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The long term goal of our group is to develop new methods to manipulate many-body states in a regime where the quantum mechanical aspects dominate their behavior and their properties. On the one hand, this should lead to new tools that allow one to probe physical laws and to measure fundamental constants with increasing precision. On the other hand, the progress of experimental methods also drives the advances in our understanding of the ever mysterious, beautiful, accurate, yet deeply dissatisfying structure of quantum mechanics. This interplay between theoretical concepts and experimental realizations promises to be very fertile in fields such as quantum control, quantum feedback and its limits, many-particle quantum systems, and many-particle entanglement (quantum computing).
We use various methods, but most include laser cooled atoms (to be able to keep atoms localized, and attain long coherence time) and laser-light interaction to manipulate the atoms, the photons, or both, at the quantum level. Using internal states of atoms in combination with laser light, that has essentially zero entropy, allows us to reduce thermal noise without having to cool the atoms to very low (sub-microkelvin) temperatures.
Cavity quantum electrodynamics with atomic ensembles
The collective interaction of many atoms with a single mode of an optical resonator also allows one to prepare entangled states of large samples of atoms by detection of the photons emitted by the atoms. When the atoms interact with the mode in a way that makes it fundamentally impossible to determine which atoms, e.g. emitted a photon into the resonator, the system must be described by an entangled state of the atomic ensemble (Dicke state). Under appropriate conditions, these states interact collectively, and therefore very strongly with photons.
Such systems allow one to generate single photons on demand in a single transverse electromagnetic mode, to store, detect, and release photons without touching their polarization state, and to generate various forms of non-classical light. New experiments will focus on realizing a quantum gate between two trapped atoms via their strong coupling to a cavity mode.
New laser cooling methods for atoms, ions or molecules: Cavity Doppler cooling and cavity sideband cooling by coherent scattering
Laser cooling of atoms has not only supplied the basis for the control and manipulation of matter at the quantum limit, e.g. in form of Bose-Einstein condensation, but has also resulted in a number of important applications and devices, many of which are tied to precision measurements and atomic clocks. However, laser cooling has so far been limited to atoms with a particular internal structure, and the cooling of molecules or even of atoms with a complicated level scheme has not been possible. If we could learn how to cool, trap and manipulate larger molecules in the same way as atoms, this would open the door for important developments in chemistry and possibly even in biology.
Doppler cooling  is the dominant laser cooling mechanism at all but the lowest temperatures. In Doppler cooling counterpropagating laser beams are tuned to the red of a closed transition between an atomic ground and an atomic excited state. An atom that is moving towards a laser beam will experience photons that are blue-shifted into resonance with the atomic transition, while photons from a beam propagating in the same direction as the atom will be red-shifted further out of resonance. The momentum transfer associated with the preferred absorption of photons from the counterpropagating beam leads to slowing and cooling of the atoms, while the randomly emitted photons on average do not contribute to the force. The net effect is cooling to temperatures in the millikelvin to microkelvin range, corresponding to atomic velocities in the range of a few millimeters to a few centimeters per second.
This principle behind laser cooling also entails its limitation. Since the momentum “kick” associated with each photon absorption event is much smaller than the momentum of a thermal atom, a larger number of absorption-emission events (on the order of thousand or more) is required to significantly change the atom’s velocity. Therefore laser cooling has only been demonstrated with atoms that can be optically cycled many times back to their initial ground state. However, most atoms (and all molecules) have multiple ground states to which the excited state can decay. Once the atom reaches a different ground state, the laser no longer has the correct detuning relative to the atomic transition, and the cooling stops. In particular, molecules have many vibrational and rotational levels, and consequently no laser cooling of molecules has been demonstrated.
The novel proposed method, cavity cooling, [2,3] is based on coherent scattering, rather than on spontaneous emission from an excited state. Coherent scattering dominates when the laser is far detuned from atomic or molecular transitions and when its intensity is not too large. Coherent scattering is generic to all polarizable particles, independent of their internal structure, and describes the emission of radiation by an oscillating atomic dipole that is driven by an external (classical) electric field. The basic idea behind the proposed technique is that energy is conserved in the scattering process, and that therefore events where the scattered photon carries away a larger energy than the incident-photon energy are accompanied by a corresponding reduction of the atom’s energy. Such scattering events can be enhanced in an optical resonator that is tuned to be resonant with a frequency that is higher than that of the incident light. The new cooling mechanism depends only on the finesse (i.e. on the reflectivity of the cavity mirrors) and on the detuning of the photons relative to the cavity resonance, while it is independent of the detuning relative to atomic transitions. Therefore this new technique should be generic and be applicable to any sort of material. The target can be an atom in different ground states, a molecule in different rotational and vibrational states, or possibly even a scattering center (impurity) inside a solid. The only requirement is that at the given intensity and laser frequency the emission rate by the scatterer is large enough to produce efficient cooling. The cooling power is given by the product of the scattering rate and the energy difference between the incident and the scattered photon .
 T.W. Hänsch and A.L. Schawlow, Opt. Commun. 13, 68 (1975).
 V. Vuletic and S. Chu, Phys. Rev. Lett. 84, 3787 (2000).
 P. Horak, G. Hechenblaikner, K.M. Gheri, H. Stecher, and H. Ritsch, Phys. Rev. Lett. 79, 4974 (1997).
Spin squeezing for atomic clocks beyond the standard quantum limit
The precision of a standard atomic clock improves with the square root of the number of particles (standard quantum limit). This limit arises from the projection noise in the final readout of the atomic phase. It is possible to overcome the standard quantum limit by means of quantum correlations (entanglement) between particles, such that the quantum noise is redistributed away from the quantity of interest (squeezing of spin noise, or short spin squeezing). Such correlation can only be induced via an interaction between the atoms. Interestingly, it is possible to replace the direct interaction between the atoms (collisions, typically not desirable in a precision experiment) with an effective long-distance interaction between atoms mediated by a light field. We have invented a simple effective method that yields almost 6dB of spin squeezing, and have demonstrated an atomic clock operating beyond the standard quantum limit. In the future, we will investigate ways to improve the spin squeezing further, and to prepare more complex many-body quantum states.
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