# Cavity Quantum Electrodynamics

# Cavity Quantum E-Dyn.

## Prof. Helmut Ritsch's Theory Group | Universität Innsbruck

# CQED Theory

## Helmut Ritsch

# Research

This page details our research efforts and interests. Below you will find a selection of topics we are currently working on. For a list of publications please see the links.

#### General research statement

Our research covers the fields of theoretical quantum optics and ultra cold gas physics with strong connections to quantum information theory, foundations of quantum physics and quantum theory of condensed matter systems. We focus on full quantum descriptions of matter and light waves, which are strongly coupled by momentum exchange. Our aim is an effective theoretical description of real physical systems in a close connection with experiments, where genuine quantum phenomena as quantum phase transitions, entanglement and macroscopic super positions can be studied in a well-controlled and understood environment.

#### Publications

For an (almost) complete list of publications that have emerged from our research, please visit

or contact us directly.

## Lightforces in high-Q cavities

**Cavity Cooling**

Freezing particles in very small regions in space is the prerequisite for any investigation (like spectroscopy) or manipulation (like quantum computation). As photons carry energy and momentum, absorption, emission, and coherent scattering of light creates forces on the involved particles. For light enclosed between two highly reflective mirrors, i.e. an optical resonator, these forces are strongly enhanced. They can be tailored to control the quantum motion of the particles. This allows for trapping atoms and molecules as well as cooling them to temperatures very close to the absolute zero.

## Crystallization of atoms bound by light

**Self-Organization**

Photons carry momentum and their scattering thus not only modifies light propagation but induces forces on particles. Confining mobile scatterers and light in an optical resonator thus generates complex coupled nonlinear dynamics. An illumination at sufficient power induces a phase transition from random order to a crystalline structure. This minimizes the optical potential energy of the particles in concurrence with a maximization of light scattering into the resonator. Applying several illumination colors and cavity modes particles adapt to various illumination conditions dynamically to ensure maximal simultaneous scattering of all frequencies. This constitutes a self-optimizing light collection system with a built-in memory.

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 it enables the exploration of uncharted regions of multi-particle phases allowing for a simulation of the Dicke superradiant phase transition, Hopfield networks, associative memories or generalized Hamiltonian mean field models.

Recently we have shown that closely related self-ordering phenomena appear in nanooptical geometries as tapered optical nanofibres, which mediate long-range dipole-dipole interaction and collective scattering.

## The smallest possible laser

**Superradiant Lasing**

A single inverted atom in an optical micro resonator forms the smallest possible laser system as a coherent source of light. The laser light generated by the atom through stimulated emission exhibits strong forces which in turn provide for self-trapping and cooling of the atom. When operated on an ultra narrow clock transition one enters the super radiant operating regime which allows precise and accurate operation on the atomic clock transition wavelength.

## Protected subspace Ramsey spectroscopy

**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.

## C++QED: a framework for simulating open quantum systems

**Simulating the dynamics of open quantum systems**

C++QED is a framework for simulating open quantum dynamics in general. Historically, it has in the first place been developed for problems in moving-particle cavity QED, but since then has been applied in several other fields in quantum optics. It is known to be able to simulate full Master equation up to several thousand, and quantum trajectories up to several hundred thousand dimensions.

The basic idea of the framework is to allow users to build arbitrarily complex interacting quantum systems from elementary free subsystems and interactions between them (these are commonly referred to as elements), and simulate their time evolution with a number of available time-evolution drivers. Operating with elementary physical systems, the interface is of much higher level than in the popular Quantum Optics toolbox for Matlab, or the much less known, but venerable QSD C++ library, as in the latter two the interface is built on quantum operators.

More details and download links can be found on the C++QED homepage.