Graphene Josephson Junctions for Engineering Motional Quanta

Abstract

We propose a hybrid quantum device based on the graphene Josephson junctions, where the vibrational degrees of freedom of a graphene membrane couple to the superconducting circuits. The flexural mode-controlled tunneling of the Cooper pairs introduces a strong and tunable coupling even at the zero-point fluctuations level. By employing this interaction, we show that a parametric process can be efficiently implemented. We then investigate foundational and technological applications of our hybrid device empowered by nonlinear interactions, with fast generation of non-classical mechanical states, and critically enhanced quantum sensing under suitable quantum control. Our work provides the possibility of employing the graphene motional degree of freedom for quantum information processing in circuit quantum nanomechanical structures.

Figures (5)

• Figure 1: (a) Sketch of a Graphene Josephson junction with zero-point fluctuations perpendicular to the static plane. (b) The quadratic coupling strength as a function of the graphene chemical potential. The inset shows that for suitable $\mu$ the effective coupling can even surpass the critical strength (the dashed line).
• Figure 2: (a) An energy level diagram for the parametric cooling process. (b) Steady-state occupation number for vibrational mode and the corresponding coupling strength $G_2$ for optimal detuning. (c) Absolute value of the lowest elements of the vibrational mode steady-state density matrix after the parametric cooling process. (d) Steady-state occupations for different detuning and coherent drive strength for $\mu=0$. The white dashed-dot line indicates the minimal occupation under different $A$.
• Figure 3: (a) The control sequences for the $m-$ component cat states generation and preservation. Without loss of generality, this sequence can be repeated, as illustrated for the second state generation pulse. (b-c) The Wigner function for the vibrational mode after $\tau_1=\tau_0/2, \tau_0/4$, which generates the 2- and 4-component cat state, respectively. The parameters are chosen as $\xi=10^{-4}\omega$, $\Lambda=0.8\Lambda_c$.
• Figure 4: QFI for zero temperature. (a) The maximal QFI (solid blue line) and the corresponding optimal time $t^*$ (dotted red line) for different $\Lambda$. The lines indicate the $\xi=0$ while the triangles correspond to $\xi=10^{-4}\omega$. The dashed black line is the function $(\Lambda_c -\Lambda)^{-1}$ with a proper fitting factor. (b) The fitted parameters $\zeta$ and $\beta$ under zero temperature. The blue lines indicate $\xi=0$ while the red markers correspond to $\xi=10^{-4}\omega$. (c) Steady state QFI vs $\Lambda$ under different $\xi$. (d) The steady state intuitive $l_1$ norm of coherence under computational basis $\{|n\rangle\}$.
• Figure 5: QFI for finite temperature. (a) The maximal QFI and the corresponding optimal $t^{*}$ vs temperature $T$ when $\xi=0$. (b) The steady states QFI for finite temperatures. The dashed-dot lines correspond to the steady state result for $\xi=0$ while the solid lines indicate the steady states with $\xi=5\times 10^{-5}\omega$. Inset: steady-state QFI for $\xi=0$, the red and the green dashed lines correspond to the high and the low temperature limits, respectively, see Eq. \ref{['eq:ss_Qfi_T']} and the discussion below. In this plot, we choose $\Lambda=0.8\Lambda_c$.