Rydberg atoms that have been excited to a quantum state with large principal quantum number n possess some extraordinary properties. For example, their exaggerated size, growing as n², implies large dipole moments that also grow as n² as well as dipole polarisabilities with an n⁷ scaling. Rydberg physics was so far limited to excitations in atomic systems. In collaboration with colleagues from the TU Dortmund, we have recently shown that Rydberg excitations can also be observed in semiconductor systems [1]. Here, the material in which the excitons were formed was a natural cuprous oxide (Cu₂O) crystal. Rydberg excitons with principal quantum numbers up to n=25 have been observed in transmission spectroscopy (see Figure) which corresponds to an extension of the exciton wavefunction of more than one micrometer.

Similar to atoms, the binding energies of Rydberg excitons deviate systematically from the hydrogenic Rydberg series. This deviation can be cast into the form of a quantum defect which we showed to derive from the nonparabolicity of the valence bands [2,3]. We have shown further that the proximity of the Rydberg exciton resonances provides a route to detect coherent phenomena in semiconductor Rydberg excitons already in the absorption spectra [4]. There, additional resonances appear in the absorption spectrum that correspond to dressed states consisting of two Rydberg exciton levels coupled to the excitonic vacuum, forming a V-type three-level system, but driven only by one laser light source] (see Figure). Our result is based on the solution of the valence band Hamiltonian associated with the cubic crystal symmetry of Cu₂O that corresponds to a modified Schrödinger equation in momentum space.

In crossed electric and magnetic fields, the potential landscape may be altered to provide additional quasi-bound states with giant dipoles [5], where we computed the eigenenergies of these giant-dipole excitons [6]. Stray electric fields on the other hand, such as those produced by charged impurities, leads to the vanishing of Rydberg resonances into an apparent continuum [7]. The appearance of additional absorption lines due to the broken rotational symmetry, together with spatially inhomogeneous Stark shifts, leads to a modification of the observed line shapes that agrees qualitatively with the changes observed in the experiment.

Additional potentials that modify the excitonic spectra include strain that could be used to trap Rydberg excitons [8] (see Figure).

Similar to atoms, dipole-dipole interactions dominate the overall interaction at the large distances relevant under experimental conditions of Rydberg exciton blockade. We have evaluated the long-range interactions between pairs of Rydberg excitons in Cu₂O, which are due to direct Coulomb forces rather than short-range collisions typically considered for ground-state excitons [9], and found signatures of Rydberg blockade in pump-probe spectra [10]. For future experiments involving transitions between different exciton series in Cu₂O, we have studied the infrared optical transitions between excitons of the yellow, green and blue series in Cu₂O [11]. We showed that in many cases the dipole approximation is inadequate and, in particular, that it breaks down in yellow-blue transitions even for moderate principal quantum numbers.

For an introduction to Rydberg physics, we would like to refer you to Quantum Kate (en).

One of the fundamental problems in understanding the interaction between light and dielectrics can be traced back to the question how to quantize the electromagnetic field in the presence of absorbing bodies. A consistent quantization scheme has been developed over the last 10 years or so which is based on a source-quantity representation of the electromagnetic field in terms of a bosonic vector field that describes collective excitations of field and absorbing matter [1,2]. In the linear-response approximation, this procedure is exact and has been used to treat atomic decoherence processes (spontaneous decay, dephasing, spatial decoherence etc.) as well dispersion forces (Casimir force, Casimir-Polder force) [3].

More recently, we have been able to extend this quantization scheme to include nonlinearly responding, absorbing dielectrics [4,5,6]. This enables us to study the effect of nonlinear absorption mechanisms in a quantum-mechanically consistent way. In the context of nonlocal or even nonreciprocal media, we have shown that the principle of macroscopic duality can still be upheld [7,8].

Verification of quantum states and processes requires a reconstruction of density matrices and CP maps that describes them. Together with K.M.R.Audenaert (Royal Holloway College) we are developing a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations that also provides complete information about measurement uncertainties (error bars) [1]. This method allows also for a consistent treatment of imperfect photon detection [2].

With the advent of microfabricated structures (atom chips) that enable one to confine small numbers of neutral atoms near dielectric surfaces, we are able to study atom-surface interactions in great detail. The effects we investigate range from thermally induced spin flips [1] to spatial decoherence [2] and Casimir-Polder forces. More recently, we are beginning to understand effects of electromagnetic absorption in superconducting surfaces on coherence properties of atomic samples [3,4], and we will explore their potential use in high-precision measurements. Recently, we found evidence of directional spontaneous emission of atoms near a nanofiber [5].