Engineering bilinear mode coupling in circuit QED: Theory and experiment

Abstract

Photonic states of high-Q superconducting microwave cavities controlled by superconducting transmon ancillas provide a platform for encoding and manipulating quantum information. A key challenge in scaling up the platform towards practical quantum computation is the requirement to communicate on demand the quantum information stored in the cavities. It has been recently demonstrated that a tunable bilinear interaction between two cavity modes can be realized by coupling the modes to a bichromatically-driven superconducting transmon ancilla, which allows swapping and interfering the multi-photon states stored in the cavity modes [Gao et al., Phys. Rev. X 8, 021073(2018)]. Here, we explore both theoretically and experimentally the regime of relatively strong drives on the ancilla needed to achieve fast SWAP gates but which can also lead to undesired non-perturbative effects that lower the SWAP fidelity. We develop a theoretical formalism based on linear response theory that allows one to calculate the rate of ancilla-induced interaction, decay and frequency shift of the cavity modes in terms of a susceptibility matrix. We go beyond the usual perturbative treatment of the drives by using Floquet theory, and find that the interference of the two drives can strongly alter the system dynamics even in the regime where the standard rotating wave approximation applies. The drive-induced AC Stark shift on the ancilla depends non-trivially on the drive and ancilla parameters which in turn modify the strength of the engineered interaction. We identify two major sources of infidelity due to ancilla decoherence. i) Ancilla dissipation and dephasing lead to incoherent hopping among Floquet states which occurs even when the ancilla is at zero temperature; this hopping results in a sudden change of the SWAP rate, thereby decohering the SWAP operation. ii) The cavity modes inherit finite decay from the relatively lossy ancilla through the inverse Purcell effect; the effect becomes particularly strong when the AC Stark shift pushes certain ancilla transition frequencies to the vicinity of the cavity mode frequencies. The theoretical predictions agree quantitatively with the experimental results, paving the way for using the developed theory for optimizing future experiments and architecture designs.

Hardware-Efficient Quantum Random Access Memory with Hybrid Quantum Acoustic Systems

“…We note that the expression for β (1) matches the leading order expression derived in Ref. [54]. Contributions to β (1,2) at higher orders in λ can be neglected since we have assumed the dispersive regime, λ 1.…”

“…) denotes the dressed decay rate of mode j, which includes a contribution from the inverse Purcell effect [3,54] and a drive-dependent correction β (γ) [55]. The second term in each expression accounts for spectral crowding.…”

“…Then, in order to verify the accuracy of these expressions, we compare them to numerical results obtained using the Floquet theory methods of Ref. [54].…”

“…Were the corrections not included, this relative shift would result in a systematic overestimation of the coupling rates for blue-detuned phonon modes. [54]. It is important to carefully avoid these peaks in the experiments.…”

All Dielectric Terahertz Left-Handed Metamaterial Based on Mie Resonance Coupling Effects

“…Since the relative permittivity of the dielectric resonator is generally high, there are more resonant modes and coupling effect between the structures [22]- [25]. However, the quantitative description of the coupling effect in the dielectric resonant structure has not yet been considered [26]- [29]. Therefore, this study focuses on the internal principle of coupling effect and proposes the combination of Mie scattering theory and coupled mode theory to quantitatively describe the complex coupling effect in dielectric metamaterials at the resonant frequencies.…”