# Research

### Complex Lasers

This project is focused on the physics of novel coherent light sources and generally, non-linear optical devices in the micro- and nano-scale. With the continuing demand for compact and power-efficient lasers and the tremendous progress in nanotechnology, a number of new laser systems have appeared that are far from the initial conception based on a Fabry-Perot type cavity. The underlying reason is the difficulty to produce highly reflective “mirrors” to trap light at small length scales. The novel lasers we study rely on rather unconventional mechanisms to confine light to tiny volumes and operate in regimes where traditional techniques of laser theory and non-linear optics fail. An important theoretical challenge posed by these novel photonic devices is their openness (leakiness) combined with their structural complexity. A few examples in this category are lasers based on mesoscopic dielectric cavities (particularly those in the wave-chaotic regime), photonic crystal defect cavities, hybrid cavities (plasmonic/dielectric) and random lasers.

A key component of this direction of research is the development of powerful numerical methods for realistic photonic devices, both in the quantum optical regime and the non-linear optical regime. A complementary, more mesoscopic physics inspired research direction is the generalization of certain concepts from condensed matter physics, such as quantum chaos, diffusive transport and Anderson localization physics, to nonequilibrium and non-linear (interacting) bosonic systems.

### Wave-chaotic Microcavities

For instance, wave-chaotic lasers rely on chaotic scattering of light within a tiny non-symmetric dielectric body to produce a fine balance between confinement and out-coupling. Despite the chaotic trajectory of light rays, due to a subtle interplay of interference and optical leakage, these lasers provide highly directional light emission. With respect to their electronic counterparts (electrically gated quantum dots) studied by quantum chaos theory, the novel feature here is unavoidable refractive leakage. This new field of optics, while producing a number of new devices, such as the high-power semiconductor ARC (Asymmetric Resonant Cavity) microlaser (a) and highly efficient spiral-shaped GaN blue/UV lasers (b), has also offered a major impetus for extending quantum chaos theory to mesoscopic optical systems.

### Random Lasers

In the case of random lasers, light confinement is achieved by multiple optical scattering from randomly distributed aggregate of sub-wavelength particles. The situation here is even more extreme. From device physics perspective, multiple optical scattering is generally thought to be detrimental to the operation of a conventional laser, such as for instance caused by rough surfaces in a Fabry-Perot cavity. However, the concept of random lasers turns this around: When the light scattering due to disorder is strong enough (and even if it’s weak, as found later) it can actually facilitate lasing action and this can be accomplished in the absence of any conventional mirrors. Considering that most of the effort in the fabrication process of microlasers goes into producing high-quality mirrors (e.g. DBR or photonic crystal defect cavities), random lasers are liable to offer robust and inexpensive sources of coherent light in future applications. For this reason, they are sometimes dubbed as “laser paint”.

In a particular variety of random lasers, namely the diffusive random lasers (DRLs), the diffusive escape of light is so rapid that such lasers exhibit no isolated resonances in the absence of gain. In conventional laser theory it is the long-lived linear resonances which evolve into non-linear and competing lasing modes in the presence of gain; hence the coherence of the lasing state and the nature of the lasing modes in DRLs has been controversial. Ongoing work together with collaborators at Yale and Nice University (Sophia Antipolis) aims to bring insight into this regime. Read about recent work uncovering some intriguing properties of DRLs.

### Numerical Methods for Complex Photonic Structures

Of important practical interest in photonics is the development of efficient numerical methods to calculate resonances of complex photonic systems and multi-component devices. This problem is particularly hard due to the open nature of the systems studied coupled with the fact that typically, the system we study are generally several optical wavelengths across (i.e. in the mesoscopic regime). We have developed highly efficient boundary methods which are O(N) faster than the standard boundary solvers based on singular value decomposition, where N is the number of wavelengths on the boundary. Boundary methods in turn typically employ numerical resources that are O(N) less than domain solvers based on discretization of the Laplacian on a discrete grid. This comes about by capturing solutions only in a spectral interval around a given frequency, ideal for most problems in photonics. Currently, we are working on extending these highly efficient methods to treat hybrid photonic structures (plasmonic/dielectric). The “low level” methods developed here form an integral part of our studies on lasing, non-linear optics and cavity QED in complex media.

