Utilizing optical nonlinearity for generating the entanglement is still a most widely used approach due to its quality and simplicity. Here in this paper, we propose a theoretical scheme to generate bipartite and tripartite entanglement in a cavity quantum electrodynamics (QED) system with one Yttrium iron garnet (YIG) sphere by using a squeezed drive. In such a system, the parametric down-conversion process is used to generate the nonlinearity and further increase the coupling between cavity and YIG. Thus, the enhanced coupling between the microwave cavity photons and the ferromagnetic resonance (FMR) mode/magnetostatic (MS) mode results in bipartite entanglements. By using the mean field theory, we show that the bipartite entanglements strongly depend on the detuning of the cavity and magnon mode. When the driving field is tuned to be resonant with the FMR mode, but the MS mode is far off-resonant, the entanglement between photons and the FMR mode reaches its maximum. However, when the driving field is tuned to be resonant with the MS mode, but the FMR mode is detuned very well, the entanglement between photons and the MS mode reaches its maximum. We show that the dissipation of the FMR/MS mode affects the entanglement greatly, and the bipartite entanglement decreases as the dissipation rate of the FMR/MS mode increases. Under the steady-state approximation, we also show that the tripartite entanglement can be generated, and the minimum residual contangle increases with the enhancement of the nonlinear gain coefficient. With the nonlinearity induced by the parametric down conversion process, the interaction between the driving field and the magnetic-cavity QED system leads to the tripartite entanglement involving the cavity photons, FMR mode and the MS mode. Likewise, we show that the tripartite entanglement also strongly depends on the dissipation rate of MS mode, and the minimum residual contangle increases as the dissipation rate of the MS mode decreases. We also show that the squeezed field induced tripartite entanglement is insensitive to the temperature and has good robustness. Our results suggest that the magnetic-cavity QED system could provide a promising platform for studying the macroscopic quantum phenomena, and the squeezing field opens a new method of generating the entanglement.
Utilizing optical nonlinearity for generating the entanglement is still a most widely used approach due to its quality and simplicity. Here in this paper, we propose a theoretical scheme to generate bipartite and tripartite entanglement in a cavity quantum electrodynamics (QED) system with one Yttrium iron garnet (YIG) sphere by using a squeezed drive. In such a system, the parametric down-conversion process is used to generate the nonlinearity and further increase the coupling between cavity and YIG. Thus, the enhanced coupling between the microwave cavity photons and the ferromagnetic resonance (FMR) mode/magnetostatic (MS) mode results in bipartite entanglements. By using the mean field theory, we show that the bipartite entanglements strongly depend on the detuning of the cavity and magnon mode. When the driving field is tuned to be resonant with the FMR mode, but the MS mode is far off-resonant, the entanglement between photons and the FMR mode reaches its maximum. However, when the driving field is tuned to be resonant with the MS mode, but the FMR mode is detuned very well, the entanglement between photons and the MS mode reaches its maximum. We show that the dissipation of the FMR/MS mode affects the entanglement greatly, and the bipartite entanglement decreases as the dissipation rate of the FMR/MS mode increases. Under the steady-state approximation, we also show that the tripartite entanglement can be generated, and the minimum residual contangle increases with the enhancement of the nonlinear gain coefficient. With the nonlinearity induced by the parametric down conversion process, the interaction between the driving field and the magnetic-cavity QED system leads to the tripartite entanglement involving the cavity photons, FMR mode and the MS mode. Likewise, we show that the tripartite entanglement also strongly depends on the dissipation rate of MS mode, and the minimum residual contangle increases as the dissipation rate of the MS mode decreases. We also show that the squeezed field induced tripartite entanglement is insensitive to the temperature and has good robustness. Our results suggest that the magnetic-cavity QED system could provide a promising platform for studying the macroscopic quantum phenomena, and the squeezing field opens a new method of generating the entanglement.
We propose a scheme to generate entanglement between two cavity modes and squeeze magnon mode in a magnon-cavity QED system, where the two microwave cavity modes are coupled with a massive yttrium iron garnet (YIG) sphere through magnetic dipole interaction. The nonlinearity used in our system originates from a squeezed driving via parametric down-conversion process, which is the reason to cause entanglement and squeezing. By using the mean field approximation and employing experimentally feasible parameters, we demonstrate that the system shows zero entanglement and squeezing without squeezed driving. Meanwhile, our QED system denotes that the entanglement between squeezed cavity mode and magnon mode can be transferred to the other cavity mode and magnon mode via magnon-cavity coupling interaction, and then the two cavity modes get entangled. A genuinely tripartite entangled state is formed. We also show that magnon mode can be prepared in a squeezed state via magnon-cavity beam-splitter interaction, which is as a result of the squeezed field. Moreover, we show that it is a good way to enhance entanglement and squeezing by increasing the nonlinear gain coefficient of squeezed driving. Our results denote that magnon-cavity QED system is a powerful platform for studying macroscopic quantum phenomena, which illustrates a new method to photon-photon entanglement and magnon squeezing.
