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arXiv:1201.6293 · Bulletin of the American Physical Society

Quantum transducer in circuit optomechanics

Nicolas Didier, Pugnetti, Stefano, Yaroslav M. Blanter, Rosario Fazio

Published Jan 30, 2012• 0 citations
arXivHTMLPDF

Abstract

Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon state can be synthesized and measured with a quantum tomography. We show that a linear coupling, strong and controlled with a gate voltage, between the mechanical and the microwave resonators enables to create quantum phonon states, manipulate hybrid entanglement between phonons and photons and generate entanglement between two mechanical oscillators. In circuit quantum optomechanics, the mechanical resonator acts as a quantum transducer between an auxiliary quantum system and the microwave resonator, which is used as a quantum bus.

DOI
10.48550/arxiv.1201.6293

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Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon state can be synthesized and measured with a quantum tomography. We show that a linear coupling, strong and controlled with a gate voltage, between the mechanical and the microwave resonators enables to create quantum phonon states, manipulate hybrid entanglement between phonons and photons and generate entanglement between two mechanical oscillators. In circuit quantum optomechanics, the mechanical resonator acts as a quantum transducer between an auxiliary quantum system and the microwave resonator, which is used as a quantum bus.
In the past several years, the field of optomechanics has progressed from proof-of-principle experiments to the realization of mechanical oscillators and measurements in the quantum regime. Mechanical oscillators are of great interest because they can have small dissipation rates, can couple to many different systems of interest, and are the fundamental elements of ultrasensitive force detectors. Coupling these mechanical oscillators to microwave or optical fields provides a twofold advantage. Firstly, information about mechanical position can be encoded in the interrogating field, enabling sensitive readout of the mechanical oscillator. Secondly, the radiation pressure force of that field can be used to control the state of the mechanical oscillator. Including a high-quality microwave or optical cavity enhances both of these effects, as the field strength is resonantly increased.\nThe major questions in the field of optomechanics in the last several years have dealt with using mechanical oscillators for ultrasensitive measurements and as tools for quantum information. Both of these goals have the prerequisite that we be able to read out the motion of the mechanical oscillator in a quantum efficient manner. To that end, we developed a nearly shot-noise limited microwave interferometer capable of measuring mechanical motion with an imprecision below that at the standard quantum limit. This achievement is not only a critical improvement for the electromechanical experiments we do, but is also an important tool for any experiment that encodes the information of interest in microwave fields. In order to use mechanical oscillators as tools for quantum information, the mechanical oscillator must also be cooled into the quantum regime and fully controllable by the interrogating fields. To this end, we used the radiation pressure of microwave fields to cool our macroscopic mechanical oscillator to less than one phonon. We also demonstrated coherent transfer between itinerant microwave states and the mechanical oscillator, even for incident fields with less than one photon of energy.\nThese accomplishments have set the foundation for further experiments to extend the quantum information abilities of optomechanical systems, couple diverse quantum systems via a mechanical intermediary, and potentially explore the foundations of quantum mechanics at macroscopic scales.
We review the use of mechanical oscillators in circuit quantum electrodynamics. The capacitive coupling of nano-electromechanical systems with quantum bits and superconducting microwave resonators gives rise to a rich quantum physics involving electrons, photons and phonons. We focus in particular on the linear coupling between a mechanical oscillator and a microwave resonator and present the quantum dynamics that stems from the phonotonic Josephson junction. The microwave cavity turns out to be a powerful device to detect quantum phonon states and manipulate entangled states between phonons and photons.
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.
Summary form only given. The motion of a micromechanical resonator coupled simultaneously to a high-finesse optical cavity and a microwave resonator can be used to transduce the fragile quantum states generated in the realm of microwave superconducting circuits into optical photons that can transport quantum information over large distances in telecom optical fibers at room temperature. We have engineered the optical and mechanical properties of thin membranes patterned in a suspended high-stress Si3N4 film to realize such a hybrid opto-electro-mechanical system. An optical Fabry-Perot cavity with a finesse exceeding 12 000 was realized between a highly reflective photonic crystal patch realized on the suspended membrane and a conventional high-reflectivity mirror. The electromechanical coupling with a nearby planar superconducting circuit is achieved by approaching the membrane at a sub-micron distance from an on-chip interdigitated capacitor. By operating the hybrid opto-electro-mechanical system in a cryogenic environment, the photon-phonon swap rates between microwave, mechanical, and optical degrees of freedom is expected to overcome the mechanical decoherence rate. An artist view of the device envisioned is depicted on Figure 1.
Quantum states encoded in microwave photons or qubits can be effectively manipulated, whereas optical photons can be coherently transferred via optical fibre and waveguide. The reversible conversion of quantum states between microwave and optical photons will hence enable the distribution of quantum information over long distance and significantly improve the scalability of hybrid quantum systems. Owning to technological advances, mechanical resonators couple to quantum devices in distinctly different spectral range with tunable coupling, and can serve as a powerful interface to connect those devices. In this review, recent theory and experimental progress in the coherent conversion between microwave and optical fields via optoelectromechanical transducers are summarized. The challenges and perspectives in achieving single‐photon‐level quantum state conversion are also discussed.
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton-mechanical mode and a nonlinear transmon-mechanical mode interaction in the strong coupling regime. Together with the strong resonator-transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.