From Institute for Theoretical Physics II / University of Erlangen-Nuremberg
- 1 Overview Talk: Optomechanics
- 2 General Review: Optomechanics
- 3 Light interacting with mechanical motion
- 4 Optomechanics: A playground for nonlinear classical dynamics
- 5 Optomechanics: Into the quantum regime
- 6 Interesting physics in the quantum regime
- 7 New directions
- 8 The radiation pressure challenge
Overview Talk: Optomechanics
- At a special APS March Meeting session (Portland meeting 2010), Florian Marquardt talked about optomechanics. Watch the video
General Review: Optomechanics
- We wrote an easily understandable review on optomechanics: F. Marquardt and S. M. Girvin, Physics 2, 40 (2009) Journal PDF Cite
Light interacting with mechanical motion
In recent years, the fields of micro-/nanomechanics and cavity quantum electrodynamics have seen considerable progress, and people have started to investigate their combination. The simplest possible system to consider in this regard is an optical cavity with a movable mirror (for example, attached to a cantilever). Long-term efforts are directed towards observing quantum dynamics both in the light field and the mechanical part, and creating entanglement between optical and mechanical degrees of freedom.
Optomechanics: A playground for nonlinear classical dynamics
The interaction of radiation with the mechanical motion of a macroscopic object can give rise to intricate nonlinear dynamics. This holds in particular for the standard optomechanical setup, where both the intensity of the radiation and its sensitivity to the mechanical motion are amplified by exploiting an optical cavity. Beyond a certain threshold in input laser power, the cantilever suddenly starts to oscillate by itself, extracting the required energy from the radiation field. This is similar to lasing action, but here the result is a self-amplified mechanical oscillation, pumped by the optical field. The existence of the instability itself was known for some time (particularly as a potential nuisance in interferometric gravitational wave detection), when we started a more detailed analysis. This led to our finding a rather surprising attractor diagram, with many possible attractors for the long-time dynamics of the system: "Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities" F. Marquardt, J. G. E. Harris, and S. M. Girvin, Phys. Rev. Lett. 96, 103901 (2006)
Indications of the instability in micro-optomechanical systems had been observed before, [T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005)], but the existence of the attractor diagram was not anticipated or concluded from the data. Therefore, after the theoretical predictions of our work were made, this inspired a systematic experimental exploration of this attractor diagram. This was performed in the group of Khaled Karrai at the LMU, with whom we collaborated on this topic. The outcomes of that experiment confirmed the theory as applied to the experimentally accessible regime, where dynamical bistability was found. In addition, completely unexpected behaviour at higher driving strengths led us to the insight that there are regimes where multiple mechanical modes go unstable simultaneously:
Self-Induced Oscillations in an Optomechanical System Constanze Metzger, Max Ludwig, Clemens Neuenhahn, Alexander Ortlieb, Ivan Favero, Khaled Karrai, and Florian Marquardt, Phys. Rev. Lett. 101, 133903 (2008)
As pointed out in our 2006 PRL, the nonlinear attractor diagram might be exploited in ultrasensitive measurements, a proposal yet to be implemented. By now, the optomechanical nonlinear attractor diagram has also been predicted to occur in other systems. The following theory work by the Armour group finds that they can (surprisingly) directly map our theory to a system where the driven optical cavity is replaced by a current-biased superconducting single electron transistor, which at first glance looks very different from the harmonic oscillator representing the optical mode [Dynamical instabilities of a resonator driven by a superconducting single-electron transistor, DA Rodrigues, J Imbers, TJ Harvey, AD Armour, New J. Phys. 9, 84 (2007)].
