A continuous-wave atom laser formed by the outcoupling of atoms from a trapped Bose-Einstein condensate (BEC) potentially has a range of metrological applications. However, in order for the device to be truly continuous, a mechanism to replenish the atoms in the BEC is required. Here we calculate the temporal coherence properties of a continuously pumped atom laser beam outcoupled from a trapped Bose-Einstein condensate that is replenished from a reservoir at finite temperature. We find that the thermal fluctuations of the condensate can significantly decrease the temporal coherence of the output beam due to atomic interactions between the trapped BEC and the beam, and this can impact the metrological usefulness of the device. We demonstrate that a Raman outcoupling scheme imparting a sufficient momentum kick to the atom laser beam can lead to a significantly reduced linewidth.
A continuous-wave atom laser formed by the outcoupling of atoms from a trapped Bose-Einstein condensate (BEC) potentially has a range of metrological applications. However, in order for the device to be truly continuous, a mechanism to replenish the atoms in the BEC is required. Here we calculate the temporal coherence properties of a continuously pumped atom laser beam outcoupled from a trapped Bose-Einstein condensate that is replenished from a reservoir at finite temperature. We find that the thermal fluctuations of the condensate can significantly decrease the temporal coherence of the output beam due to atomic interactions between the trapped BEC and the beam, and this can impact the metrological usefulness of the device. We demonstrate that a Raman outcoupling scheme imparting a sufficient momentum kick to the atom laser beam can lead to a significantly reduced linewidth.
Research in the field of ultra-cold quantum gases provides a testbed to examine Hamiltonians from other areas of physics such as the Bose-Hubbard Hamiltonian, as well as interesting phenomena such as superconductivity and superfluidity. Of emerging interest in the field is the analysis of non-equilibrium behaviour. This thesis focuses on the non-equilibrium dynamics of Bose gases in two different elongated systems: a continuously-pumped atom laser, and the formation of solitons as a result of a rapid quench through the Bose-Einstein condensation phase transition. We begin by introducing the theoretical tools required to model these systems, including the Stochastic Projected Gross-Pitaevskii formalism that describes the dynamics of a condensate in contact with a thermal cloud. We apply the Stochastic Projected Gross-Pitaevskii formalism to model a Raman-outcoupled atom laser continuously outcoupled from a replenished condensate reservoir at finite temperature. We investigate the first and second order coherence of the output as a function of the temperature of the condensate reservoir. For large momentum kicks given to outcoupled atoms, we show for the first time that the coherence of the atom laser beam is linked to that of the condensate reservoir. We observe a decrease in first order coherence of the condensate reservoir as its temperature is increased, and show that this decrease is caused by the dephasing of thermal fluctuations. We also investigate the effects of varying the outcoupling rate and the momentum kick on the first order coherence of the beam. We demonstrate that the first order coherence of the atom laser beam deviates from that of the condensate reservoir for small momentum kicks which we identify as due to interactions between the condensate and atom laser beam. Thermal density fluctuations in the condensate cause the atom laser beam to experience a stochastic force and the temporal coherence of the atom laser beam is reduced. We find that the condensate reservoir is significantly depleted for large outcoupling rates, resulting in a reduction in the steady state condensate fraction and in the first order coherence of the atom laser beam. In a second study, the momentum linewidth of a guided atom laser outcoupled using a radio-frequency transition is investigated at zero and finite temperature. We examine the momentum distribution of the beam by measuring the transmission of atoms over a potential barrier following the experimental scheme of the group of Professor Alain Aspect at Institut d'Optique. We observe a noisy momentum distribution for outcoupling rates in the weak-outcoupling limit at zero temperature. We show that the noise is caused by bulk excitations within the condensate reservoir as a result of a density depression caused by the non-adiabatic switch-on of outcoupling. We show that these excitations can be prevented by increasing the outcoupling rate to its final value linearly over time. In addition, we demonstrate that a thermally-broadened linewidth could potentially be measured using this experimental technique, and discuss challenges associated with the measurement scheme. Finally, we focus on the non-equilibrium dynamics of condensate growth in elongated geometries. Following a rapid quench through the Bose-Einstein condensation phase transition, we observe the spontaneous appearance of density dips which we identify as solitons. We develop an algorithm for counting these solitons in order to observe the temporal dependence of the soliton number as a function of the quench rate. To compare with the predictions of the Kibble-Zurek mechanism describing topological defect formation as a result of the dynamics of phase transitions in homogeneous systems, we calculated the scaling exponent of the soliton number with respect to the quench rate. Our results were qualitatively consistent with the Kibble-Zurek predictions, but quantitative comparisons were inconclusive. In trapped systems the phase transition proceeds inhomogeneously, with a phase front that propagates in space with a velocity. If this is lower than a critical value it has been predicted that this can inhibit defect formation. However, our results do not show conclusive evidence of this in the parameter regime that we study. We find that the number of solitons reduces as the condensate reaches equilibrium as a result of the damping included in the Stochastic Projected Gross-Pitaevskii formalism.