The generation of robust entanglement in quantum system arrays is a crucial aspect of the realization of efficient quantum information processing. Recently, the field of quantum magnonics has garnered significant attention as a promising platform for advancing in this direction. In our proposed scheme, we utilize a one-dimensional array of coupled cavities, with each cavity housing a single yttrium iron garnet (YIG) sphere coupled to the cavity mode through magnetic dipole interaction. To induce entanglement between YIGs, we employ a local squeezed drive, which provides the necessary nonlinearity for entanglement generation. Our results demonstrate the successful generation of bipartite and tripartite entanglement between distant magnon modes, all achieved through a single quantum drive. Furthermore, the steady-state entanglement between magnon modes is robust against magnon dissipation rates and environment temperature. Our results may lead to applications of cavity-magnon arrays in quantum information processing and quantum communication systems.
We present a proposal to produce bipartite and tripartite entanglement in a hybrid magnon cavity QED system. Two macroscopic yttrium iron garnet (YIG) spheres are coupled to a single-mode microwave cavity, where the cavity photons are generated via a two-photon process induced by a strong pump field. Using mean-field theory, we show that nonlinear pumping can result in strong bipartite entanglement between the cavity photon and magnon under two conditions, i.e., ${\ensuremath{\delta}}_{c}{\ensuremath{\delta}}_{m}=2{g}^{2}$ and ${\ensuremath{\delta}}_{c}=\ensuremath{-}{\ensuremath{\delta}}_{m}$. For the latter one, we also show the possibility for producing bipartite entanglement between two magnon modes as well as tripartite entanglement among three modes. Combining these two conditions, we further derive a third condition, i.e., ${\ensuremath{\delta}}_{m}^{2}\ensuremath{-}{\ensuremath{\phi}}^{2}+2{g}^{2}=0$, where tripartite entanglement can be achieved when two magnon modes have different resonant frequencies.
Abstract A scheme to entangle two cavity modes and squeeze magnon mode in a magnon–cavity QED system is presented, where the two microwave cavity modes are coupled to a massive yttrium iron garnet sphere. The nonlinearity used in our system originates from parametric down-conversion. By using the mean field approximation and employing experimentally feasible parameters, we indicate that the entanglement between squeezed cavity mode and magnon mode can be transferred to the other cavity mode and magnon mode, and then the two cavity modes get entangled. Meanwhile, the magnon mode is squeezed in our QED system. Furthermore, we show that it is a good way to enhance entanglement and squeezing by increasing the nonlinear gain. Our results denote that magnon–cavity QED system is a powerful platform for studying macroscopic quantum phenomena, which illustrates a new approach to photon–photon entanglement and magnon squeezing.
In this work, we employ logarithmic negativity to rigorously investigate bipartite entanglements in a lossy cavity magnomechanical system incorporating both photon and magnon Kerr nonlinearities. The system comprises two optical cavity modes, two yttrium-iron-garnet (YIG) spheres, which support magnon and phonon modes, and two electromagnetic fields that drive the magnons. Through numerical simulations, we systematically examine the influence of significant parameters, including photon-magnon and phonon-magnon coupling strengths, dissipation rates, Kerr nonlinearities, environmental temperatures, and normalized detuning on the bipartite entanglements between distinct subsystems. Our findings reveal that the amounts of bipartite entanglements can be precisely tuned by optimizing these parameters. Specifically, increasing either dissipation or Kerr nonlinearity diminishes the maximum values of entanglement. Furthermore, when the magnomechanical coupling is stronger, the entanglement becomes more robust and can endure across a broader spectrum of temperatures. Moreover, the entanglement generated within the subsystems demonstrates remarkable robustness against environmental temperature. Additionally, the maximum survival temperature of bipartite entanglements varies across different entangled pairs, and can be effectively controlled by the optical-magnon coupling strength. Notably, entanglement between subsystems persists even at cryogenic temperatures.
We present a scheme to generate distant bipartite and tripartite entanglement between an atomic ensemble and an yttrium iron garnet (YIG) sphere in coupled microwave cavities. We consider an atomic ensemble in a single-mode microwave cavity which is coupled with a second single-mode cavity having a YIG sphere. Our system, therefore, has five excitation modes, namely, cavity-1 photons, an atomic ensemble, cavity-2 photons, a magnon and a phonon mode in the YIG sphere. We show that significant bipartite entanglement exists between indirectly coupled subsystems in the cavities which is robust against temperature. Moreover, we present suitable parameters for a significant tripartite entanglement of the ensemble, magnon, and phonon modes. We also demonstrate the existence of tripartite entanglement between the magnon and phonon modes of the YIG sphere with indirectly coupled cavity photons. Interestingly, this distant tripartite entanglement is of the same order as that previously found for a single-cavity system. We show that cavity-cavity coupling strength affects both the degree and transfer of quantum entanglement between various subsystems. Therefore, an appropriate cavity-cavity coupling optimizes the distant entanglement by increasing the entanglement strength and its robustness against temperature.