Accelerated adiabatic passage in cavity magnomechanics

Cavity magnomechanics provides a readily controllable hybrid system, consisting of a cavity mode, magnon mode, and phonon mode, for quantum state manipulation and transfer. To implement a fast-and-robust state transfer between the hybrid photon-magnon mode and the phonon mode, we apply two accelerated-adiabatic-passage protocols based on the counterdiabatic Hamiltonian for transitionless quantum driving and the Levis-Riesenfeld invariant for inverse engineering. We construct the counterdiabatic Hamiltonian in a state-resolved way and express it through the creation and annihilation operators rather than the system eigenstates and their time derivatives. We can optimize the invariant-based inverse-engineering protocol with respect to the stability against the systematic errors of the coupling strength and frequency detuning. Both protocols apply for continuous-variable systems with arbitrary target states. We also discuss the decoherence effects from the thermal environment and the counterrotating interactions on both protocols. Our work contributes to the quantum memory for photonic and magnonic quantum information.

Figure 1

Schematic diagram of a YIG sphere placed in a microwave cavity near the maximum magnetic field of the cavity mode. The uniform bias magnetic field exciting the Kittel mode in the YIG and establishing the magnon-photon coupling is aligned along the $z$ axis. The photon mode is driven by a microwave source along the $x$ axis (with a Rabi frequency ${\epsilon }_p$). The inset shows how the dynamic magnetization of a magnon (vertical black arrows) causes the deformation (compression along the $y$ direction) of the YIG sphere (and vice versa), which rotates at the magnon frequency.

Figure 2

(a): The time dependence of the driving-enhanced coupling strength $g$, the effective frequency of the lower-frequency hybrid mode $\mathrm{\Delta }$, and the time derivative of the control parameter $\dot{\theta }$, in units of the coupling strength $\mathrm{\Omega }=\pi /T$. (b)–(d) The target-state population of the phonon mode $b$ for the initial state of the hybrid mode $m$ prepared as the Fock state $|n=4\rangle$, the cat state with $\zeta =1$, and the cat state with $\zeta =4$, respectively.

Figure 3

(a) The shapes of the real and imaginary parts of the driving-enhanced coupling strength $g_R$ and $g_I$ and the effective frequency of the hybrid mode $\mathrm{\Delta }$, in units of the coupling strength $\mathrm{\Omega }=\pi /T$. (b) The dynamics of the state population of mode $b$ under various initial cat states of the hybrid mode $m$. Here the control parameters are set as $\beta =\pi t/T, \alpha =-4/3{sin}^3\beta$, and $\kappa =\beta -sin\left(2\beta \right)/2$.

Figure 4

State-transfer population $P\left(T\right)$ of the phonon mode $b$ as a function of the systematic errors associated with the coupling strength $\gamma$ or the frequency detuning $\eta$ for various target states and shape functions of the TQD protocol. In (a) and (b), the initial state is the Fock state $|4\rangle$, and in (c) and (d), it is the cat state with $\zeta =1$. $T=\pi /\mathrm{\Omega }$.

Figure 5

State-transfer population $P(T=\pi /\mathrm{\Omega })$ of the phonon mode $b$ in the space of the systematic-error parameters $\gamma$ and $\eta$. The target state is chosen as the cat state with $\zeta =1$.

Figure 6

State-transfer population $P(T=\pi /\mathrm{\Omega })$ of the phonon mode $b$ as a function of the systematic errors associated with the coupling strength $\gamma$ for various protocols. The initial state in (a) is the Fock state $|4\rangle$, and in (b) it is the cat state with $\zeta =1$.

Figure 7

The dynamics of the target-state population in mode $b$ in the presence of thermal baths with various temperatures. In (a) we use the TQD protocol as described in Fig. 2, and in (b) we use the LR-invariant protocol as described in Fig. 3. Here the initial state is set as the cat state with $\zeta =1$.

Figure 8

The population dynamics in the presence of the counterrotating interaction for various state-transfer protocols. In (a) and (b), the initial state is the Fock state $|1\rangle$, and in (c) and (d), it is the cat state with $\zeta =1$. The phonon-mode frequency is set as ${\omega }_b/\mathrm{\Omega }=10$ in (a) and (c) and as ${\omega }_b/\mathrm{\Omega }=4$ in (b) and (d). $\mathrm{\Omega }T=\pi$.