Phonon Laser Demonstrated Using Trapped Ions
For decades there has been interest in phonon lasers, a device that operates in analogy to optical lasers, except replacing light with vibrational energy. Phonon lasers would amplify motion to the point of coherence through the process of stimulated emission, whereby the presence of energy quanta increases the chances that additional quanta are emitted. Now, researchers at the Max Planck Institute of Quantum Optics in Garching, Germany have realized such a device using a cold, harmonically bound, magnesium ion.
Reporting in the journal Nature Physics , the ion was first laser cooled to a temperature of around 1 milliKelvin in an electromagnetic trap, and then a second laser was applied, whose wavelength was precisely adjusted so as to create mechanical (not optical) amplification through the process of stimulated emission of phonons. The phonons are associated with the center-of-mass motion of the ion in the electromagnetic trap. As such, phonon stimulated emission causes the ion to oscillate, once a threshold condition is achieved (figure).
Sequence of time-averaged images showing coherent motion of the phonon laser. At the far left, the magnesium ion is cooled to approximately 1 milli-Kelvin using a red-detuned laser. In each subsequent image, an additional, blue-detuned pump laser is stepped in intensity. Beginning around the fifth trace, laser threshold is achieved at which point mechanical amplification compensates mechanical damping. Beyond this threshold pumping level, the motion is sustained by stimulated emission of phonons and stabilized by saturation of the amplification. The ions oscillate vertically in the figure, and the brighter end points in each image result from the ion slowing and eventually stopping to reverse motion.
“The possibility of phonon laser action has been considered dating back to the earliest days of the optical laser, nearly 50 years ago,” notes Kerry Vahala, who is currently a guest scientist at the Max Planck Institute of Quantum Optics in Garching, on leave from Caltech. He adds that the possible ways to realize these devices are as numerous as those used for conventional optical lasers, and ultimately, many other types of phonon lasers including those in the solid-state are possible.
“Laser-cooled ions are, however, a very good starting point to explore the physics of these intriguing devices,” notes Thomas Udem. Udem observes that they can be precisely controlled and manipulated, because of a multi-decade effort directed towards exploration of quantum phenomena using chains of cold ions. That history is also interesting in another respect.
“The physical mechanism that is responsible for amplification and stimulated emission of phonons has, over the last decades, been misunderstood as a different phenomenon referred to as heating,” says Maximilian Herrmann. He explains that the regime of heating was always associated with laser pumping using a wavelength that is blue-detuned, relative to an optical transition of the trapped ion. In stark contrast, the Garching team was able to show that the regime is, in fact, one of phonon laser action.
In the experiment, the ion was simultaneously cooled using a red-detuned laser and also pumped to create stimulated phonon amplification using the blue-detuned beam. The cooling laser also allowed the researchers to introduce a controlled amount of damping into the system. To understand the origin of amplification in the ion system, consider the so-called small-signal regime with the blue detuned pumping beam. This interaction involves a second-order quantum process in which a pump photon is absorbed, followed by emission of center-of-mass phonon.
Herein, the role of atomic transition damping is crucial. As is also true in a conventional optical laser oscillator, the transition damping is fast enough so as to quench the underlying Rabi dynamic. As a result, the rate of emission of phonons can be shown to contain a stimulated component that is proportional to the number of phonons, and also a component that is purely spontaneous (and responsible for starting the motion in the first place). The stimulated term, as in a conventional laser, produces the amplification that ultimately creates the coherent motion.
The transition from purely thermal motion to coherent motion is marked by a threshold pumping power, where stimulated amplification balances ion motional damping. As pumping is further increased through this threshold, coherence emerges and is visible in images of the ion motion (figure). Ultimately, the large signal motion of the ion saturates the stimulated amplification. The saturation process in the ion is, itself, interesting as it involves a competing phonon absorption process. In effect, as the coherent motion grows in amplitude, this phonon absorption competes more effectively with the stimulated emission and saturates the net amplification. Generally speaking, saturation of amplification is an essential feature of all regenerative oscillators, and makes possible stable coherent motion.
The mechanism of amplification through scattering of a pump photon and generation of a stimulated phonon is in some ways analogous to the process of Raman optical amplification in which a pump photon scatters to produce a stimulated (and amplified) optical Stokes wave . In that process, a phonon is also produced, but is so strongly damped that it effectively serves to only assist the overall amplification of light as an intermediate process. In the ion phonon laser system, on the other hand, this situation changes dramatically.
The researchers note that the pump photon creates both a polarization excitation and a phonon; but in a peculiar twist, the phonon switches out of its conventional “supporting” role, and, because of the very low damping rate of phonons in the ion system, takes-on the lead role analogous to the optical Stokes mode in the conventional optical Raman process. This feature of the stimulated phonon process in the ionic system can be made mathematically precise; and also helps to explain, as is true in optical Raman lasers, operation without an obvious inversion.
Current research is directed towards controlling the phonon laser using tools and techniques that can be adapted from the laser world. One example is a process called injection locking whereby a weak, external control field is used to phase-synchronize the phonon laser with an external reference. The team has recently used this method to image the coherent motion of the ion as it oscillates. Also interesting is the possibility of studying excitations in chains of ions and even two-dimensional arrays of ions.
Concerning applications, Professor Theodor Hänsch notes, “the fact that the forces involved here are so weak suggests that this phenomenon might prove useful as a weak force probe.” He adds, “it is always important when a phenomenon or idea can be reduced to practice.” Along these lines, the Garching work has already inspired realization in a very different system of phonon laser action .
 K. Vahala, M. Herrmann, S. Knünz, V. Batteiger, G. Saathoff, T. W. Hänsch & Th. Udem, “A phonon laser,” Nature Physics, 5, 682 – 686 (2009). Abstract.
 Shen, Y. R. & Bloembergen, N. “Theory of stimulated Brillouin and Raman
scattering,” Phys. Rev. 137, 1787–1805 (1965). Abstract.
 Ivan S. Grudinin, O. Painter, Kerry J. Vahala, “Phonon laser action in a tunable, two-level photonic molecule,” arXiv:0907.5212v1 (2009).