Quantum-Limited Amplification via Reservoir Engineering

We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.

Figure 1

(a) Schematic showing the optomechanical realization of the dissipative amplification scheme. Two driven cavities (1,2) are both coupled parametrically to a third auxiliary mechanical mode. The mechanics mediates a dissipative interaction between modes 1 and 2. Signals incident on either cavity are amplified in reflection. (b) Alternate realization, where two pump modes ${\omega }_{1,P}$, ${\omega }_{2,P}$ are used to generate the required interaction Hamiltonian, Eq. (2); this setup could be directly implemented using superconducting microwave circuits [46].

Figure 2

(a) Black curves: photon number gain versus cooperativity $\mathcal{C}$ for parameters corresponding to a microwave-cavity optomechanical realization of the dissipative amplification scheme. We take ${\omega }_M/(2\pi )=20\mathrm{MHz}$ and $\kappa /(2\pi )=1\mathrm{MHz}$ (solid curve); the latter includes internal loss ${\kappa }^{\text{int}}/(2\pi )=10\mathrm{kHz}$. The dotted line includes the effect of asymmetric cavity damping (see legend); the dashed line shows instead the effects of $G_1\ne G_2$ (see legend). We assume that the mechanical resonator is coupled to a third auxiliary cavity which is used to both cool and optically damp it, leading to a total mechanical damping rate of $\gamma /(2\pi )=200\mathrm{kHz}$. Red dashed-dotted curve: bandwidth (defined as the full-width at half-maximum of ${\mathcal{G}}_1[\omega ]$) versus $\mathcal{C}$, same parameters as the solid curve. (b) Amplifier added noise ${\overline{n}}_{\text{add}}$ versus $\mathcal{C}$. Solid curve: mechanics and cavity 2 driven by vacuum noise only. Dashed-dotted curve: mechanics now driven by thermal noise. Dashed curve: both mechanics and cavity 2 driven by thermal noise. Other parameters identical to solid black curves in (a) and with ${\overline{n}}_{b,d_{1,2}}^T$ as denoted in the graph. All curves are produced without making the RWA (though they are well described by the RWA theory).