O. Abah, S. Felicetti, R. Puebla, Quantum Sci. Technol. 2022, 7, 035010.
- 34W. P. Bowen, G. J. Milburn, Quantum Optomechanics, CRC Press, New York 2016
- 35M. Aspelmeyer, T. J. Kippenberg, F. Marquardt, Rev. Mod. Phys. 2014, 86, 1391.
- 36G. Huang, A. Beccari, N. J. Engelsen, T. J. Kippenberg, Nature 2024, 626, 512.
- 37Y. F. Jiao, S. D. Zhang, Y. L. Zhang, A. Miranowicz, L. M. Kuang, H. Jing, Phys. Rev. Lett. 2020, 125, 143605.
- 38Y. F. Jiao, J. X. Liu, Y. Li, R. Yang, L. M. Kuang, H. Jing, H. Jing, Phys. Rev. Applied 2022, 18, 064008.
- 39Y. Wang, H. L. Zhang, J. L. Wu, J. Song, K. Yang, W. Qin, H. Jing, L. M. Kuang, Sci. China-Phys. Mech. Astron. 2023, 66, 110311.
- 40X. Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, F. Nori, Phys. Rev. Lett. 2015, 114, 093602.
- 41X. W. Xu, J. Q. Liao, H. Jing, L. M. Kuang, Sci. China-Phys. Mech. Astron. 2023, 66, 100312.
10.1007/s11433-023-2187-7 Google Scholar
- 42T. X. Lu, Y. Wang, K. Xia, X. Xiao, L. M. Kuang, H. Jing, H. Jing, Sci. China-Phys. Mech. Astron. 2024, 67, 1.
10.1007/s11425-022-2085-3 Google Scholar
- 43N. Hu, Z. X. Tang, X. W. Xu, Phys. Rev. A 2023, 108, 063516.
- 44X. Tang, X. W. Xu, New J. Phys. 2023, 25, 123028.
- 45J. Huang, D.-G. Lai, C. Liu, J. F. Huang, F. Nori, J. Q. Liao, Phys. Rev. A 2022, 106, 013526.
- 46J. Huang, D. G. Lai, J. Q. Liao, Phys. Rev. A 2022, 106, 063506.
- 47J. Huang, D. G. Lai, J. Q. Liao, Phys. Rev. A 2023, 108, 013516.
- 48L. Y. Zhu, Y. Dong, J. Zhang, C. L. Zhai, Y. Zhai, L. M. Kuang, Quantum Inf. Process. 2021, 20, 1.
10.1007/s11128-020-02935-8 Google Scholar
- 49Y. Li, Y. F. Jiao, J. X. Liu, A. Miranowicz, Y. L. Zuo, L. M. Kuang, H. Jing, Nanophotonics 2021, 11, 67.
10.1515/nanoph-2021-0485 Google Scholar
- 50Y. H. Liu, X. L. Yin, J. F. Huang, J. Q. Liao, Phys. Rev. A 2022, 105, 023504.
- 51X. L. Yin, Y. H. Zhou, J. Q. Liao, Phys. Rev. A 2022, 105, 013504.
- 52J. Liu, Y. H. Zhou, J. Huang, J. F. Huang, J. Q. Liao, Phys. Rev. A 2021, 104, 053715.
- 53C. L. Zhai, W. Lu, Y. F. Jiao, L. M. Kuang, Ann. Phys. (Berlin) 2024, 2300465.
10.1002/andp.202300465 Google Scholar
- 54B. B. Li, L. Ou, Y. Lei, Y. C. Liu, Nanophotonics 2021, 10, 2799.
- 55D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. Aspelmeyer, Phys. Rev. Lett. 2007, 98, 030405.
- 56T. A. Palomaki, J. D. Teufel, R. W. Simmonds, K. W. Lehnert, Science 2013, 342, 710.
- 57R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, S. Gröblacher, Nature 2016, 530, 313.
- 58I. Marinković, A. Wallucks, R. Riedinger, S. Hong, M. Aspelmeyer, S. Gröblacher, Phys. Rev. Lett. 2018, 121, 220404.
- 59R. Ghobadi, S. Kumar, B. Pepper, D. Bouwmeester, A. I. Lvovsky, C. Simon, Phys. Rev. Lett. 2014, 112, 080503.
- 60D. G. Lai, Y. H. Chen, W. Qin, A. Miranowicz, F. Nori, Phys. Rev. Reserch 2022, 4, 033112.
- 61S. Mancini, V. Giovannetti, D. Vitali, P. Tombesi, Phys. Rev. Lett. 2002, 88, 120401.
- 62S. Mancini, D. Vitali, V. Giovannetti, P. Tombesi, Eur. Phys. J. D 2003, 22, 417.
- 63S. Huang, G. S. Agarwal, New J. Phys. 2009, 11, 103044.
