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Journal of the Korean Physical Society

Widely Tunable Coupling between a Mechanical Mode and Cavity Photons via a Superconductor

Joonho Jang

Published Nov 20, 2020• 0 citations
Publisher

Abstract

Inducing strong coupling between a mechanical degree of freedom and optical modes has been of great scientific interest itself, but also important for the applications to the quantum information technology. However, photons and mechanical modes usually are weakly interacting due to very small momentum exerted by photons. Here, we demonstrate a scheme for coupling a resonance mode of a mechanical oscillator with an optical cavity, by utilizing the magneto-optical effect of a mesoscopic superconductor attached to the mechanical oscillator. The absorption of cavity photons by the superconductor in external magnetic fields gives rise to a retarded force that modifies the damping and frequency of the oscillator. Measurements using NbSe 2 achieved approximately a factor of 17 reduction in the mode temperature from 5.0 K to 260 mK.

DOI
10.3938/jkps.77.927

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Inducing strong coupling between a mechanical degree of freedom and optical modes has been of great scientific interest itself, but also important for the applications to the quantum information technology. However, photons and mechanical modes usually are weakly interacting due to very small momentum exerted by photons. Here, we demonstrate a scheme for coupling a resonance mode of a mechanical oscillator with an optical cavity, by utilizing the magneto-optical effect of a mesoscopic superconductor attached to the mechanical oscillator. The absorption of cavity photons by the superconductor in external magnetic fields gives rise to a retarded force that modifies the damping and frequency of the oscillator. Measurements using NbSe 2 achieved approximately a factor of 17 reduction in the mode temperature from 5.0 K to 260 mK.
Microscale and nanoscale mechanical resonators have been used in advanced technological applications, from high precision time keeping and mass sensing, to processing high frequency signals in mobile communications. In the last few decades, they have been an important part of progress in the field of quantum information and metrology and have been proposed as quantum memories or transducers for measuring or connecting different types of quantum systems. The field of cavity optomechanics and electromechanics is concerned with coupling the electromagnetic field of a resonant optical cavity or electrical circuit to mechanical motion. These systems provide potential means to control and engineer the state of a mechanical object at the quantum level. This thesis contains the description of mechanical systems in megahertz to a few hundred megahertz frequency range formed by nano-fabricating photonic, phononic, and electrical circuits on a chip. These structures are designed to provide a large radiation pressure coupling between mechanical motion and electromagnetic fields to address and manipulate motional degrees of freedom. Qualitatively novel quantum effects are expected when one takes a step beyond linear coupling and exploits higher order interactions. To that end, we integrate electrical, mechanical and photonic structures in a multimode photonic crystal structure to observe "x2-coupling", where the optical cavity frequency is coupled to the square of the mechanical displacement. Moreover, we have developed two integrated on-chip platforms based on Si3N4 and Si nanomembranes capable of interfacing superconducting qubits and optical photons and realizing reversible microwave-to-optical conversion. We employ radiation pressure to cool these mechanical resonators to their quantum ground state. Finally, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons of frequency ωm/2π = 0.425 GHz by capacitively coupling a phononic crystal acoustic cavity to a superconducting microwave resonator. Moving to higher frequency acoustic cavities not only facilitates the integration of electromechanical circuits and nanophotonic systems capable of operation in the resolved sideband limit of optomechanics for noise-free quantum signal conversion, but it opens up the possibility of using phonons as information carriers via phononic circuits. Utilizing a two-photon resonance condition for efficient microwave pumping and phononic bandgap shield to eliminate acoustic radiation, we achieve large cooperative electromechanical coupling (C ≈ 30) and intrinsic decay time of 2.3 ms. Moreover, electrical read-out of the phonon occupancy shows that the acoustic mode thermalizes close to its quantum ground-state of motion (phonon occupancy nm=1.5) at a fridge temperature of Tf = 10 mK. We conclude by considering several designs and fabrication improvements to the hypersonic electromechanical crystals that would enable them to perform quantum conversion between the electrical and acoustic domain.
