We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability for the process, resulting in a pair of outcoming fast atoms for each incoming one, as well as of its time reversed counterpart, turns out to be given by the Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section of these processes. Several most interesting cases of scattering - from a single condensate containing a vortex, and from a split condensate characterized by some phase difference - are discussed.
We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability for the process, resulting in a pair of outcoming fast atoms for each incoming one, as well as of its time reversed counterpart, turns out to be given by the Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section of these processes. Several most interesting cases of scattering - from a single condensate containing a vortex, and from a split condensate characterized by some phase difference - are discussed.
We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by the scattering of fast atoms in a pure momentum state off the cloud. The lowest-order probability for the process, resulting in a pair of outcoming fast atoms for each incoming one, as well as of its time-reversed counterpart, turns out to be given by the Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross section of these processes. Several most interesting cases of scattering --- from a single condensate containing a vortex and from a split condensate characterized by some phase difference --- are discussed.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
The use of temporal correlations in scattered photons to probe the microscopic dynamics of ultracold quantum gases has emerged as a powerful, minimally destructive approach for in situ analysis. Here, we demonstrate that temporal coherence spectroscopy can quantitatively characterize atomic motion in a magnetic trap, despite the perturbative effects of the probing light. By measuring the first-order correlation function g (1) (τ ) of light scattered by a 87 Rb cloud confined in a quadrupole trap, we identify radiation-pressure-induced acceleration and heating as the origin of the apparent discrepancy between coherence spectra and temperatures inferred from time-of-flight measurements. A simple dynamical model incorporating these effects restores agreement between theory and experiment, establishing coherence spectroscopy as a reliable in situ probe of velocity distributions in trapped atomic ensembles. Our results pave the way for time-resolved studies of nonequilibrium dynamics and thermalization processes in confined cold gases, complementing conventional destructive imaging techniques.
Trapped gases of ultracold metastable helium atoms are a unique experimental sys- tem. The trapped cloud’s low temperatures, the ability to selectively trap and ma- nipulate individual atomic states and the isolation provided in a vacuum chamber are all conducive to the measurement of precision atomic parameters, such as atomic transition rates. Due to it’s atomic structure helium - the simplest multi-electron atom - is a favourite test-bed for precision QED theoretical calculations compared to experimentally determined parameters. This thesis reports on a number of tran- sition rates measured for the first time with high accuracy, including the first excited metastable state lifetime, found to be 7870(510)s, the longest of any neutral atomic species yet measured. Transition rates from the 23P level to the ground state were also measured for the first time and found to be in excellent agreement with theory. Further cooling of helium produces a Bose-Einstein condensate (BEC), where all atoms are in an identical quantum state, the analogue of an optical laser. One par- ticularly interesting property a BEC posesses is long-range coherence to all orders, meaning all component particles are described by a single wavefunction. While first order coherence is measured in an interference experiment like Young’s double slit, higher order coherence is the ability for correlations to exist between groups of two, three or more particles, quantified by the measurement of correlation functions. Prior to the work in this thesis correlation functions for atoms had only been measured for second order. Here we develop a new technique which we use to show that a BEC is coherent to second and third order to 0.1% accuracy, compared to a thermal cloud which we show is incoherent. At small inter-particle spacings, there is an enhanced probability of measuring double and triple events in the thermal cloud (termed bunching). A drawback of all previous atomic correlation measurements is that the small de-Broglie wavelengths compared to the detector resolution leads to a significant reduction in the measured bunching amplitudes compared to theory. By altering our trapping configuration and temperature we are able to measure a two-particle bunching amplitude which is 88% of the theoretical maximum. This system also allowed the measurement of correlations up to 5th order in thermal gases. The near ideal bunching allowed us to demonstrate perturbations to the correlation functions due to the 1D nature of the system. These advances should lead to correlation measurements being used as a probe to characterise more exotic system properties such as low dimensionality, engineered quantum states and paticle pairing. Finally, a waveguide was created using a dipole laser beam and used to guide atoms in analogy to an optical laser in a fibre. Guided ‘atom lasers’ are likely to be important components for practical devices such as precision sensors. We demonstrate that a guided atom laser has a gaussian profile matching the lowest transverse mode of the waveguide and is first and second order coherent. In contrast guided thermal atoms show matter-wave speckle and are incoherent.
This thesis features fundamental experiments on the coherence properties of Bose-Einstein condensates (BEC) and atom lasers, made possible by a newly developed apparatus combining a Bose-Einstein condensate with an ultrahigh nesse optical cavity.Using the cavity as a single atom detector, atoms extracted from a trapped cloud are detected with unprecedented sensitivity, and the rst time-resolved counting of single atoms from a quantum degenerate source was demonstrated.O-diagonal long-range order is a dening property of a BEC and equivalent to longrange phase coherence.Its formation is a complex process accompanied by spontaneous symmetry breaking.We witnessed this formation in an ultracold cloud of 87 Rb atoms crossing the phase transition of BEC.Two overlapping atomic beams originating from dierent positions inside the condensate propagated downwards into the cavity.They showed a matter wave interference pattern with a visibility determined by the coherence of the probed regions.The modulation of the ux of atoms, recorded with single-atom resolution, yields the visibility, whereas its mean value gives information about the density of the sample.By shock cooling, a cloud of atoms was prepared in a highly nonequilibrium state slightly above the phase transition.While the ensemble subsequently relaxed, it crossed the phase transition into an equilibrium with a small condensate fraction.Employing our minimally invasive measurement method, the growth of both the rst-order coherence and the density of the sample was tracked in real time while the system crossed the phase transition.The growth of the coherence was found to start later, proceed faster and nish earlier than the increase in density.The coherent region increased at one fth of the speed of sound.Employing time-resolved single atom counting with the cavity detector, the full counting statistics of an atom laser beam was recorded.In a Hanbury Brown and Twiss type experiment, the second-order correlation function was found to be constant g (2) (τ ) = 1.00±0.01,proving the atom laser's second-order coherence and the absence of excess intensity uctuations that were observed in a pseudothermal beam.An analysis of the time interval distributions of atoms in the beam conrmed these ndings.The iii