Exploring entanglement dynamics in an optomechanical cavity with a type-\(V\) qutrit and quantized two-mode field. (English) Zbl 07820924
Summary: In this work, the main objective is to measure the degree of interaction of a type-\(V\) qutrit with a two-mode quantized field in an optomechanical cavity. To achieve this objective, we first deduce the Hamiltonian in the interaction picture to identify the oscillatory terms. Using the Coarse-Grained Method (CGM), we obtain the effective Hamiltonian analytically. By selecting initial conditions for the atom, the two-mode field, and the moving mirror, we can determine the state vector of the entire system through a first-order approximation of the effective Hamiltonian. With this information, we proceed to solve the Schrödinger equation, generating a coupled set of differential equations that is solved numerically based on the initial conditions. In this context, the atomic von Neumann entropy allows us to obtain the temporal evolution of the degree of entanglement of the qutrit in the cavity and the atomic population inversion. The results indicate that entanglement in this tripartite system, composed of the qutrit and the mirror-field subsystems, as well as the population inversion, can be manipulated by the initial state conditions of the system, the qutrit-field and mirror-field coupling coefficients, the pump field, and the dissipation rates of the two-mode field and the movable mirror, respectively.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
References:
| [1] | Tsukanov, Alexander V., Optomechanical systems and quantum computing. Russ. Microelectron., 333-342 (2011) |
| [2] | Aspelmeyer, Markus; Kippenberg, Tobias J.; Marquardt, Florian, Cavity optomechanics. Rev. Modern Phys., 4, 1391 (2014) |
| [3] | Kippenberg, Tobias J.; Vahala, Kerry J., Cavity optomechanics: Back-action at the mesoscale. Science, 5893, 1172-1176 (2008) |
| [4] | Favero, Ivan; Karrai, Khaled, Optomechanics of deformable optical cavities. Nat. Photonics, 4, 201-205 (2009) |
| [5] | Aspelmeyer, Markus; Gröblacher, Simon; Hammerer, Klemens; Kiesel, Nikolai, Quantum optomechanics throwing a glance. J. Opt. Soc. Amer. B, 6, A189-A197 (2010) |
| [6] | Kronwald, Andreas; Marquardt, Florian, Optomechanically induced transparency in the nonlinear quantum regime. Phys. Rev. Lett. (2013) |
| [7] | Sohail, Amjad; Zhang, Yang; Zhang, Jun; Yu, Chang-shui, Optomechanically induced transparency in multi-cavity optomechanical system with and without one two-level atom. Sci. Rep., 1, 28830 (2016) |
| [8] | Vitali, David; Gigan, Sylvain; Ferreira, Anderson; Böhm, HR; Tombesi, Paolo; Guerreiro, Ariel; Vedral, Vlatko; Zeilinger, Anton; Aspelmeyer, Markus, Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett., 3 (2007) |
| [9] | Jaynes, Edwin T.; Cummings, Frederick W., Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE, 1, 89-109 (1963) |
| [10] | Vaughan, M., The Fabry-Perot Interferometer: History, Theory, Practice and Applications (2017), Routledge |
| [11] | Metcalfe, Michael, Applications of cavity optomechanics. Appl. Phys. Rev., 3 (2014) |
| [12] | Xiong, Hao; Wu, Ying, Fundamentals and applications of optomechanically induced transparency. Appl. Phys. Rev., 3 (2018) |
| [13] | Xia, Ji; Qiao, Qifeng; Zhou, Guangcan; Chau, Fook Siong; Zhou, Guangya, Opto-mechanical photonic crystal cavities for sensing application. Appl. Sci., 20, 7080 (2020) |
