Hybrid Mechanical Systems

The coupling of mechanical modes to quantized electronic states represents an active and growing area of research whose pursuit has produced a series of interesting results. Various groups have observed nanomechanical effects in mesoscopic transport devices, most notably in suspended nanotube and nanowire (NW) transistors. Coupling of nanomechanical resonators to controllable quantum systems such as quantum dots (QDs) and superconducting qubits is in its early stages. These developments, combined with the recently demonstrated ability to initialize nanomechanical oscillators in their ground state, mean that researchers can begin to couple a quantum nanomechanical harmonic oscillator to a quantum two-level system. Such an experimental system is a veritable playground for experiments on quantum coherence and measurement theory. We are working to carry out several experiments in this direction including the continuation of attempts to couple quantum point contacts (QPCs), QDs, and eventually an electronic Mach-Zehnder interferometer to a mechanical oscillator. From a practical perspective, such systems provide an avenue for designing sensitive detectors of mechanical displacement — detectors which approach the quantum limit.

The ability to make single electron transistors (SETs) and QDs out of nanotube and NW devices has allowed researchers to study electro-mechanical couplings in these systems. In particular, the effect of mechanical modes has been studied in both nanotube QDs [1] and NW field effect transistors (FETs) [2]. At the same time, the electronic transport has been observed to actuate mechanical modes in these devices. The development of these strongly coupled systems looks to be a fertile ground for future NEMS research and could lead to the coupling of a quantum twolevel system made from a QD electron spin and a quantum mode of mechanical motion. The combination of micromechanical structures with more complex mesoscopic systems such as an electronic Mach-Zehnder interferometer offers further opportunities. Theoretical work on the possibility of an electromechanical which-path interferometer by Armour and Blencowe suggests it as an intriguing system for testing fundamental ideas of decoherence [3]. An entirely different scheme for coupling mechanical motion to mesoscopic transport phenomena is illustrated by work in the group of Prof. Peter Grutter at McGill University. In 2010, his group demonstrated the use of AFM to image and characterize the energy levels of few-electron InAs QDs [4]. Their experiments show how sensitive electrostatic force detection can reveal Coulomb blockade phenomena, tunneling rates, charging energy, and even QD interaction energies of individual and coupled QDs. These kinds of “off-board” experiments in which a mechanical sensor — typically a cantilever — is coupled and scanned over a mesoscopic transport device may prove to be useful for characterizing transport devices in the future. An pertinent example of such work that has contributed to our understanding of QPCs and two-dimensional electron gases (2DEGs) is the development of scanning gate microscopy [5].

Our group has worked and continues to work on the development of sensitive detectors of nanomechanical motion. We have demonstrated the use of a QPC as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever [6]. The QPC was included in an active feedback loop designed to cool the cantilever’s fundamental mechanical mode, achieving a squashing of the QPC noise at high gain. The minimum achieved effective mode temperature of 0.2 K and the displacement resolution of 10-11 m/Hz1/2 was limited by the performance of the QPC as a one-dimensional conductor and by the cantilever-QPC capacitive coupling. Recently we have started a fundamentally new line of inquiry: the study of electro-mechanical couplings in NW FETs and QD devices. The short term goals of this effort include the measurement of the coupling of spin-dependent transport through a NW QD with mechanical modes in the NW itself. The coupling of a suspended NW QD to an “off-board” cantilever will then be investigated. The motivation here is similar to the motivation behind the QPC transducer experiments: we intend to make a sensitive transducer of cantilever displacement. The NWs could be ideal transducers as their 1D transport can be localized far closer to the cantilever motion than can the sub-surface transport through a QPC. This smaller spacing should result in larger capacitive couplings between the transport and the cantilever tip — resulting in better transduction efficiencies. In the long term, we intend to also investigate the NW QD using our ultra-sensitive cantilever force transducers. As shown by Cockins et al. [4], sensitive electrostatic force detection can reveal Coulomb blockade phenomena, tunneling rates, charging energy, and interaction energies in QDs. With our unique apparatus capable of coupling a cantilever and a suspended NW QD, we should be able to do similar experiments in these novel systems.

 

[1] G. A. Steele et al., Science 325, 1103 (2009).
[2] H. S. Solanki et al., Phys. Rev. B 81, 115459 (2010).
[3] A. D. Armour and M. P. Blencowe, Phys. Rev. B 65, 035311 (2004).
[4] L. Cockins et al., Proc. Nat. Acad. Sci. U.S.A. 107, 9496 (2010).
[5] M. A. Topinka et al., Science 289, 2323 (2000).
[6] M. Montinaro et al., Appl. Phys. Lett. 101, 133104 (2012).