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.

, the macroscopic accumulation of bosonic particles in the energetic ground state below a critical temperature, has been demonstrated in several physical systems [2][3][4][5][6][7][8] . The perhaps best known example of a bosonic gas, blackbody radiation 9 , however exhibits no Bose-Einstein condensation at low temperatures 10 . Instead of collectively occupying the lowest energy mode, the photons disappear in the cavity walls when the temperature is loweredcorresponding to a vanishing chemical potential. Here we report on evidence for a thermalized two-dimensional photon gas with a freely adjustable chemical potential. Our experiment is based on a dye-filled optical microresonator, acting as a 'white wall' box for photons. Thermalization is achieved in a photon-number-conserving way by photon scattering off the dye molecules, and the cavity mirrors provide both an effective photon mass and a confining potential-key prerequisites for the Bose-Einstein condensation of photons. As a striking example of the unusual system properties, we demonstrate a yet unobserved light concentration effect into the centre of the confining potential, an effect with prospects for increasing the efficiency of diffuse solar light collection 11. Following the achievement of atomic Bose-Einstein condensation 2-4 , we have witnessed interest in light sources where a macroscopically populated photon mode is not the consequence of laser-like amplification, but rather results from a thermal equilibrium phase transition. Work in this direction includes the proposal of a superfluid phase transition of photons in a nonlinear cavity [12][13][14] and, albeit in the strong-coupling regime, the demonstration of a quasiequilibrium phase transition of excitonpolariton quasiparticles to 'half matter, half light' condensates 6-8 . In the weak-coupling regime (as in our case), optical cavities have been used to achieve a modified spontaneous emission of atoms and molecules [15][16][17] . The main idea of our experiment is to study thermalization of a photon gas, to a heat bath near room temperature (dye molecules), in a system with reduced spatial dimensionality and an energy spectrum restricted to values far above the thermal energy. The photons are trapped in a curved-mirror optical microcavity, and repeatedly scatter off dye molecules. The longitudinal confinement (along the cavity axis) introduces a large frequency spacing between adjacent longitudinal modes and modifies spontaneous emission coupling such that basically only photons of longitudinal mode number q = 7 (Fig. 1a) are observed to populate the cavity. By this, an effective low frequency cutoff ω cutoff (the eigenfrequency for the corresponding TEM 00 transverse mode) is introduced, withhω cutoff ∼ 2.1 eV, much larger than the thermal energy k B T (∼1/40 eV at room temperature). The two remaining transverse modal degrees of freedom of light thermalize to the (internal rovibrational) temperature of the dye solution, and the photon frequencies will be distributed by an amount ∼k B T/h abov...

We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10(14). Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.

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 85 Rb and 87 Rb was compared, yielding a difference ∆g/g = (1.2 ± 1.7) · 10 −7 . We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of ∆g/g = (0.4 ± 1.2) · 10 −7 .

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.