## Overview

### QED in linear and nonlinear dielectric materials

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).

More recently, we have been able to extend this quantization scheme to include nonlinearly responding, absorbing dielectrics [3,4]. This enables us to study the effect of nonlinear absorption mechanisms in a quantum-mechanically consistent way.

[1] S.Scheel, L.Knöll, and D.-G.Welsch, Phys. Rev. A **58** , 700 (1998).

[2] C.Raabe, S.Scheel, and D.-G.Welsch, Phys. Rev. A **75** , 053813 (2007).

[3] S.Scheel and D.-G.Welsch, Phys. Rev. Lett. **96** , 073601 (2006).

[4] J.A.Crosse and S.Scheel, Phys. Rev. A **81**, 033815 (2010).

### Ultracold trapped neutral atoms, atom chips

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.

[1] P.K.Rekdal, S.Scheel, P.L.Knight, and E.A.Hinds, Phys. Rev. A **70**, 013811 (2004).

[2] S.Scheel, P.K.Rekdal, P.L.Knight, and E.A.Hinds, Phys. Rev. A **72**, 042901 (2005).

[3] U.Hohenester, A.Eiguren, S.Scheel, and E.A.Hinds, Phys. Rev. A **76**, 033618 (2007).

[4] B.Kasch *et al.*, New J. Phys. **12**, 065024 (2010).

### Dispersion forces

Dispersion forces such as Casimir forces between bodies, Casimir-Polder forces between atoms and bodies and van der Waals forces between atoms are effective electromagnetic forces that arise as consequences of correlated ground-state fluctuations. We are investigating dispersion forces in and out of thermal equilibrium [1,2] that are particularly relevant for long-wavelength atomic transitions as found in Rydberg atoms [3], and study universal scaling laws [4] and friction forces [5].

[1] S.Y.Buhmann and S.Scheel, Phys. Rev. Lett. **100**, 253201 (2008).

[2] S.A.Ellingsen, S.Y.Buhmann, and S.Scheel, Phys. Rev. Lett. **104**, 223003 (2010).

[3] J.A.Crosse *et al.*, Phys. Rev. A **82**, 010901(R) (2010).

[4] S.Y.Buhmann, S.Scheel, and J.R.Babington, Phys. Rev. Lett. **104**, 070404 (2010).

[5] S.Scheel and S.Y.Buhmann, Phys. Rev. A **80**, 042902 (2009).

### Quantum tomographic reconstruction with error bars

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].

[1] K.M.R.Audenaert and S.Scheel, New J. Phys. **11**, 023028 (2009).

[2] K.M.R.Audenaert and S.Scheel, New J. Phys. **11**, 113052 (2009).

## Collaborators

Dr Koenraad Audenaert, Royal Holloway College, University of London, quantum tomographic reconstruction

Prof Ed Hinds, Imperial College London, Ultracold atoms, atom chips

Profs Jozsef Fortagh and Tom Judd, University of Tuebingen, cold atoms, superconducting surfaces, carbon nanotubes

Dr Simen Ellingsen, NTNU Trondheim, Casimir-Polder forces

Prof Dirk-Gunnar Welsch, Friedrich-Schiller-University Jena, Germany, QED in dielectrics, Casimir effect

## Research Staff

Buhmann,SY

## Research Student Supervision

Butcher,DT

Crosse,JA