Self-organization

Photons carry momentum and their scattering thus not only modifies light propagation but induces forces on particles. Hence, coupling mobile scatterers to the modes of nonlinear optical devices such as optical resonators or optical nano-fibers generates complex coupled nonlinear dynamics. The induced long-range dipole-dipole interactions and collective scattering induces a phase transition from random order to a crystalline structure for illumination at sufficient power. This minimizes the optical potential energy of the particles in concurrence with a maximization of light scattering into the resonator. Such adaptive self-ordering dynamics in optical resonators can be implemented in a wide range of systems from cold atoms and molecules to mobile nanoparticles in solution.

In the quantum regime ultracold atoms in resonators establish a promising platform for investigating emergent phases of complex quantum matter in a well-controlled environment. This enables the exploration of intriguing many-body effects such as Dicke superradiance, supersolidity, spontaneous quasi-crystallization and spin self-ordering.

Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose-Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. Recent developments and the current status in the field of quantum-gas cavity QED are described pedagogically in our extensive review article.

• F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch: arXiv:2102.04473 (2021)
• S. Ostermann, F. Piazza and H. Ritsch: Phys. Rev. X 6, 021026 (2016)
• F. Mivehvar, H. Ritsch and F. Piazza: Phys. Rev. Lett. 122, 113603 (2019)
• E. Colella, S. Ostermann, W. Niedenzu, F. Mivehvar and H. Ritsch: New J. Phys. 21, 043019 (2019)
• D. Holzmann and H. Ritsch: New J. Phys. 18 103041 (2016)

Quantum optimization

The self-consistent optimization of cavity field and atomic distribution due to the non-linear interaction establishes a nice tool for the solution of specific quantum optimization problems with atoms in resonators. For example, as we showed recently, ultracold atoms in an optical lattice with cavity-mediated long-range interactions constitute a quantum simulator for the excluded diagonals N-queens completion problem. If several illumination colors and cavity modes are applied, particles adapt to various illumination conditions dynamically to ensure maximal simultaneous scattering of all frequencies. This constitutes a system with a built-in memory to simulate Hopfield networks and associative memories.

• V. Torggler, P. Aumann, H. Ritsch and W. Lechner: Quantum 3, 149 (2019)

Quantum heat engines and refrigerators

Heat engines such as steam engines or internal combustion engines, are machines that convert thermal energy into mechanical work. The endeavour to increase their performance and efficiency has significantly contributed to the development of classical thermodynamics and the formalisation of its underlying laws. While thermodynamics is a macroscopic theory, the question whether, or to what extent, its rules translate to the microscopic, quantum, domain is a major driving force in the emerging field of quantum thermodynamics. In the thermodynamic tradition of "learning by example" the study of quantum thermal machines, e.g., refrigerators or heat engines, constituted by a few (or even a single) atoms, not only helps to answer those fundamental questions but is also aimed at identifying whether quantum features (like entanglement) may be beneficial for the operation of thermal machines.

• W. Niedenzu, I. Mazets, G. Kurizki and F. Jendrzejewski: Quantum 3, 155 (2019)
• W. Niedenzu, M. Huber and E. Boukobza: Quantum 3, 195 (2019)

Quantum metrology: Making time measurements more precise

Quantum physics tells us that the energies an electron can have within an atom are directly associated with frequencies and can therefore be used to count time. This is usually done in an atomic clock, a setup that has been well established over the last 50 years.

As a matter of fact, atomic clocks have become that good that even the smallest interactions between atoms now constitute a perturbation that fundamentally limits the accuracy of such a device. In our work, we have suggested an alteration of the standard measurement procedure, the so-called Ramsey spectroscopy method, that leverages the unwanted interactions amongst the atoms and turns them into an advantage, yielding much better sensitivities and ultimately a more precise clock.

In a nutshell, the suggested alteration makes use of subradiant, i.e. slowly decaying states, that emerge as a consequence of the mutual dipole-dipole interaction amongst the atoms. Therby population can be retained much longer during the phase of free evolution during the Ramsey measurement procedure.

This, of course, has many applications ranging from fundamental physics over high-speed communications to improved GPS navigation and beyond.

• L. Ostermann, H. Ritsch and C. Genes: Phys. Rev. Lett. 111, 123601 (2013)
• L. Ostermann, C. Meignant, C. Genes and H. Ritsch: New J. Phys. 21, 025004 (2019)