Optomechanics: Into the quantum regime
Currently, a lot of groups in the field focus on getting mechanical oscillators into the ground state of motion, to observe quantum effects. Cooling in optomechanical systems was investigated first by active feedback cooling mechanisms (Paris group; Heidmann, Pinard, Cohadon). In 2004, Constanze Metzger and Khaled Karrai at the LMU Munich published the first experiment on intrinsic cooling. In their setup, it was a bolometric light force that induced the effect (though the theory for this case is the essentially the same as for the radiation pressure force, in the regime they considered). Subsequently, groups in Paris (see above; Arcizet et al.), Munich (Kippenberg group), and Vienna (Aspelmeyer) quickly reported cooling using the radiation pressure force, in a series of papers in 2006. In the meantime, novel kinds of setups like the one of Jack Harris in Yale (see below), Konrad Lehnert at Boulder, and Nergis Mavalvala at MIT, have joined the race to the ground state of a macroscopic mechanical oscillator.
In our 2007 work on the quantum theory of optomechanical cooling, we pointed out that ground-state cooling will be possible only if one reaches the 'resolved sideband' regime (large optical finesse, high mechanical quality):
Quantum Theory of cavity-assisted sideband cooling of mechanical motion F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Phys. Rev. Lett. 99, 093902 (2007)
A theory that pointed out the similarities to ion trap sideband cooling was simultaneously developed by I. Wilson-Rae, N. Noshi, W. Zwerger, and T. Kippenberg, coming to the same essential conclusion. By now, several groups have reached this regime, although actual ground-state cooling itself still remains to be demonstrated in the lab. See, in particular: Schliesser, A.; Riviere, R.; Anetsberger, G.; Arcizet, O.; et al.; Resolved Sideband Cooling of a Micromechanical Oscillator. Nature Physics 2008, 4, 415; and Teufel, J.D.; Regal, C.A.; Lehnert, K.W. Prospects for cooling nanomechanical motion by coupling to a superconducting microwave resonator. arXiv:0803.4007 (2008).
Interesting physics in the quantum regime
Once one is in the quantum regime, there is a wealth of possibilities. One might entangle the light and the mechanical motion, or produce nonclassical states of the cantilever. We recently analyzed the quantum version of the optomechanical instability: The optomechanical instability in the quantum regime M. Ludwig, B. Kubala, and F. Marquardt, New Journal of Physics 10, 095013 (2008)
We found that there is a certain "quantum parameter" that characterizes how strong the genuinely quantum effects will be. This parameter is quite small in typical setups with a movable mirror. However, recent experiments on cold atoms coupled to radiation inside a cavity have now reached a regime, where this parameter can become on the order of one, making it possible in principle to see the quantum effects we predicted: Brennecke, F., Ritter, S., Donner, T. & Esslinger, T.: Cavity opto-mechanics with a Bose-Einstein condensate (2008). arXiv:0807.2347.
As soon as one is able to make the cantilever motion quantum, it would be interesting to find ways of directly detecting the 'quantumness' of motion in a convincing way. Probably the most obvious proof would be to detect 'quantum jumps' between different cantilever quantum states, i.e. detect the phonon number in a time-resolved fashion. This is not simple to do using the standard setups. Recently however, the experimental group of Jack Harris (in collaboration with Steve Girvin and us) came up with an experimental setup that holds the potential for QND phonon number measurements: Strong dispersive coupling of a high finesse cavity to a micromechanical membrane J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, Nature 452, 72 (2008)
More details on the theoretical side of this work can be found in the following publication, where you learn about the intricate dynamics in this system as well as about a more detailed analysis of the QND measurement process:
Dispersive optomechanics: a membrane inside a cavity A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, New Journal of Physics 10, 095008 (2008)
The field of optomechanics is recently branching out into new directions. These include coupling light to the motion of cold trapped atoms, and using microwaves in superconducting circuits instead of optical radiation. For a brief review of these recent developments, see our 'News&Views' contribution, "Optomechanics: Push towards the quantum limit" F. Marquardt, Nature Physics 4, 513 (2008)
All of the previously mentioned topics and findings (nonlinear dynamics in the classical and quantum regimes, theory of ground-state cooling, QND phonon number detection) will find new applications in these alternative implementations of the basic optomechanical system.
The radiation pressure challenge
Go to the Prize Challenge page to learn more about how to win 2000 EUR by coming up with a clever simple design for demonstrating radiation pressure!