492. WE-Heraeus-Seminar: Micro & Macro-Cavities in Classical and Non-Classical Light

Scientific background:

In recent years Whispering-Gallery Mode resonators changed from “A solution that seeks a problem” to a versatile tool in a multitude of fields, from precise frequency standards and frequency combs, opto-mechanical resonators, single virus detection, and ultra-efficient squeezed light sources, to efficient coherent frequency converters. Their success stems mainly from the strong confinement of light on a small footprint. Record quality factors from 108 to 1011 have been achieved, allowing for internal field intensities of peta-Watt per m2 at moderate pump powers, enabling the observation of nearly any non-linear effect in a small table-top experiment.

The basic idea behind dielectric resonators and in particular whispering gallery mode (WGM) resonators is the confinement of light via total internal refection at the dielectric interface. In a circular geometry, the angle of incidence of a light-ray inside the dielectric is conserved. Thus light that is trapped via total internal reflection can only leak out via scattering at a rough boundary, or by curvature-induced radiation. Such a travelling wave along the perimeter of a circular geometry is called whispering gallery mode, due to the analog to the acoustic phenomenon. Though this principle is common for most dielectric resonators, the experimental manifestation is vastly different. Mie Scattering, the scattering of electromagnetic radiation from dielectric spheres, can be seen as the first study of WGM (Mie 1908). Their results were important for understanding radar scattering from rain and hail. Thus, one of the first thoroughly studied WGM resonators were droplets (Benner et al. 1980). Surface tension induces a nearly perfect interface and reduces scattering from boundary roughness. Liquid droplets have been studied in pulsed preparation, caught in optical or ion-traps (S. Arnold and Hessel 1985), or planted onto hydrophobic surfaces (Sennaroglu et al. 2007). Their quality factors (Q) where in the order of 104-106 thus Raman lasing (Snow et al. 1985) and by including lasing dye or quantum dots into the solution, conventional lasing was readily achievable (Schäfer et al. 2008).

Another surface tension induced resonator type is the molten glass sphere. Braginsky and co-workers (Braginsky et al. 1989) were the first to realize that by melting high-grade silica glass fibers, nearly perfect spheres are formed at the end of the fiber. These microspheres are by now 20 years old, and find their use in applications from single virus detection (Vollmer and Arnold 2008) and by including rare earth dopants into the glass, lasing (Miura et al. 1996).

Lithographical fabrication of dielectric resonators has the benefit of mass-production of nearly any geometry and any material (McCall et al. 1992). Efficient add-drop filters, division multiplexer, etc. have been achieved based on the principle of coupling waveguides to resonators (Little et al. 1997). They are only limited by the surface roughness of the resonators. The flexibility in the geometry opened the whole field of asymmetric resonant cavities, with records in high power quantum cascade laser (Gmachl et al. 1998) and sub-wavelength laser (Song et al. 2009). Theoretical descriptions of modal structures in deformed cavities cannot be solved in the framework of Mie resonances, due to the non-integrability of the geometric system, leading to wave-chaotic formulations (Nöckel and Stone 1997). The full interaction of such non-trivial resonance structures with non-uniform gain regions was only recently solved in the framework of a self-consistent lasing theory (Türeci et al. 2008).

Vahala and co-workers managed to combine the benefits of lithographic production and surface tension induced smoothness, by creating micro-toroids out of silica on silicate (Armani et al. 2003). Recently these resonators showed a coupling of their WGM resonances to their mechanical resonances via the radiation pressure of the light (Kippenberg et al. 2005). Such opto-mechanical coupling allowed for sideband cooling of a single mechanical mode close to the quantum-mechanical ground-state (Kippenberg and Vahala 2008). In 2005, the invention of the frequency comb by Ted Hänsch was honored with the Nobel Prize. Recently, toroidal cavities achieved frequency comb generation on a chip (Del'Haye et al. 2007) and very recently octave spanning operation.

A limit in the quality factor of all of the above resonators is the absorption of light in the material. Crystalline materials with record low absorption can only be formed into WGM resonators by polishing the material. Record quality factors of 1011 have been achieved in CaF2 resonators (Grudinin et al. 2006). Another field for crystalline resonators are microwave standards, where cryogenic sapphire disks are used (McNeilage et al. 2004; Locke et al. 2008).

