Strong and tunable couplings in flux-mediated optomechanics

Abstract

We investigate a superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and the cross-Kerr type interactions arise and are modified by the asymmetry. The cross-Kerr type coupling is the leading term at the extremum points where the radiation pressure is zero. In the second case, the main interaction is the single-photon beam splitter, which exists only at a finite asymmetry. Another interaction in this regime is of cross-Kerr type, which exists at all asymmetries, but is generally much weaker than the beam splitter interaction. Increasing magnetic field can substantially enhance the optomechanical couplings strength with a potential for the radiation pressure coupling to reach the single-photon strong coupling regime, even the ultrastrong coupling regime, in which the single-photon coupling rate exceeds the mechanical frequency.

Optomechanical measurement of a millimeter-sized mechanical oscillator approaching the quantum ground state

“…As already mentioned, systems described by equation (1) can be physically built from very different ingredients. In qubit-mediated cavity optomechanics [25][26][27][28]34], see figure 1(b), the qubit can drastically enhance the intrinsically small radiation-pressure coupling g 0 between the mechanics and an microwave cavity. This is because a large linear coupling, created by applying a dc bias to the qubit, becomes converted into an effective parametric coupling as reviewed in the following.…”

“…A voltage-biased conductive mechanical oscillator was proposed to this end in [25,26], and the scheme was experimentally demonstrated in [27]. An analogous setup has been proposed using a flux-biased qubit [28]. The main motivation for introducing a qubit is that the qubit can dramatically enhance the effective optomechanical interaction, possibly allowing for entering the elusive single-photon strong coupling regime.…”

Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

“…1(a)], the two junctions form a gradiometric superconducting quantum interference device (SQUID), so the qubit frequency is set by the flux difference ΔΦ between the two loops. This flux difference is tuned primarily by means of a variable perpendicular field ΔB ⊥ ðtÞ, while mechanical coupling is flux mediated using a static in-plane field B jj [45][46][47]. This type of concentric transmon is insensitive to uniform magnetic fields, which has two advantages for this proposal: The qubit can be operated coherently away from a flux sweet spot [37], and any misaligned static flux will not perturb the energy levels.…”

“…This is the ultrastrong coupling regime, where λ 0 > Ω [47]. It is possible that a device similar to that of Fig.…”

“…Accessing the ultrastrong coupling regime (λ 0 > Ω) is more challenging but may be possible [47]: If the suspended length could be increased to l ≈ 2.9 μm and the tension reduced to zero while keeping other parameters unchanged, the coupling would be λ 0 =2π ≈ Ω=2π ≈ 8 MHz. However, in the simulations, we do not make this assumption but instead assume that effective ultrastrong coupling is engineered by toggling λðtÞ as in Eq.…”