# Quantum amplification of boson-mediated interactions [(link)](https://www.nature.com/articles/s41567-021-01237-9.pdf) [local](paper.pdf) 2021-07-26 PTB Journal Club ## Yellow ### general formalism * *amplified boson-mediated interaction* * realizable by many physical systems #### 1st two terms: unamplified * $\hat S$ : collective degree of freedom $\hat S = \sum_i \beta_i \hat s_i$ * $\hat a, \hat a^{\dagger}, \omega$ : harmonic oscillator mode (coupled) * $\delta$ : system dependant offset * $\Omega_0$ : coupling strength #### 2nd term: parametric modulation of *boson channel* * $g$ : modulation strength * $\theta$ : relative phase, modulation - coupling interaction ## Blue ### 1 Trapped ion qubits: * $\hat a, \hat a^{\dagger}$ : *normal mode* of motion * $\hat s_i$ : Pauli matrix $\hat\sigma_j^i$ for the $i$-th ion * $\delta$ : detuning of spin-motion coupling drive from * $\omega$ : phonon mode implementing interaction * $\beta_i$ : participation of $i$-th ion ### 2 OOP mode coupling; *g* = 0 * $\hat S = \hat \sigma_x^1 - \hat \sigma_x^2$ * $|+-\rangle$ and $|+-\rangle$ displaced, loops in phase space (see fig. 1a) * $H_M$ $\leadsto$ $\Phi$ (enclosed area) acquired geometric phase * $\tau = 2\pi/\delta$ * $\leadsto$ returns oscillator to initial state * disentangles motion from spin state * $\hat U = \exp\bigg(i \frac{\Phi}{4}\hat S^2\bigg)$ , $\Phi = 2\pi (\Omega_0/\delta)^2$ * effective spin-spin interaction * $\leadsto$ $\Phi$-rotation in Bloch sphere with $|\uparrow\uparrow\rangle$ and $|\downarrow\downarrow\rangle$ at the poles * $\delta = 2\Omega_0 \curvearrowright\Phi = \pi/2$ $\leadsto$ maximally entangled state * $t_{\text{gate}} \propto \frac{1}{\Omega_0}$ ? ### 3 squeezing * (see fig. 1b) * normal mode *transformation* * interaction strength amplification * $\Phi = 0 \leadsto$ maximal amplification ## Magenta ### 1 description of their trap * $^{25}\text{Mg}^+$ ions * hyperfine qubits * $30\ \mu \text{m}$ above surface * surface-electrode radio-frequency trap * 15 K (cryo) * OOP mode @ 5.9 MHz * $|\downarrow\rangle$,$|\uparrow\rangle$ within electronic ground state * 21.3 mT * microwaves ### 2 quantum operations in their trap * init in $|\downarrow\downarrow\rangle$ * resolved SB cooling to $\bar n \approx 0.3$ * state dependant fluorescence detection * microwave MS Gate * gate time 342 $\mu\text{s}$ * oscillating potential into trap RF drive ### 3 Experiments