# Publications by Martin Kiffner

## Resonant interferometric lithography beyond the diffraction limit

Optics InfoBase Conference Papers (2008)

We discuss interferometric optical subwavelength lithography using resonant light-matter interactions only. As compared to previous schemes, no multiphoton processes are required, such that the scheme works at low light intensities. © 2007 Optical Society of America.

## Quantum control of interacting multiatom systems

AIP Conference Proceedings **963** (2007) 756-759

Control schemes in dipole-dipole interacting two-particle systems are discussed. In contrast to single-particle systems, in such collective systems vacuum-induced dipole-dipole interactions can couple transitions regardless of the orientation of the two involved dipole moments. We show that these couplings gives rise to a significant modification of the system properties, and demonstrate how they can be exploited to alter the system dynamics. In particular, we discuss a setup where the long-time dynamics crucially depends on the relative position of the two atoms, and demonstrate that such systems are a promising candidate for the realization of a multidimensional decoherence free subspace. © 2007 American Institute of Physics.

## Breakdown of the few-level approximation in dipole-dipole interacting systems

Proceedings of SPIE - The International Society for Optical Engineering **6603** (2007)

The validity of the few-level approximation is investigated in a system of two dipole-dipole interacting four-level atoms. Each atom is modelled by two complete sets of angular momentum multiplets. We provide two independent arguments demonstrating that the few-level approximation in general leads to incorrect predictions if it is applied to the Zeeman subleveis of the atomic level scheme. First, we show that the artificial omission of subleveis generally leads to incorrect eigenenergies of the system. The second counterexample involves an external laser field and illustrates that the relevant states in each atom are not only determined by the laser field polarization, but also by the orientation of the atomic separation vector. As the physical origin of this outcome, we identify the dipole-dipole interaction between orthogonal dipole transitions of different atoms. Our interpretation enables us to identify conditions on the atomic level structure as well as special geometries in which (partial) few-level approximations are valid.

## Breakdown of the few-level approximation in collective systems

Physical Review A - Atomic, Molecular, and Optical Physics **76** (2007)

The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As an example system, we study the archetype case of two dipole-dipole interacting atoms, each modeled by two complete sets of angular momentum multiplets. We establish the breakdown of the few-level approximation by first proving the intuitive result that the dipole-dipole induced energy shifts between collective two-atom states depend on the length of the vector connecting the atoms, but not on its orientation, if complete and degenerate multiplets are considered. A careful analysis of our findings reveals that the simplification of the atomic level scheme by artificially omitting Zeeman sublevels in a few-level approximation generally leads to incorrect predictions. We find that this breakdown can be traced back to the dipole-dipole coupling of transitions with orthogonal dipole moments. Our interpretation enables us to identify special geometries in which partial few-level approximations to two- or three-level systems are valid. © 2007 The American Physical Society.

## Two-mode single-atom laser as a source of entangled light

Physical Review A - Atomic, Molecular, and Optical Physics **75** (2007)

A two-mode single-atom laser is considered, with the aim of generating entanglement in macroscopic light. Two transitions in the four-level gain medium atom independently interact with the two cavity modes, while two other transitions are driven by control laser fields. Atomic relaxation as well as cavity losses are taken into account. We show that this system is a source of macroscopic entangled light over a wide range of control parameters and initial states of the cavity field. © 2007 The American Physical Society.

## Coherent control in a decoherence-free subspace of a collective multilevel system

Physical Review A - Atomic, Molecular, and Optical Physics **75** (2007)

Decoherence-free subspaces (DFS's) in systems of dipole-dipole interacting multilevel atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows us to populate the antisymmetric states of the DFS by means of a laser field, without the need for a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a microwave field. Typical operation times of these qubit rotations can be significantly shorter than for a nuclear spin system. © 2007 The American Physical Society.

## Breakdown of the few-level approximation in collective systems

Optics InfoBase Conference Papers (2007)

In contrast to single atoms, in collective systems, the vacuum couples transitions with orthogonal dipole moments. This leads to a geometry-dependent dynamics and to a breakdown of the few-level approximation in collective systems. © 2007 Optical Society of America.

