Creating multicomponent Schrödinger cat states in a coupled qubit-oscillator system

Abstract

We present a method for preparing various exotic modifications of Schrödinger cat states by coupling a semiclassical oscillator to a system of qubits. Varying the number of qubits and parameters of the quantum quench performed in the coupled system, we bring the oscillator into a~highly non-classical state composed of an arbitrary number of partly coherent wavepackets in tunable proportions and motion relations. The method can be implemented with the aid of current experimental techniques and may find applications in quantum information and sensing protocols.

Figures (4)

• Figure 1: The evolving oscillator Wigner functions $W_{\rm osc}(q,p,t)$ (with red/blue indicating positive/negative values) for systems with spins ${j=\frac{1}{2}}$ and $2$ after the quantum quench from ${\lambda_{\rm in}=1.5}$ to ${\lambda_{\rm fi}=-0.283}$, with ${\delta=0.5}$ and ${R=20}$. The evolution starts at ${t=0}$ from a single wavepacket in the leftmost (${q<0}$) position. Times $t/\tau$ of all snapshots are indicated within the panels (for ${j=\frac{1}{2}}$ they are also marked in Fig. \ref{['Puri']}). Color bullets and the oval curves indicate classical trajectories $(q(t),p(t))$. The displayed phase-space domain in all cases is $q,p\in[-1.5,+1.5]$. See videos supp for full dynamics.
• Figure 2: (a) Spectrum (black lines) of Hamiltonian \ref{['Ham']} and representation of the quench from Fig. \ref{['Wig']} for ${j=\frac{1}{2}}$. The final energy distribution $|c_k|^2$ is split to blue and green parts corresponding to ${m=-\frac{1}{2}}$ and ${+\frac{1}{2}}$, respectively. (b) Oscillator Wigner function (red blob) on the energy contours of $\hat{H}_{\rm osc}^{(-1/2)}$ (gray lines) and the spin orientation on the Bloch sphere at $\lambda_{\rm in}$. (c) Cuts of the oscillator effective Hamiltonians $\hat{H}_{\rm osc}^{(\pm 1/2)}$ (blue and green curves) and the spin orientation at $\lambda_{\rm fi}$.
• Figure 3: Purity $\gamma(t)$ and negativity $\nu(t)$ after the quench from Fig. \ref{['Wig']} for ${j=\frac{1}{2}}$. Inserted Bloch-sphere diagrams depict motions of the average spin $\langle{\boldsymbol J}(t)\rangle$ in two time intervals indicated by the gray zones.
• Figure 4: Cat-state parameters for ${\lambda_{\rm in}=1.5}$ and variable $\lambda_{\rm fi}$ with (a) ${j=\frac{1}{2}}$ and (b) ${j=2}$. Upper panels: Weights $|\alpha^{(m)}|^2$ of individual wavepackets from Eq. \ref{['psina']}. Solid and dashed curves (practically coinciding) are calculated, respectively, from $d$-functions supp and by summing $|c_k|^2$ in the corresponding peaks, cf. Fig. \ref{['Schema']}(a). Lower panels: Periods of classical orbits for ${\mu=\frac{m}{j}=-1,\cdots,+1}$ and two values $\delta=0.5$ (solid lines) and $\delta=0$ (dashed lines). The vertical gray line indicates the quench used in the previous figures. We set $R=50$.