PhD Defense by Christoffer Østfeldt

Quantum Optomechanics for Hybrid Spin–Membrane Entanglement

The second quantum revolution, signaled by the emergence of practical quantum technologies such as secure quantum communication, quantum computing and quantum limited and enhanced sensing, is pushing the need for ever better experimental control and design of quantum systems.
However, with this development has come the realization that one single quantum system may not efficiently implement all the different tasks needed for, e. g., a “Quantum Internet”, or generalized quantum computers. To this end, hybrid quantum systems, incorporating fundamentally disparate material systems have been proposed, efficiently harnessing the advantages and capabilities of the different sub-systems.

In this thesis, we report on the continued development of a hybrid spin–mechanics quantum system, ultimately showcased by the successful demonstration of steady-state conditional entanglement between the spin and mechanics, as witnessed by the conditional variance 𝑉_c = 0.83 ± 0.02 < 1, below the separability limit. The optomechanical system consists of a out-of-plane vibrational mode of a soft-clamped, highly stressed silicon nitride membrane, which is embedded in a high-finesse free-space optical cavity, realizing a Membrane-in-the-Middle optomechanical system, and mounted in a 4 K cryostat. Significant improvements to the optomechanical assembly over previous work allow for a much easier implementation of optomechanical systems into hybrid setups, and allows for full electronic control of cavity resonance as well as membrane position in the cavity standing wave.

The spin system is prepared in a warm (330 K) ensemble of optically pumped cesium atoms confined in a spin-preserving microcell. The collective atomic spin is co-aligned with an external magnetic field around which the spin performs Larmor precession. This effectively prepares the spin in the highest energy state, thus implementing an effective negative mass reference frame for the optomechanical system.

The itinerant light field probing the two systems reads out their collective degrees of freedom, and, together with the effective negative mass of the spin, allows for a Quantum Back-Action Evading measurement, reducing the probeinduced measurement noise by 2.6 dB compared to the mechanics-only case, or 4.6 dB compared to the case with two detuned systems, both significant improvements over previously reported results.
Furthermore, a non-local cooling of the Einstein–Podolsky–Rosen (epr) variables reduces the combined thermal noise of the systems by 2.5 dB.

Implementation of optimized Wiener filtering of the measured photo current, together with the noise suppressing mechanisms, allows state estimation at an uncertainty level of the (entangled) continuous variable epr-like state, with deterministic conditional variance below the separability limit, demonstrating entanglement.

The implemented hybrid quantum system paves the way towards teleportation based quantum protocols in spin-mechanics hybrid interfaces, as well as measurements of motion beyond the standard quantum limits of sensitivity.