## Interference in the resonance fluorescence of two incoherently coupled transitions

Physical Review A - Atomic, Molecular, and Optical Physics **73** (2006)

The fluorescence light emitted by a four-level system in J=12 to J=12 configuration driven by a monochromatic laser field and in an external magnetic field is studied. We show that the spectrum of resonance fluorescence emitted on the π transitions shows a signature of spontaneously generated interference effects. The degree of interference in the fluorescence spectrum can be controlled by means of the external magnetic field, provided that the Landé g factors of the excited and the ground state doublet are different. For a suitably chosen magnetic field strength, the relative weight of the Rayleigh line can be completely suppressed, even for low intensities of the coherent driving field. The incoherent fluorescence spectrum emitted on the π transitions exhibits a very narrow peak whose width and weight depend on the magnetic field strength. We demonstrate that the spectrum of resonance fluorescence emitted on the σ transitions shows an indirect signature of interference. A measurement of the relative peak heights in the spectrum from the σ transitions allows us to determine the branching ratio of the spontaneous decay of each excited state into the σ channel. © 2006 The American Physical Society.

## Quantum interference enforced by time-energy complementarity.

Phys Rev Lett **96** (2006) 100403-

The interplay of the concepts of complementarity and interference in the time-energy domain are studied. In particular, we theoretically investigate the fluorescence light from a J = 1/2 to J= 1/2 transition that is driven by a monochromatic laser field. We find that the spectrum of resonance fluorescence exhibits a signature of vacuum-mediated interference effects, whereas the total intensity is not affected by interference. We demonstrate that this result is a consequence of the principle of complementarity, applied to time and energy. Since the considered level scheme can be found, e.g., in (198)Hg(+) ions, our model system turns out to be an ideal candidate to provide evidence for as yet experimentally unconfirmed vacuum-induced atomic coherences.

## Geometry-dependent dynamics of two -Type atoms via vacuum-induced coherences

Physical Review A - Atomic, Molecular, and Optical Physics **73** (2006)

The dynamics of a pair of atoms can significantly differ from the single-atom dynamics if the distance of the two atoms is small on a scale given by the relevant transition wavelengths. Here, we discuss two nearby three-level atoms in ̂ configuration, and focus on the dependence of the optical properties on the geometry of the setup. We find that in general transitions in the two atoms can be dipole-dipole coupled by interactions via the vacuum field even if their transition dipole moments are orthogonal. We give an interpretation of this effect and show that it may crucially influence the system dynamics. In particular, for a fixed setup of driving fields and detectors, the spatial orientation of the two-atom pair decides if the system reaches a true constant steady state or if it exhibits periodic oscillations in the long-time limit. As an example observable, we study the resonance fluorescence intensity, which is either constant or is modulated periodically in the long-time limit. © 2006 The American Physical Society.

## Detection of atomic entanglement and electromagnetically induced transparency in velocity-selective coherent population trapping

2005 European Quantum Electronics Conference, EQEC '05 **2005** (2005) 290-

A gas of atoms that is cooled by velocity-selective coherent population trapping (VSCPT) [ 1 ] ideally ends up in an entangled superposition of states with different spin and center-of-mass momenta. Since this state is not only a periodic state of matter but also a dark state for the pair of counterpropagating pump lasers, the optical properties of a VSCPT gas are very interesting. We demonstrate theoretically that the entangled coherences of an atomic VSCPT gas give rise to a distinctive optical signal, a backscattered beam of light, when the VSCPT gas is probed with a weak signal laser pulse. This signal is absent when the entangled atomic state is replaced by an incoherent mixture of the same spin-momentum states. We estimate the magnitude of the effect both for atoms in the ideal VSCPT state and for a mixture of atoms with a nite momentum width and predict that the backscattered beam should be observable for a VSCPT gas of Rubidium atoms under realistic conditions. If the probe pulse and the pump beams are simultaneously applied the VSCPT gas also exhibits the phenomenon of electromagnetically induced transparency (EIT). Due to the coupling between the probe pulse and the backscattered pulse, the propagation of the beam is more complex than usual. In addition, the backscattered pulse is split into two parts because of the EIT dispersion relation. We furthermore show that, despite being a periodic state of matter, a VSCPT gas does not lead to photonic band gaps in the spectrum of the probe beam. Finally, we investigate the behaviour of a quantized probe eld of light in a VSCPT gas. © 2005 IEEE.

## Detection of atomic entanglement and electromagnetically induced transparency in velocity-selective coherent population trapping

Physical Review A - Atomic, Molecular, and Optical Physics **71** (2005)

We investigate theoretically the optical properties of an atomic gas that has been cooled by the laser cooling method of velocity-selective coherent population trapping. We demonstrate that the application of a weak laser pulse gives rise to a backscattered pulse, which is a direct signal for the entanglement in the atomic system, and which leads to single-particle entanglement on the few-photon level. If the pulse is applied together with the pump lasers, it also displays the phenomenon of electromagnetically induced transparency. We suggest that the effect should be observable in a gas of rubidium atoms. © 2005 The American Physical Society.

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