Amplification of bosonic interactions through squeezing in the presence of decoherence

Abstract

We consider the amplification of bosonic interactions through parametric control that implements squeezing along orthogonal quadratures. We show that bosonic interactions described by certain classes of quadratic and quartic Hamiltonians can be enhanced in this way while simultaneously overcoming noise and decoherence. In general, the amplification method enhances both desired and undesired interactions present in the system. Depending on the case, however, detrimental processes can be less amplified than the desired couplings. We leverage this observation to improve the fidelity for preparing Bell-type entangled states between two bosonic modes in the presence of noise and losses. We also investigate noise models for which the protocol either fails or partially achieves a loss-tolerant state preparation speedup. Our work facilitates faster preparation of complex quantum states and implementation of entangling gates in the presence of decoherence mechanisms.

Figures (3)

• Figure 1: Schematic illustration of parametric control (green) used to enhance the interaction strength between two quantum harmonic oscillators, here represented as pendulums coupled via a spring, in the presence of noise and decoherence (orange arrows). We study high-frequency periodic parametric controls implementing squeezing sequences that can amplify bosonic interactions more than detrimental processes, thereby outperforming the effect of noise and decoherence.
• Figure 2: Average infidelity in the preparation of (a) the entangled state \ref{['eq:entangledstate1']} via the beamsplitter interaction \ref{['eq:beamsplitter']} and (b) the entangled state \ref{['eq:entangledstate2']} through the cross-Kerr interaction \ref{['eq:cross-Kerr']}. Infidelities are plotted as a function of the noise strength $\sigma \Delta t$, with noise modeled as random displacements as described in \ref{['eq:noisemodel_displacements']}. Here $\sigma$ is the standard deviation of the Gaussian distribution $\mathcal{N}(0,\sigma^2)$ from which displacement amplitudes are sampled, and $\Delta t$ is a fixed reference time step given by $\frac{t_{\Phi}}{2N}$ in (a) and $\frac{t_{\Psi}}{4N}$ in (b). The squeezing strength is choosen to achieve the amplification factors $\lambda_{2} = 2$ (blue), $\lambda_{2} = 5$ (yellow), $\lambda_{2} = 10$ (green), $\lambda_{2} = 20$ (red). For comparison, the averaged infidelity when no squeezing is present is shown in grey. In all cases, we set the number of Trotter steps to $N = 5$ in the squeezing sequences employed to amplify the desired interactions. The results were averaged over $10^3$ samples.
• Figure 3: Infidelity in the generation of the entangled states \ref{['eq:entangledstate1']} and \ref{['eq:entangledstate2']} via the squeezing sequences \ref{['eq:two mode HA sequence beamsplitter']} and \ref{['eq:two mode HA sequence cross-Kerr']} respectively, as a function of squeezing strength employed in the amplification protocol. Noise is modeled as random displacements in (a) and (c) and as excitation losses in (b) and (d). Subplots (a) and (b) correspond to beamsplitter interactions, while (c) and (d) were calculated for cross-Kerr couplings. The number of amplification steps is $N = 1$ (violet), $N= 2$ (orange), $N= 3$ (blue), $N= 5$ (yellow) and $N= 10$ (green). In all cases, we choose noise parameters such that in the absence of amplification, the infidelity is $\sim 0.5$. In subplots (a) and (c), the results were averaged over $10^3$ samples; for the case of losses, the evolution was modeled as a Lindblad equation (more details are given in Sec. \ref{['subsec:noisemodels']}). The black line in (b) and (d) corresponds to taking the limit $N\to\infty$ in the expression for the full time evolution.