- 64H. Tan, L. F. Buchmann, H. Seok, G. Li, Phys. Rev. A 2013, 87, 022318.
- 65C. Genes, D. Vitali, P. Tombesi, New J. Phys. 2008, 10, 095009.
- 66J. Q. Liao, Q. Q. Wu, F. Nori, Phys. Rev. A 2014, 89, 014302.
- 67C. J. Yang, J. H. An, W. Yang, Y. Li, Phys. Rev. A 2015, 92, 062311.
- 68J. Li, I. M. Haghighi, N. Malossi, S. Zippilli, D. Vitali, New J. Phys. 2015, 17, 103037.
- 69D. G. Lai, J. Q. Liao, A. Miranowicz, F. Nori, Phys. Rev. Lett. 2022, 129, 063602.
- 70R. Y. Teh, L. Rosales-Zarate, P. D. Drummond, M. D. Reid, Prog. Quantum Electron. 2023, 90, 100396.
10.1016/j.pquantelec.2022.100396 Google Scholar
- 71R. Peng, C. Zhao, Z. Yang, J. Yang, L. Zhou, Phys. Rev. A 2023, 107, 013507.
- 72X. W. Xu, Y. J. Zhao, Y. X. Liu, Phys. Rev. A 2013, 88, 022325.
- 73R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, S. Gröblacher, Nature 2018, 556, 473.
- 74S. Kotler, G. A. Peterson, E. Shojaee, F. Lecocq, K. Cicak, A. Kwiatkowski, S. Geller, S. Glancy, E. Knill, R. W. Simmonds, J. Aumentado, J. D. Teufel, Science 2021, 372, 622.
- 75C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, M. A. Sillanpää, Nature 2018, 556, 478.
- 76L. Mercier de Lépinay, C. F. Ockeloen-Korppi, M. J. Woolley, M. A. Sillanpää, Science 2021, 372, 625.
- 77B. Wang, F. Nori, Z. L. Xiang, Phys. Rev. Lett. 2024, 132, 053601.
- 78J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, J. G. E. Harris, Nature 2008, 452, 72.
- 79X. W. Xu, A. X. Chen, Y. X. Liu, Phys. Rev. A 2017, 96, 023832.
- 80M. J. Hwang, R. Puebla, M. B. Plenio, Phys. Rev. Lett. 2015, 115, 180404.
- 81M. J. Hwang, M. B. Plenio, Phys. Rev. Lett. 2016, 117, 123602.
- 82M. J. Hwang, M. B. Plenio, Phys. Rev. Lett. 2017, 118, 073001.
- 83M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, L.-M. Duan, Nat. Commun. 2021, 12, 1126.
- 84X. Chen, Z. Wu, M. Jiang, X. Y. Lu, X. Peng, J. Du, Nat. Commun. 2021, 12, 6281.
- 85C. Liu, J.-F. Huang, Sci. China-Phys. Mech. Astron. 2024, 67, 210311.
10.1007/s11433-023-2243-7 Google Scholar
- 86X. Zhu, J.-H. Lü, W. Ning, F. Wu, L.-T. Shen, Z.-B. Yang, S.-B. Zheng, Sci. China-Phys. Mech. Astron. 2023, 66, 250313.
10.1007/s11433-022-2073-9 Google Scholar
- 87J. Liu, M. Zhao, Y. T. Yang, H. G. Luo, Phys. Rev. A 2024, 109, 023721.
- 88Y. Q. Lu, Y. Y. Zhang, New J. Phys. 2024, 26, 063010.
10.1088/1367-2630/ad503c Google Scholar
- 89C. Leroux, L. C. G. Govia, A. A. Clerk, Phys. Rev. A 2017, 96, 043834.
10.1103/PhysRevA.96.043834 Google Scholar
- 90X.-Y. Chen, Y.-Y. Zhang, L. Fu, H. Zheng, Phys. Rev. A 2020, 101, 033827.
- 91V. Giovannetti, S. Lloyd, L. Maccone, Nat. Photon. 2021, 5, 222.
10.1038/nphoton.2011.35 Google Scholar
- 92V. Giovannetti, S. Lloyd, L. Maccone, Science 2004, 306, 1330.
- 93X. T. Chen, R. Zhang, W. J. Lu, Y. Zuo, Y. F. Jiao, L. M. Kuang, Phys. Rev. A 2024, 109, 042609.
- 94Z. Li, M. Xu, R. A. Norte, A. M. Aragn, P. G. Steeneken, F. Alijani, Commun. Phys. 2024, 7, 53.
- 95N. E. Flowers-Jacobs, S. W. Hoch, J. C. Sankey, A. Kashkanova, A. M. Jayich, C. Deutsch, J. Reichel, J. G. E. Harris, Appl. Phys. Lett. 2012, 101, 221109.
