Mechanical systems in the quantum regime

Abstract

Mechanical systems are ideal candidates for studying quantum behavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum mechanics

Single-crystal diamond nanomechanical resonators with quality factors exceeding one million

“…To explore the potential of diamond nanomechanical resonators for millikelvin applications 3,8 , we have investigated dissipation in the best electronic-grade resonator down to about 0.1 K. These data are shown in Fig. 2b.…”

“…7). Resonators coupled to optical cavities 8 or spins 9 are furthermore intensively explored as quantum mechanical device elements in quantum science and technology.…”

Lifting the Franck-Condon blockade in driven quantum dots

“…Such a quantum dot may be realized on a suspended CNT using electronic back gates to confine an electron in a specific section of the nanotube. 6,[9][10][11][12][15][16][17]20 The vibrations of the CNT can be strongly coupled to the charge degree of freedom of the electron and thus have a great influence on its conductive properties. 12,20,21 Additionally, a back gate can be used to apply an ac voltage, thus modulating the dot energy level.…”

“…Interestingly, the situation is different at the mesoscale, where the interplay between the electronic and mechanical degrees of freedom can be engineered in a fashion that allows for the incorporation of mesoscopic constituents into a wide variety of setups. [5][6][7][8] Suspended carbon nanotubes (CNTs) which are free to vibrate comprise exactly such mesoscopic electromechanical systems. 6 CNTs are superb mechanical oscillators due to (i) their high Q-factors and stiffness, 9,10 (ii) high vibrational frequencies in the GHz range, 11 and (iii) large electron-phonon coupling.…”

“…[5][6][7][8] Suspended carbon nanotubes (CNTs) which are free to vibrate comprise exactly such mesoscopic electromechanical systems. 6 CNTs are superb mechanical oscillators due to (i) their high Q-factors and stiffness, 9,10 (ii) high vibrational frequencies in the GHz range, 11 and (iii) large electron-phonon coupling. 12 Besides these mechanical properties, the electronic and transport properties of CNTs can also be tuned depending on the setup.…”