Martin Weitz

Bose–Einstein condensation of photons in an optical microcavity

Bose–Einstein condensation (BEC)—the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density—has been observed in several physical systems, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons or photon–photon scattering in a nonlinear resonator configuration. Number-conserving thermalization was experimentally observed for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a ‘white-wall’ box. Here we report the observation of a Bose–Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose–Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases and new coherent ultraviolet sources.

Atomic interferometer with amplitude gratings of light and its applications to atom based tests of the equivalence principle

We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb and 87Rb was compared, yielding a difference Deltag/g=(1.2+/-1.7)x10(-7). We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of Deltag/g=(0.4+/-1.2)x10(-7).

Directed Transport of Atoms in a Hamiltonian Quantum Ratchet

Moving Cold Atoms with Quantum Ratchets The nanoscale dimensions of biological motors make them susceptible to thermal noise, but such motors can produce force in one direction by alternating application of an asymmetric potential, or ratchet, with periods of thermal drift in the motion. The quantum version of such motors can operate without dissipation, as long as there is some means to break time-reversal symmetry in the system. Salger et al. (p. 1241) report on a coherent quantum ratchet device consisting of Bose-Einstein condensate cold atoms placed into an asymmetric sawtooth-potential created by optical lattices. Symmetry breaking was accomplished by phase shifts in the driving potentials. As expected for such a quantum ratchet, the current depended on the initial phase of the driving potential. A quantum ratchet, which operates without dissipation, is created with a Bose-Einstein condensate and optical potentials. Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

Atomic Landau-Zener Tunneling in Fourier-Synthesized Optical Lattices

We report on an experimental study of quantum transport of atoms in variable periodic optical potentials. The band structure of both ratchet-type asymmetric and symmetric lattice potentials is explored. The variable atom potential is realized by superimposing a conventional standing wave potential of lambda/2 spatial periodicity with a fourth-order multiphoton potential of lambda/4 periodicity. We find that the Landau-Zener tunneling rate between the first and the second excited Bloch band depends critically on the relative phase between the two spatial lattice harmonics.

Theory of the Energy Levels and Precise Two-Photon Spectroscopy of Atomic Hydrogen and Deuterium

In last few years significant progress has been achieved both in the experimental technique and the theoretical methods for the determination of the energy levels of simple hydrogenic systems. We review recent two-photon spectroscopic measurements performed in Garching and the relevant theoretical predictions for the hydrogen energy levels. Good agreement is achieved when all theoretical contributions are included, showing the importance of recently calculated higher order corrections. .

Thermalization of a two-dimensional photonic gas in a /`white wall/' photon box

It has now been demonstrated that a dye-filled optical microresonator can trap photons such that their number doesn’t decrease even when the trap is cooled. The idea could lead to a Bose–Einstein condensate of light.

Laser cooling by collisional redistribution of radiation

The general idea that optical radiation may cool matter was put forward 80 years ago. Doppler cooling of dilute atomic gases is an extremely successful application of this concept. More recently, anti-Stokes cooling in multilevel systems has been explored, culminating in the optical refrigeration of solids. Collisional redistribution of radiation has been proposed as a different cooling mechanism for atomic two-level systems, although experimental investigations using moderate-density gases have not reached the cooling regime. Here we experimentally demonstrate laser cooling of an atomic gas based on collisional redistribution of radiation, using rubidium atoms in argon buffer gas at a pressure of 230 bar. The frequent collisions in the ultradense gas transiently shift a highly red-detuned laser beam (that is, one detuned to a much lower frequency) into resonance, whereas spontaneous decay occurs close to the unperturbed atomic resonance frequency. During each excitation cycle, kinetic energy of order kBT—that is, the thermal energy (kB, Boltzmann’s constant; T, temperature)—is extracted from the dense atomic sample. In a proof-of-principle experiment with a thermally non-isolated sample, we demonstrate relative cooling by 66 K. The cooled gas has a density more than ten orders of magnitude greater than the typical values used in Doppler-cooling experiments, and the cooling power reaches 87 mW. Future applications of the technique may include supercooling beyond the homogeneous nucleation temperature and optical chillers.

Observation of Grand-Canonical Number Statistics in a Photon Bose-Einstein Condensate

We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve as both heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of the order of the total particle number extending deep into the condensed phase. Our results demonstrate that Bose-Einstein condensation under grand-canonical ensemble conditions does not imply second-order coherence.

Resonance beating of light stored using atomic spinor polaritons.

We investigate the storage of light in atomic rubidium vapor using a multilevel-tripod scheme. In the system, two collective dark polariton modes exist, forming an effective spinor quasiparticle. Storage of light is performed by dynamically reducing the optical group velocity to zero. After releasing the stored pulse, a beating of the two reaccelerated optical modes is monitored. The observed beating signal oscillates at an atomic transition frequency, opening the way to novel quantum limited measurements of atomic resonance frequencies and quantum switches.

Fourier synthesis of optical potentials for atomic quantum gases

We demonstrate a scheme for the Fourier synthesis of periodic optical potentials with asymmetric unit cells for atoms. In a proof of principle experiment, an atomic Bose-Einstein condensate is exposed to either symmetric or sawtooth-like asymmetric potentials by superimposing a conventional standing wave potential of {lambda}/2 spatial periodicity with a fourth-order lattice potential of {lambda}/4 periodicity. The high periodicity lattice is realized using dispersive properties of multiphoton Raman transitions. Future applications of the demonstrated scheme could range from the search for novel quantum phases in unconventionally shaped lattice potentials up to dissipationless atomic quantum ratchets.