In cavity quantum electrodynamics (QED), the key physical systems include Fabry-Pérot cavity resonators and multilevel cold atoms. Since ultra-strong electromagnetic interaction between photons and quantized cavity modes occurs in cavity QED, many novel quantum optical effects such as optical Rabi oscillation, quantum collapse/revival of atomic-level population and atom-field quantum entanglement can be realized in such quantum microcavities. As is known in quantum optics, these schemes can be generalized to circuit QED, which is a circuit analog of cavity QED. Fundamental devices in circuit QED are superconducting coplanar waveguide microwave resonators and mesoscopic Cooper-pair boxes. Here, the coplanar waveguide resonator with photons stored can be identified as a resonant cavity and the Cooper-pair boxes with large electric dipoles play the role of multilevel cold atoms. Thus, all the quantum optical effects in conventional cavity QED can also be exhibited in the present superconducting circuit QED system. We consider the theoretical working mechanism of superconducting charge qubits based on tunable Josephson junction coupling. It can be found that an analog of optical Rabi oscillation in Cooper-pair boxes can be achieved by tuning an applied external magnetic field. Time evolution of energy levels in a Cooper-pair box, which is manipulated by a time-dependent magnetic flux through its Josephson-junction ring, is studied within the framework of time-dependent quantum mechanics.
High-frequency mechanical resonators subjected to low thermal phonon occupancy are easier to be prepared to the ground state by direct cryogenic cooling. Their extreme stiffness, however, poses a significant challenge for external interrogations. Here we demonstrate a superconducting cavity piezoelectromechanical system in which multiple modes of a bulk acoustic resonator oscillating at 10 GHz are coupled to a planar microwave superconducting resonator with a cooperativity exceeding 2×10^{3}, deep in the strong coupling regime. By implementation of the noncontact coupling scheme to reduce mechanical dissipation, the system exhibits excellent coherence characterized by a frequency-quality-factor product of 7.5×10^{15} Hz. Interesting dynamics of classical temporal oscillations of the microwave energy is observed, implying the coherent conversion between phonons and photons. The demonstrated high-frequency cavity piezoelectromechanics is compatible with superconducting qubits, representing an important step towards hybrid quantum systems.
Cavity optomechanics represents a flexible platform for the implementation of quantum technologies, useful in particular for the realization of quantum interfaces, quantum sensors and quantum information processing. However, the dispersive, radiation-pressure interaction between the mechanical and the electromagnetic modes is typically very weak, harnessing up to now the demonstration of interesting nonlinear dynamics and quantum control at the single photon level. It has already been shown both theoretically and experimentally that if the interaction is mediated by a Josephson circuit, one can have an effective dynamics corresponding to a huge enhancement of the single-photon optomechanical coupling. Here we analyze in detail this phenomenon in the general case when the cavity mode and the mechanical mode interact via an off-resonant qubit. Using a Schrieffer-Wolff approximation treatment, we determine the regime where this tripartite hybrid system behaves as an effective cavity optomechanical system in the strong coupling regime.
We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a significant change in the cavity resonance. Conversely, a single photon in the cavity causes a shift in the mechanical resonator position on the order of its zero point motion. As a result, the cavity-Cooper pair transistor coupled to a mechanical resonator will be able to access a regime in which single photons can affect single phonons and vice versa. Realizing this ultra-strong coupling regime will facilitate the creation of non-classical states of the mechanical resonator, as well as the means to accurately characterize such states by measuring the cavity photon field.
We investigate a hybrid optomechanical system in which a membrane oscillator is coupled to a collective spin of ground states of an intracavity ΛΛΛ-type three-level atomic medium. The cavity field response is greatly modified by atomic coherence and the anomalous dispersion generated by two Raman pumping beams near two-photon resonance. The optomechanical interaction, therefore radiation pressure force, is substantially enhanced due to superluminal propagation of photons in the cavity. Such improvement facilitates ground-state cooling of the mechanical oscillator with room temperature thermal environment. Moreover, it can greatly improve the sensitivity and bandwidth of displacement measurement. In such system, optically-controlled strong-coupling interaction between the mechanical oscillator and cavity field could be implemented on small intracavity photon number, even at the single quanta level, which is important for weak-light nonlinear photonics and the generation of nonclassical quantum states in the mechanical field.