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arXiv:cond-mat/0601019 · Physical Review B

Quantum electromechanics: Quantum tunneling near resonance and qubits from buckling nanoscale bars

Sergey E. Savel'ev, Aleksandr L Rakhmanov, Xuedong Hu, Alik Yu. Kasumov, Franco Nori

Published Apr 25, 2007• 33 citations
arXivHTMLPDF

Abstract

Analyzing recent experimental results [Reulet et al., Phys. Rev. Lett. 85, 2829 (2000); Izmalkov et al., Europhys. Lett. 65, 844 (2004)], we find strikingly similar behaviors between two very different systems: three-junction superconducting qubits and suspended carbon nanotubes. When these different systems are ac-driven near their resonances, the resonance single-peak, observed at weak driving amplitudes, splits into two subpeaks for strong driving amplitudes. We describe this unusual behavior by considering quantum tunneling in a double well potential. Inspired by these experiments, we propose a mechanical qubit based on buckling nanoscale bars (nanobars)---a nanoelectromechanical system so small as to be quantum coherent. We consider how this nanomechanical qubit can be manipulated. A comparison between nanobars and superconducting qubits suggests several future experiments on quantum electromechanics.

DOI
10.1103/physrevb.75.165417

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Analyzing recent experimental results [Reulet et al., Phys. Rev. Lett. 85, 2829 (2000); Izmalkov et al., Europhys. Lett. 65, 844 (2004)], we find strikingly similar behaviors between two very different systems: three-junction superconducting qubits and suspended carbon nanotubes. When these different systems are ac-driven near their resonances, the resonance single-peak, observed at weak driving amplitudes, splits into two subpeaks for strong driving amplitudes. We describe this unusual behavior by considering quantum tunneling in a double well potential. Inspired by these experiments, we propose a mechanical qubit based on buckling nanoscale bars (nanobars)---a nanoelectromechanical system so small as to be quantum coherent. We consider how this nanomechanical qubit can be manipulated. A comparison between nanobars and superconducting qubits suggests several future experiments on quantum electromechanics.
We propose a mechanical qubit based on buckling nanobars—a nano-electromechanical system so small as to be quantum coherent. To establish buckling nanobars as legitimate candidates for qubits, we calculate the effective buckling potential that produces the two-level system and identify the tunnel coupling between the two local states. We propose different designs of nanomechanical qubits and describe how they can be manipulated. Also we outline possible decoherence channels and detection schemes. A comparison between the well-studied charge and flux superconducting qubits suggests several experimental setups which could be realized using available technology.
We propose a mechanical qubit based on buckling nanobars--a NEMS so small as to be quantum coherent.To establish buckling nanobars as legitimate candidates for qubits, we calculate the effective buckling potential that produces the two-level system and identify the tunnel coupling between the two local states. We propose different designs of nanomechanical qubits and describe how they can be manipulated. Also we outline possible decoherence channels and detection schemes. A comparison between the well studied charge and flux superconducting qubits suggests several experimental setups which could be realized using available technology.
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or a superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device to a superconducting circuit. Suspended carbon nanotubes act as both superconducting junctions and moving elements in a Superconducting Quantum Interference Device (SQUID). We observe a strong modulation of the flux through the SQUID from displacements of the nanotube. Incorporating this SQUID into superconducting resonators and qubits should enable the detection and manipulation of nanotube mechanical quantum states at the single-phonon level.
We introduce the “displacemon” electromechanical architecture that comprises a vibrating nanobeam, e.g., a carbon nanotube, flux coupled to a superconducting qubit. This platform can achieve strong and even ultrastrong coupling, enabling a variety of quantum protocols. We use this system to describe a protocol for generating and measuring quantum interference between trajectories of a nanomechanical resonator. The scheme uses a sequence of qubit manipulations and measurements to cool the resonator, to apply two effective diffraction gratings, and then to measure the resulting interference pattern. We demonstrate the feasibility of generating a spatially distinct quantum superposition state of motion containing more than 10^6 nucleons using a vibrating nanotube acting as a junction in this new superconducting qubit configuration.
Superconducting fluxonium qubits show a highly tunable energy-level structure, with transition frequencies spanning from a few MHz to few GHz. This range is well-aligned to the operational frequencies of highly coherent micro- and nano-mechanical resonators, making fluxonium an attractive candidate for hybrid electromechanical systems. In this work, we theoretically investigate a flux-tunable electromechanical system consisting of a fluxonium qubit coupled to a suspended mechanical resonator. The coupling arises from the motion-induced modulation of magnetic flux through the fluxonium loop, enabling both transverse and longitudinal electromechanical interactions that are tunable via external magnetic fields. By optimizing the design parameters of the fluxonium qubit, we demonstrate the feasibility of achieving strong resonant single-photon coupling near the flux-frustration point. We analyze the system dynamics across different coupling regimes, identifying signatures of electromagnetically induced transparency (EIT) in the longitudinal regime and mode splitting in the transverse regime. Additionally, we show that ground-state preparation of both subsystems is possible through sideband cooling of the mechanical resonator. These results suggest that a fluxonium-based hybrid electromechanical device could be a promising platform for studying macroscopic quantum phenomena and for applications in quantum technology.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.