| [14] | Barzanjeh, Shabir; Xuereb, André; Gröblacher, Simon; Paternostro, Mauro; Regal, Cindy A.; Weig, Eva M., Optomechanics for quantum technologies. Nat. Phys., 1, 15-24 (2022) |
| [15] | Lau, Hoi-Kwan; Clerk, Aashish A., Ground-state cooling and high-fidelity quantum transduction via parametrically driven bad-cavity optomechanics. Phys. Rev. Lett., 10 (2020) |
| [16] | Meenehan, Seán M.; Cohen, Justin D.; MacCabe, Gregory S.; Marsili, Francesco; Shaw, Matthew D.; Painter, Oskar, Pulsed excitation dynamics of an optomechanical crystal resonator near its quantum ground state of motion. Phys. Rev. X, 4 (2015) |
| [17] | Goss, Noah; Morvan, Alexis; Marinelli, Brian; Mitchell, Bradley K.; Nguyen, Long B.; Naik, Ravi K.; Chen, Larry; Jünger, Christian; Kreikebaum, John Mark; Santiago, David I., High-fidelity qutrit entangling gates for superconducting circuits. Nat. Commun., 1, 7481 (2022) |
| [18] | Roy, Tanay; Li, Ziqian; Kapit, Eliot; Schuster, David I., Realization of two-qutrit quantum algorithms on a programmable superconducting processor (2022), arXiv preprint arXiv:2211.06523 |
| [19] | Luo, Kai; Huang, Wenhui; Tao, Ziyu; Zhang, Libo; Zhou, Yuxuan; Chu, Ji; Liu, Wuxin; Wang, Biying; Cui, Jiangyu; Liu, Song, Experimental realization of two qutrits gate with tunable coupling in superconducting circuits. Phys. Rev. Lett., 3 (2023) |
| [20] | Quezada, Luis Fernando; Dong, Shi-Hai, Quantum key-distribution protocols based on a quantum version of the Monty Hall game. Ann. Phys., 6 (2020) · Zbl 07763919 |
| [21] | McCoss, Angus, It from qutrit: Braided loop metaheuristic. J. Quantum Inf. Sci., 2, 78-105 (2018) |
| [22] | Kumar, K. Pradheep, Fuzzy approach for quantum processors using qutrits. Int. J. Adv. Sci. Technol., 2, 96-103 (2019) |
| [23] | Konar, Debanjan; Bhattacharyya, Siddhartha; Panigrahi, Bijaya K.; Behrman, Elizabeth C., Qutrit-inspired fully self-supervised shallow quantum learning network for brain tumor segmentation. IEEE Trans. Neural Netw. Learn. Syst., 11, 6331-6345 (2021) |
| [24] | Pepper, Alex; Tischler, Nora; Pryde, Geoff J., Experimental realization of a quantum autoencoder: The compression of qutrits via machine learning. Phys. Rev. Lett., 6 (2019) |
| [25] | Toffano, Zeno; Dubois, François, Adapting logic to physics: The quantum-like eigenlogic program. Entropy, 2, 139 (2020) |
| [26] | López-Peña, Ramón; Cordero, Sergio; Nahmad-Achar, Eduardo; Castaños, Octavio, Storing quantum information in a generalised dicke model via a simple rotation. J. Phys. A (2023) |
| [27] | Gröblacher, Simon; Jennewein, Thomas; Vaziri, Alipasha; Weihs, Gregor; Zeilinger, Anton, Experimental quantum cryptography with qutrits. New J. Phys., 5, 75 (2006) |
| [28] | Kaszlikowski, Dagomir; Oi, Daniel KL; Christandl, Matthias; Chang, Kelken; Ekert, Artur; Kwek, Leong Chuan; Oh, C. H., Quantum cryptography based on qutrit Bell inequalities. Phys. Rev. A, 1 (2003) |
| [29] | Cozzolino, Daniele; Da Lio, Beatrice; Bacco, Davide; Oxenløwe, Leif Katsuo, High-dimensional quantum communication: Benefits, progress, and future challenges. Adv. Quantum Technol., 12 (2019) |
| [30] | Cervera-Lierta, Alba; Krenn, Mario; Aspuru-Guzik, Alán; Galda, Alexey, Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits. Phys. Rev. A, 2 (2022) |
| [31] | Dutta, Tulika; Dey, Sandip; Bhattacharyya, Siddhartha; Mukhopadhyay, Somnath; Chakrabarti, Prasun, Hyperspectral multi-level image thresholding using qutrit genetic algorithm. Expert Syst. Appl. (2021) |
| [32] | Aspelmeyer, Markus; Meystre, Pierre; Schwab, Keith, Quantum optomechanics. Phys. Today, 7, 29-35 (2012) |