### Cavity-QED With Real Cavities

This line of research in our group addresses the control of the coupling between single quantum emitters and its surrounding electromagnetic degrees of freedom via a complex light-confining structure at a level of few photons. One issue of interest relates to Purcell factors in complex photonic media. In vacuum, an emitter in its excited state would decay to its ground state at a characteristic rate called the spontaneous emission rate. This is purely due to the quantum nature of the electromagnetic degrees of freedom surrounding the emitter. It is well-known since the pioneering work of E. Purcell that a light confining structure may inhibit or enhance the spontaneous emission rate of an emitter with respect to its vacuum value. This fact has important bearing to applications ranging from single-molecule fluorescence spectroscopy to quantum information processing. We are working on developing highly efficient Green's function based methods to overcome important technical problems in the calculation of spontaneous emission rates of emitters in micro- and nano-structured photonic environments, opening the path to design-based approach to such systems. We are currently interested in strong coupling physics in cavity arrays and quantum information processing applications of cavity-QED systems.

### Strongly Correlated Quantum Optical Systems

Strongly correlated photons at first sounds paradoxical because strong correlations require interactions and photons are known to be non-interacting. Of course, photons do interact with each other indirectly via the material medium, leading to a plethora of interesting phenomena studied by non-linear optics. However, these typically require high intensities and at few-photon level, the interactions are often weak. With recent progress in cavity-QED however, non-linearities and hence strong interactions at few- photon level are within reach. The strong-coupling of electromagnetic and material degrees of freedom makes available new quasi-particles, polaritons, that exhibit a dual character inherited from each of the subsystems: interactions and coherent tunneling. Strongly correlated quantum many body systems have been central to our current understanding of states of matter, naturally occurring or artificial. Collective behavior arising from interactions of massive particles gives rise to some of the most intriguing phenomena known: superfluidity, superconductivity, Quantum Hall states, unconventional magnets. The study of strongly correlated photonic systems offer fascinating new directions as an emerging field. Our work in this exciting and new field aims at exploration of genuine non-equilibrium generalizations of these well-known strongly correlated systems in photonic media. One long-term perspective is the fabrication of well-controlled photonic devices that can act as "Quantum Simulators".

### Many-body Correlations In Disordered/Chaotic Electron Systems

Electron-electron interactions in disordered and chaotic closed nanostructures such as metal nanoparticles and electrically gated quantum dots (QDs) in the Coulomb-blockaded regime are well-captured within the framework of the “Universal Hamiltonian”. This framework has for instance been successfully applied to understanding the transport properties of QDs and magnetic properties of metallic nanoparticles in various regimes. In earlier work, we developed a numerical scheme which employs the exact eigenstates of the Universal Hamiltonian, which are good-spin states, to study the effects of additional perturbations. This approach proves to be extremely powerful when the perturbation is a one-body operator and/or the total spin of the system is conserved. Recently, we have extended this method to study Kondo physics in the presence of exchange correlations among the conduction electrons. There is a number of interesting questions concerning the Kondo effect when the conduction electrons which are supposed to screen the magnetic impurity themselves interact. Such a situation is realized when for instance a larger QD is coupled controllably to a smaller one by electrostatic gating. One aspect of this problem concerns the question of what happens if in addition to the Kondo-coupling between the dots, the electrons in the larger dot also interact among each other. The latter interaction, to leading order in the spin sector, is a ferromagnetic interaction, leading to a competition between the tendency of the larger dot to spin-polarize and the anti-ferromagnetic coupling to the smaller dot spin.

### Optical Manipulation of Solid State Qubits

Solid-state realizations of cavity-QED systems have employed a number of emitter-cavity combinations, with substantial progress demonstrated for self-assembled quantum dots embedded in nano- and microcavities, operating in the optical regime, or Cooper-pair boxes coupled to superconducting strip-line cavities, operating in the microwave regime. The emitters used in such quantum optical investigations are immersed in solid state environments where interactions with various environmental degrees of freedom lead to a complex dynamics of the emitters. In parallel, over the past years, research on condensed matter systems has been expanding gradually from exploration to substantial control of various interactions. This trend in turn has fed back to our understanding of a number of difficult problems of condensed matter physics by making it possible to selectively study certain many-body interactions while turning off others. It seems now clear that while complicated few- and many-body interactions in condensed matter systems give rise to non-ideal emitters from the perspective of QIP applications, they also provide means for an increased level of control once these interactions are well-understood. For instance, a spin degree of freedom defined in a self-assembled QD buried in Schottky-diode structure has interactions with various reservoirs. At low magnetic fields, the dominant spin-flip mechanism is the hyperfine interaction with the nuclear spin reservoir, while at high magnetic fields the dominant spin interactions derive from the phonon-assisted spin-orbit interaction. In addition, in Schottky-diode structures, the QD layer is separated from a strongly n-doped layer by a tunnel-barrier for controlled charging, giving rise to interactions of the electronic spin with the fermionic reservoir in certain gate voltage regimes. While this interaction would give rise to standard spin relaxation at high temperatures, when the temperature is reduced, a cross-over to Kondo physics is expected. Many times, QDs can conversely be used as optical probes of complex quantum many body phenomena.