Quantum Membranes – University of Copenhagen

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Quantum Membranes

Quantum Membranes

We pursue quantum experiments with membranes that are macroscopic and nano-scale at the same time: they are a millimeter across in size, so that the can be discerned with bare eye—but only 100 nm thick, that is just some thousand atom layers.

Tensioned strongly in a frame, they vibrate harmonically like a drumhead when hit with a stick. We use electromagnetic radiation—light land radio waves—instead to interact with their vibration modes.

The goal of this approach (termed Cavity Optomechanics [1-3]) is to explore the nature of these vibrations, and to probe and control them at an unprecedented layer of precision. These investigations become particularly intriguing when the peculiar features of quantum mechanics come into play. Among them are the light’s backaction on the membrane when its position is measured, and quantum correlations between the membrane motion and the measurement apparatus. But also in a purely classical domain, such mechanical devices are useful for novel types of sensors and transducers.

Transducing radio waves to light—mechanically

For example, we could show that a high-quality mechanical membrane can be coupled simultaneously to a radio-frequency resonance circuit and a propagating laser field [4]. A radio frequency signal (such as the green radio-wave in the artistic illustration above) then enforces vibrations of the membrane, which in turn induces a modulation of the reflected laser light’s phase. This we can recover with quantum-limited sensitivity. Overall, radio waves can thus be measured very accurately.

We have implemented such a device inspired by a recent proposal [5]. The coupling of the radio frequency signal to the membrane is realized by metallizing part of the membrane, and arranging it a few microns above a set of counterelectrodes, forming a capacitor whose capacitance depends on the membrane position. Electronic signals applied to this capacitor then exert an electrostatic force directly proportional to the radio-frequency field. A rf resonance circuit further enhances the force on the membrane. The strength of the electromechanical coupling can be quantified in terms of a cooperativity parameter C=4 g^2/Gamma_LC Gamma_m, which relates the rate g at which excitations of the electronic and the mechanical resonators are exchanged, and the loss rates of the radio-frequency (Gamma_LC) and mechanical resonators (Gamma_m). In our experiment, the electromechanical coupling can be sufficiently large that the classic signature of strong coupling [6], an avoided crossing, appears (right panel above). This corresponds to cooperativities up to 6800.

One particularly interesting feature of such electro-optomechanical transducers is that they can, in principle, also suppress the thermal noise usually added by the membrane, by a factor given by the cooperativity. With large C, and sufficiently low temperatures of the membrane, the link between the electronic and optical domain can thus potentially be quantum coherent [7], a goal now pursued in many labs worldwide [8, 9].

Quantum backaction optomechanics

We have developed membrane resonators that are shielded from detrimental effects of the environment better than ever before [10]. The membrane’s frame is integrated into a ~cm long silicon bridge whose structure is periodically modulated (left panel above). The acoustic dispersion of the bridge thus exhibits a full phononic bandgap [11], in which the propagation of acoustic waves is strongly suppressed. Matching this gap with the membrane’s vibrational frequency leaves us with very clean, unperturbed membrane modes.

By means of a high-finesse optical cavity, a membrane mode can be coupled to an optical field. Using a combination of cryogenic pre-cooling (right panel above) and, if necessary, laser cooling [12, 13], we expect that the thermal noise of the membrane will be sufficiently weak to allow us to study quantum correlations induced in the light-membrane system. By coupling the same light field additionally to an atomic ensemble, it is even predicted that the membrane motion can be measured beyond the standard quantum limit [14].

Development and characterization of novel optomechanical systems

We are constantly developing and testing new optomechanical devices in collaboration with the Quantum Photonics group at NBI and DTU Nanotech. In particular, we are interested in novel optomechanical coupling mechanisms in semiconductor materials [15], and the ultimate limits of mechanical dissipation of silicon nitride resonators. To characterize the samples we fabricate, we have set up a very sensitive interferometer (left panel above) that allows us to measure mechanical vibrations at the femtometer level. By scanning the sample, we can image the mechanical modes in 2D, enabling a comparison with the simulated target modes (right panel above).

The team

People involved:

  • Anders Simonsen (PhD)
  • William Nielsen (PhD)
  • Christoffer Møller (PhD)
  • Yeghishe Tsaturyan (Master)
  • Andreas Barg (Research Assistant)
  • Willi Carlsen (Master)
  • Albert Schliesser (Assistant Professor & Team leader)
  • Eugene Polzik (Professor & Center leader)

Formerly involved:

  • Tolga Bagci (PhD)
  • Andreas Næsby Rasmussen (PhD)
  • Dalziel Wilson (Postdoc)
  • Koji Usami (Associate Professor)
  • Bo Melholt Nielsen (PhD)


[1] M. Aspelmeyer, T.J. Kippenberg and F. Marquardt. Cavity Optomechanics, ArXiv:1303.0733v1

[2] T.J. Kippenberg and K.J. Vahala. Cavity Optomechanics: Back-Action at the Mesoscale, Science 321, 1172 (2008)

[3] A. Schliesser and T. J. Kippenberg. Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators, Advances In Atomic, Molecular, And Optical Physics 58, 207 (2010)

[4] T. Bagci, A. Simonsen, S. Schmid, L.G. Villanueva, E. Zeuthen, J. Appel, J.M. Taylor, A. Sørensen, K. Usami, A. Schliesser and E. S. Polzik. Optical detection of radio waves through a nanomechanical transducer, Nature 507, 81 (2013)

[5] J.M. Taylor, A.S. Sørensen, C.M. Marcus and E.S. Polzik. Laser cooling and optical
detection of excitations in a LC electrical circuit, Phys. Rev. Lett. 107, 273601 (2011).

[6] S. Gröblacher, K. Hammerer, M.R. Vanner and M. Aspelmeyer. Observation of strong coupling between a micromechanical resonator and an optical cavity field, Nature 460, 724 (2009)

[7] E. Verhagen, S. Deléglise, S. Weis, A. Schliesser and T. J. Kippenberg. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63 (2012)

[8] J. Bochmann, A. Vainsencher, D.D. Awschalom and A.N. Cleland. Nanomechanical coupling between microwave and optical photons. Nature Physics 9, 712 (2013)

[9] R W. Andrews, R.W. Peterson, T.P. Purdy, K.Cicak, R.W. Simmonds, C.A. Regal and K.W. Lehnert. Bidirectional and efficient conversion between microwave and optical light. Nature Physics 10, 321 (2014)

[10] Y. Tsaturyan, A. Barg, A. Simonsen, L.G. Villanueva, S. Schmid, A. Schliesser and  E.S. Polzik. Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics, Optics Express 22, 203879 (2014)

[11] M. Maldovan. Sound and heat revolutions in phononics, Nature 503, 209 (2013)

[12] A. Schliesser, P. Del'Haye, N. Nooshi, K.J. Vahala and T.J. Kippenberg. Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction, Phys. Rev. Lett. 97, 243905 (2006)

[13] A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet and T. J. Kippenberg. Resolved-sideband cooling of a micromechanical oscillator, Nature Physics 4, 416 (2008)

[14] K.Hammerer, M. Aspelmeyer, E.S. Polzik and P. Zoller. Establishing Einstein-Poldosky-Rosen Channels between Nanomechanics and Atomic Ensembles, Phys. Rev. Lett. 102, 020501 (2009)

[15] K. Usami, A. Næsby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl and E.S. Polzik. Optical cavity cooling of mechanical modes of a semiconductor nanomembrane, Nature Physics 8, 168 (2012)