Design of an optical system for the uorescence imaging of tracer particles in a Bose{Einstein condensate

Understanding turbulence is one of the last great unsolved problems of classical physics. It is hoped that by studying the arguably simpler quantum analogue in an atomic Bose–Einstein condensate (BEC), new insights into the classical case may be found. Vortices are thought to play a large role in the dynamics of turbulence and it is their intersections and decays that leads to a transfer of energy from large to small length scales. To study turbulence in detail, information about the BEC must be obtained in situ, studying the dynamics of the vortices. Suitable methods have been seldom in previous studies. By introducing ‘tracer particles’ of a second atomic species into the system, it is proposed that the position of vortex cores may be imaged in situ with minimal impact upon the condensate. This will allow the possibility of tracking their motion. This thesis examines methods for visualising these tracer particles. Fluorescence imaging provides a good signal-to-noise ratio for visualising BECs with low atom numbers. To collect the light fluoresced by the tracers and visualise them with a high spatial resolution, high numerical aperture lenses will be required. The presence of aberrations caused by the experimental apparatus complicates the imaging system, and methods of overcoming these are investigated.

[1]  Daniel Freilich,et al.  Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate , 2010, Science.

[2]  A. Lance,et al.  Imaging a single atom in a time-of-flight experiment , 2010, 1002.2311.

[3]  Ashton S. Bradley,et al.  Observation of vortex dipoles in an oblate Bose-Einstein condensate. , 2009, Physical review letters.

[4]  G. Bewley.  The generation of particles to observe quantized vortex dynamics in superfluid helium , 2009 .

[5]  D. Wacks,et al.  Nonclassical velocity statistics in a turbulent atomic Bose-Einstein condensate. , 2009, Physical review letters.

[6]  Markus Greiner,et al.  A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice , 2009, Nature.

[7]  R. Bücker,et al.  Single-particle-sensitive imaging of freely propagating ultracold atoms , 2009, 0907.0674.

[8]  V. Bagnato,et al.  Emergence of turbulence in an oscillating bose-einstein condensate. , 2009, Physical review letters.

[9]  M. Greiner,et al.  The Quantum Gas Microscope , 2009 .

[10]  M. Tsubota.  Quantum Turbulence( New Frontiers of Quantum Fluids and Solids) , 2008 .

[11]  M. Tsubota,et al.  Quantum Turbulence in a Trapped Bose-Einstein Condensate under Combined Rotations around Three Axes , 2007, cond-mat/0703603.

[12]  A. Einstein.  Quantentheorie des einatomigen idealen Gases , 2006 .

[13]  A. Aftalion.  Vortices in Bose-Einstein Condensates , 2006 .

[14]  K. Sreenivasan,et al.  Lessons from hydrodynamic turbulence , 2006 .

[15]  Rafael Yuste,et al.  Fluorescence microscopy today , 2005, Nature Methods.

[16]  M. Raizen,et al.  Direct observation of sub-Poissonian number statistics in a degenerate bose gas. , 2005, Physical review letters.

[17]  K. Toyoda,et al.  Magnetic resonance imaging of Bose–Einstein condensates , 2002 .

[18]  W. Alt.  An objective lens for efficient fluorescence detection of single atoms , 2001, physics/0108058.

[19]  W. Ketterle,et al.  Vortex nucleation in a stirred Bose-Einstein condensate. , 2001, Physical review letters.

[20]  W. Ketterle,et al.  Observation of Vortex Lattices in Bose-Einstein Condensates , 2001, Science.

[21]  Robert F Fischer,et al.  Optical System Design , 2000 .

[22]  C. Wieman,et al.  Vortex precession in Bose-Einstein condensates: observations with filled and empty cores. , 2000, Physical review letters.

[23]  Theodor W. Hänsch,et al.  Resolving and addressing atoms in individual sites of a CO 2 -laser optical lattice , 2000, QELS 2000.

[24]  C. E. Wieman,et al.  Vortices in a Bose Einstein condensate , 1999, QELS 2000.

[25]  W. Ketterle,et al.  Making, probing and understanding Bose-Einstein condensates , 1999, cond-mat/9904034.

[26]  J. Maurer,et al.  LOCAL INVESTIGATION OF SUPERFLUID TURBULENCE , 1998 .

[27]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[28]  W. Ketterle,et al.  Observation of Feshbach resonances in a Bose–Einstein condensate , 1998, Nature.

[29]  C. S. Wood,et al.  Cooling the Collective Motion of Trapped Ions to Initialize a Quantum Register , 1998, quant-ph/9803023.

[30]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[31]  Smith,et al.  Decay of vorticity in homogeneous turbulence. , 1993, Physical review letters.

[32]  John L. Lumley,et al.  Some comments on turbulence , 1992 .

[33]  V. Mahajan.  Aberration Theory Made Simple , 1991 .

[34]  M L Wolbarsht,et al.  Microscope objectives, cover slips, and spherical aberration: comments. , 1988, Applied optics.

[35]  E. J. Yarmchuk,et al.  Observation of Stationary Vortex Arrays in Rotating Superfluid Helium , 1979 .

[36]  H. E. Hall,et al.  The rotation of liquid helium II I. Experiments on the propagation of second sound in uniformly rotating helium II , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[37]  A. Kolmogorov.  Dissipation of energy in the locally isotropic turbulence , 1941, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[38]  J. F. ALLEN,et al.  Flow of Liquid Helium II , 1938, Nature.

[39]  P. Kapitza,et al.  Viscosity of Liquid Helium below the λ-Point , 1938, Nature.

[40]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[41]  Peyman Milanfar,et al.  Super-resolution imaging , 2011 .

[42]  R. Srinivasan.  Vortices in Bose-Einstein condensates: A review of the experimental results , 2006 .

[43]  Parviz Moin,et al.  TACKLING TURBULENCE WITH SUPERCOMPUTERS , 1997 .

[44]  David J. Wineland,et al.  Cryogenic linear ion trap for accurate spectroscopy , 1996 .

[45]  R. P. Feynman,et al.  T5 – APPLICATION OF QUANTUM MECHANICS TO LIQUID HELIUM* , 1971 .

[46]  C. Gorter,et al.  Progress in low temperature physics , 1964 .

[47]  H. E. Hall,et al.  The rotation of liquid helium II , 1960 .