A continuous wave (cw) atom laser will most likely be realised by outcoupling from a reservoir containing a Bose-Einstein condensate at finite temperature. This will mean that the correlation properties and linewidth of the cw atom laser beam will be influenced by the thermal nature of the reservoir. Here we report on simulations using the stochastic Gross-Pitaevskii formalism for finite temperature dynamics to find the steady state properties of the outcoupled beam. We determine how the linewidth and correlation length depend on the condensate size, temperature, and outcoupling properties, and determine the optimum parameters for cw atom laser operation.
We present a model for a continuous atom laser beam in a one-dimensional waveguide. The beam is formed by continuous Raman outcoupling of a trapped one-dimensional (quasi-)condensate, which is created by imposing a tightly confining transverse optical potential on a three-dimensional magnetically trapped ultracold thermal gas. The trapped (quasi-)condensate is modeled by a stochastic Langevin equation in which pumping arises naturally from the surrounding three-dimensional thermal cloud, which acts as its heat bath. When the outcoupling is turned on, such pumping leads to continuous replenishing of the (quasi-)condensate and thus to a steady-state operation for the atom laser, which is described by a nonlinear Schrodinger equation coupled to the Langevin equation for the (quasi-)condensate. This model is used to study the temporal and spatial evolution of the coherence length of the (quasi-)condensate and the atom laser over the entire system.
We present a model for a continuous atom laser in a one-dimensional waveguide. The beam is formed by continuous Raman outcoupling of a trapped one-dimensional (quasi-)condensate, which is created by imposing a tightly confining transverse optical potential on a three-dimensional magnetically trapped ultracold thermal gas. The trapped (quasi-)condensate is modelled by a stochastic Langevin equation, in which pumping arises naturally from the surrounding three-dimensional thermal cloud, which acts as its heat bath. When the outcoupling is turned on, such pumping leads to continuous replenishing of the (quasi-)condensate, and thus to a steady-state operation for the atom laser, which is described by a nonlinear Schroedinger equation, coupled to the Langevin equation for the (quasi-)condensate. This model is used to study the temporal and spatial evolution of the coherence length of the (quasi-)condensate and the atom laser over the entire system.
Atom lasers have been demonstrated in both pulsed and semi-continuous modes. The dynamics of these devices is predicted to be dramatically different to the optical laser due to fundamental differences between the two types of boson fields, however to date it is the similarities that have been emphasized. Here we show how the atom laser dynamics are strongly affected by coupling of the output beam back to the condensate. Typically research in the field of Bose-Einstein condensation (BEC) 1 relates to studies of fundamental properties, such as collective modes 2 or to the response of the BEC to external stimuli 3. In contrast, the atom laser is one of the most promising technologies to arise from BEC, being the di-rect atomic equivalent of the optical laser 4. Mewes et al. 5 demonstrated the first atom laser, based on the application of pulsed radio-frequency (RF) fields to induce controlled spin flips from magnetically trapped to un-trapped states of a Bose-Einstein condensate. Later it was shown by Hagley et al. 6 that a pulsed Raman out-coupling could be used to achieve a quasi-continuous multi-state atomic beam. Bloch et al. 7 achieved con-tinuous RF out-coulping for up to 100ms, producing a single state atom laser beam, and showed that this beam could be coherently manipulated in direct analogy to the optical laser 8. These experiments, and others 9,10, have conclusively demonstrated that the outcoupling process can be made coherent. They have also demonstrated a number of other similarities be-tween the optical and atomic lasers such as high flux and low divergence of the output beam. In all these works, the similarities between the two sys-tems have been emphasized, however, ultimately it is the differences such as mass and wavelength that will lead to applications of the atom laser. 1
We investigate the coherence properties of an atomic beam evaporatively cooled in a magnetic guide, assuming thermal equilibrium in the quantum degenerate regime. The gas experiences two-dimensional, transverse Bose-Einstein condensation rather than a full three-dimensional condensation because of the very elongated geometry of the magnetic guide. First order and second order correlation functions of the atomic field are used to characterize the coherence properties of the gas along the axis of the guide. The coherence length of the gas is found to be much larger than the thermal de Broglie wavelength in the strongly quantum degenerate regime. Large intensity fluctuations present in the ideal Bose gas model are found to be strongly reduced by repulsive atomic interactions; this conclusion is obtained with a one-dimensional classical field approximation valid when the temperature of the gas is much higher than its chemical potential, kBT ≫ |µ|. Pacs: 03.75.Fi, 42.50.-p The first experimental achievements of Bose-Einstein condensates in atomic vapors [1, 2, 3, 4] have opened promising perspectives for atom optics: condensates constitute indeed atomic waves sources of much better coherence properties than the usual ‘thermal ’ sources like the standard magneto-optical trap. These