| [33] | Gröblacher, Simon; Hammerer, Klemens; Vanner, Michael R.; Aspelmeyer, Markus, Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature, 7256, 724-727 (2009) |
| [34] | Liu, Ni; Li, Junqi; Liang, J.-Q., Entanglement in a tripartite cavity-optomechanical system. Internat. J. Theoret. Phys., 706-715 (2013) · Zbl 1269.81012 |
| [35] | Liao, Q. H.; Nie, W. J.; Xu, J.; Liu, Y.; Zhou, N. R.; Yan, Q. R.; Chen, A.; Liu, N. H.; Ahmad, M. A., Properties of linear entropy of the atom in a tripartite cavity-optomechanical system. Laser Phys., 5 (2016) |
| [36] | Nadiki, M. Hassani; Tavassoly, M. K., Collapse-revival in entanglement and photon statistics: The interaction of a three-level atom with a two-mode quantized field in cavity optomechanics. Laser Phys., 12 (2016) |
| [37] | Nadiki, M. Hassani; Tavassoly, M. K., The amplitude of the cavity pump field and dissipation effects on the entanglement dynamics and statistical properties of an optomechanical system. Opt. Commun., 31-39 (2019) |
| [38] | Eftekhari, F.; Tavassoly, M. K.; Behjat, A., Nonlinear interaction of a three-level atom with a two-mode field in an optomechanical cavity: Field and mechanical mode dissipations. Physica A (2022) · Zbl 07511872 |
| [39] | Behunin, Ryan O.; Rakich, Peter T., Harnessing nonlinear dynamics for quantum state synthesis of mechanical oscillators in tripartite optomechanics. Phys. Rev. A, 2 (2023) |
| [40] | de Moraes Neto, G. D.; Montenegro, Victor, Dissipative optomechanical preparation of non-Gaussian mechanical entanglement. Phys. Lett. A (2022) · Zbl 1495.81017 |
| [41] | Jonas Larson, Themistoklis Mavrogordatos, The Jaynes-Cummings Model and Its Descendants, IOP Publishing, 2021. |
| [42] | Roldán, Eugenio, The Jaynes-Cummings model. Opt. Pura y Aplicada, 2, 361-379 (2011) |
| [43] | Gea-Banacloche, Julio, Jaynes-Cummings model with quasiclassical fields: The effect of dissipation. Phys. Rev. A, 2221-2234 (1993) |
| [44] | Man’ko, V. I.; Marmo, Giuseppe; Sudarshan, E. C.G.; Zaccaria, F., F-oscillators and nonlinear coherent states. Phys. Scr., 5, 528 (1997) |
| [45] | Lopez-Peña, R.; Man’ko, V. I.; Marmo, G.; Sudarshan, E. C.G.; Zaccaria, F., Photon distribution in nonlinear coherent states. J. Russ. Laser Res., 305-316 (2000) |
| [46] | de Matos Filho, R. L.; Vogel, W., Nonlinear coherent states. Phys. Rev. A, 4560-4563 (1996) |
| [47] | Bej, Subhajit; Tervo, Jani; Svirko, Yuri P.; Turunen, Jari, Form birefringence in Kerr media: Analytical formulation and rigorous theory. Opt. Lett., 12, 2913-2916 (2015) |
| [48] | James, David F. V.; Jerke, Jonathan, Effective Hamiltonian theory and its applications in quantum information. Can. J. Phys., 6, 625-632 (2007) |
| [49] | Lecocq, Florent; Teufel, John D.; Aumentado, Jose; Simmonds, Raymond W., Resolving the vacuum fluctuations of an optomechanical system using an artificial atom. Nat. Phys., 8, 635-639 (2015) |
| [50] | Dodonov, Viktor, Fifty years of the dynamical Casimir effect. Physics, 1, 67-104 (2020) |
| [51] | Dodonov, V. V., Nonstationary Casimir effect and analytical solutions for quantum fields in cavities with moving boundaries. Mod. Nonlinear Opt., 309-394 (2001) |
| [52] | Dodonov, A. V.; Dodonov, V. V., Dynamical Casimir effect in two-atom cavity QED. Phys. Rev. A, 5 (2012) |
| [53] | James, David F. V., Quantum computation with hot and cold ions: An assessment of proposed schemes. Fortschr. Phys., 9-11, 823-837 (2000) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