Experiments in quantum optics can benefit from WGM resonator setups in two different aspects. First, WGM resonators provide strong coupling of the field to other quantum systems like quantum dots, atoms, or other cavities. Second, quantum properties of the field can be influenced the via non-linearities in the WGM resonator medium. Possibilities lie in utilizing either χ(3) effects in silica micro-resonators for direct integration into integrated quantum optical circuits, or with χ(2) effects in crystalline materials, where unsurpassed optical and mechanical Q lead to extreme non-linearities. The generation of squeezing and entanglement, coherent wavelength conversions, and quantum memories are all within reach to be realized in dielectric micro and macro cavities. In addition, WGM resonators may provide efficient narrowband photon sources for quantum information protocols.

The high quality factors combined with small mode volumes of WGM resonators have made them attractive for studying effects in quantum optics. In order to reach the strong coupling regime in cavity quantum electrodynamics (cavity QED) it is of importance to have both, high quality factor and small mode volume at the same time. WGM fulfill both requirements leading to unsurpassed coupling of the light field to an atomic system. Experimental investigations with microspheres WGM resonators and atoms (Vernooy et al. 1998; Aoki et al. 2006; Mazzei et al. 2007) as well as with NV centers in diamonds, have been performed (Schietinger et al. 2008). In order to achieve coupling of a WGM resonator to a specific atomic transition, largely tuneable resonators are needed. So called “bottle resonators” have been proposed to fill this void (Louyer et al. 2005).

Non-classical light is in general generated from strongly non-linear bulk crystals. Recently the nonlinear response of crystalline WGM disk resonators made from Lithium Niobate opened the route to perform experiments to create nonclassical light in WGM resonators with unprecedented parameter regimes (Fürst et al. 2009).
With these first results new routes towards quantum information and quantum computation are opened. In general, the control of non-linearities can lead to gates, memories and efficient quantum state generation. WGM resonators can readily reach these regimes and further the possibility of large-scale integration.

Aims:

This seminar which is kindly supported by the Wilhem and Else Heraeus Foundation will try to bring together experts from the diverse communities that apply whispering gallery mode resonators to their needs. From the early adaptors, to the current players in the field, experts of complementary experience and know-how, including theoretical aspects as well as experimental issues, will be invited. The seminar is intended to provide a good introduction for newcomers from areas, such as quantum optics and metrology that are interested in harvesting the potential of WGM resonators in their fields. Thus the seminar will be a good opportunity for PhD students and young post-docs to get introduced to this exiting field. Bringing together an international group of young researchers will further initiate mutually beneficial exchanges between these groups and can be expected to stimulate stronger collaborations in the field between the participating research groups.

List of invited speakers:

Andrea Aiello, MPI for the science of light, Erlangen
Oliver Benson, Humboldt University, Berlin
Warwick Bowen, University of Queensland, Brisbane, Australia
Ingo Breunig, University of Freiburg
Hui Cao, Yale University, New Haven, USA
Tal Carmon, University of Michigan, USA
Jörg Evers, MPI for nuclear physics, Heidelberg
Stefan Götzinger, MPI for the science of light, Erlangen
Mikhail Gorodetsky, Moscow State University, Russia
Tobias Kippenberg, École Polytechnique fédérale de Lausanne, Switzerland
Ping Koy Lam, Australian National University, Australia
Florian Marquardt, University of Erlangen-Nuremberg
Thomas Pertsch, University of Jena
Arno Rauschenbeutel, Technical University of Vienna, Austria
Nathaniel Stern, California Institute of Technology, Pasadena, USA
A. Douglas Stone, Yale University, New Haven, USA
Dmitry Strekalov, Jet Propusion Laboratory, NASA, Pasadena, USA
Hakan Türeci, Princeton University, USA
Kerry Vahala, California Institute of Technology, Pasadena, USA
Frank Vollmer, MPI for the science of light, Erlangen
Jan Wiersig, University of Magdeburg
Josef Zyss, ENS de Cachan, CNRS, France