CassLab | Research
page-template,page-template-full_width,page-template-full_width-php,page,page-id-15350,page-parent,qode-quick-links-1.0,ajax_fade,page_not_loaded,,vertical_menu_enabled,side_area_uncovered_from_content,qode-theme-ver-11.1,qode-theme-bridge,wpb-js-composer js-comp-ver-5.0.1,vc_responsive


Bose-Einstein Condensation

BEC Background

The idea of condensation in an atomic gas was first introduced in the 1920’s by Satyendra Nath Bose and Albert Einstein.  Bose had just developed a new approach to counting photons (Bose statistics), and sent his paper on the subject to Einstein.  Realizing that Bose’s ideas could also be applied to other integer-spin systems, Einstein considered a gas of bosonic atoms.  He found a critical temperature below which the energy of the system was minimized if a finite fraction of the atomic population entered the lowest energy state.

The resultant ‘condensate’ has been described as a new state of matter, with exciting new properties.  BEC can be thought of as the matter analog to the laser, in that the constituent particles are identical and highly ordered.  BEC is a macroscopic quantum phenomenon where an entire population of atoms act like waves instead of particles.  Condensation occurs when the atomic de Broglie wavelenght, defined as

     \[ \lambda_{\mathrm{dB}}=(\frac{2\pi \hbar^2}{m k_\mathrm{B} T})^{\frac{1}{2}} \]

becomes comparable to the interparticle spacing.  As seen in the equation above, the de Broglie wavelength increases as the temperature of the atomic cloud decreases.  For comparison, at room temperature (about 300 K) the atomic de Broglie wavelength is on the scale of picometers, while at condensation temperatures (less than 1 µK) the atomic de Broglie wavelength has increased to the micrometer scale.

The critical temperature for condensation depends on the density of the atomic cloud, which varies from one experiment to another.  It is often more convenient to discuss the phase space density of a sample, which is defined as the number of particles contained in a cube of the de Broglie wavelength.  In any experiment, condensation occurs when the phase space density is greater than 2.612.  This condition is achieved by lowering the temperature of the cloud while simultaneously increasing its spatial density.

While Bose and Einstein laid most of the theoretical groundwork for BEC by about 1924, the first condensates were not observed until 1995.  There are many technical hurdles to be crossed in the effort to produce a condensate, and experimental physicists had to develop new ways to cool and confine a sample of atoms before observtion of BEC became feasible.  A nice tutorial on the development of BEC can be found on the JILA BEC page.

Current Experiment:
BEC Interferometry

This experiment began with an empty lab, in 2001.  Our goal was to develop an interferometer for Bose-Einstein condensates.  While other experiments were using microtraps for this purpose, ours was to be conventionally-sized.  We hoped that by utilizing a weak confinement field, our atom waveguide would be capable of making interferometry measurements for greater interaction times than previously observed.

Our efforts were divided into two parts, the first being to produce Bose-Einstein condensates.  Afterwards, we would concentrate on introducing the condensates into our waveguide for interferometry.  To make BEC, we modeled our efforts on the method described by Lewandowski, et al in the paper Simplified system for creating a Bose-Einstein condensate, J. Low Temp. Phys. 132, 309-367 (2003).   We begin with a  vacuum chamber where we use  a Ti-Sapphire laser and a pair of anti-Helmholtz coils to create a magneto-optical trap (MOT).  The sketch below is a top view of our MOT.  The red arrows indicate laser beams, with a 3rd pair of beams along our line of sight.  One B field coil is above the chamber, and the 2nd is directly below.

All 3 pairs of laser beams intersect at the center of the B field coils, which is where the MOT is formed.  We will eventually make our condensates in a purely magnetic trap.  In order to load the atoms from the MOT to the B trap, we use a compressed MOT (CMOT) and optical pumping as intermediate stages.  Our camera captures the images to the right.



B Trap

The MOT contains about $3 \times 10^9$ atoms at 800µK, and is several millimeters across.  The CMOT retains almost the entire MOT population, but reduces the temperature to 400µK.  Finally, the magnetic trap holds two-thirds of the initial MOT population, at $2 \times 10^9$ atoms while the temperature has increased again to 900µK.

To make a condensate, we will evaporatively cool the trapped atoms.  However, we need a higher vacuum for this process to work, so we transfer the atoms to a second vacuum chamber with pressure roughly $10^{-11}$ torr.  We purchased a translation track and motor to move the atoms between the two chambers.  The first diagram below shows the coil mounting system, as seen looking down the axis of the vacuum chambers.  The magnetic field coils are mounted to an aluminum support tower and suspended above and below the first vacuum chamber.  The tower is fixed to a mounting plate, which is secured to the translation carriage.  The second diagram is a top view of both vacuum chambers and the translation track.  The atoms are trapped in a MOT in the left chamber, loaded into the magnetic trap, and the the motor drives the entire magnetic trap to the science cell.  The atoms move a total of about 550mm, over a time period of 2s.

Vacuum Chambers

Once the atoms are positioned within the science cell, the population of the cloud is about $1.5 \times 10^9$ atoms with temperature of 900µK.   The resultant phase space density is $7 \times 10^{-8}$.  In order to observe BEC the phase space density must be on the order of 2, so we cool and compress the cloud using evaporative cooling.  The sketch below demonstrates evaporative cooling in a ground state with three Zeeman sub-levels.  Evaporative cooling is performed in the presence of an inhomogeneous manetic field, so that the Zeeman splitting increases with distance from the center of the trap.  At the “correct” distance, the Zeeman effect brings the energy of a transition between m-levels into resonance with the RF radiation (indicated by the two green arrows).  An atom at this location will transition from the m=+1 level, for example, to the m=0 level.

As the sketch also shows, atoms populate the trap according to their energies, which are described by a Boltzmann distribution..  The most energetic atoms, colored red, can travel further from the center of the trap than the less energetic (blue) atoms can, and are more likely to interact with the RF field.  Evaporative cooling thus preferentially removes the most energetic atoms, leaving behind a colder, denser cloud.  The atoms will then collide and rethermalize, forming another Boltzmann distribution at a lower average energy.  The high-energy tail of the Boltzmann distribution contains a disproportionate share of the total energy of the cloud, so the removal of just a small number of hot atoms can significantly impact the average energy of the cloud.  By gradually reducing the frequency of the RF field, we can lower the temperature until a Bose-Einstein condensate is formed.

These next images show the formation of the condensate.  The frequency of the RF field is noted at each stage.  The first image shows a cold cloud (about 1µK), with the atoms distributed thermally.  As the temperature is lowered, the condensate begins to form as evidenced by the dark central spot in the middle image.  The uncondensed fraction is still significant.  As the temperature is lowered further, more atoms join the condensate as seen in the third image.

The false-color images below are the density plots for the previous pictures.  Again, the frequency of the RF field is noted at each stage.  These first condensates were made on May 4, 2004.

Atom Waveguide

After a condensate is made, we must load it into an interferometry device.  We have elected to perform our BEC interferometry within an atom waveguide, which will support the atoms against gravity and permit long measurement times (ideally up to 1 second).  Our waveguide is based on a four-wire linear quadrupole, with an additional oscillating bias field.  This configuration is known as a time-orbiting potential, or TOP, trap. The mechanical sketch below depicts the four current-carrying rods and their mounts.  Each rod is actually a coaxial pair, with the inner conductors supplying the oscillating bias field and the outer conductors supplying the linear quadrupole field.  To the right of the mechanical sketch is a picture of our waveguide, before it was inserted into the vacuum chamber.  Each rod is 5mm in diameter, with 10mm separation between adjacent rods.  The end loops provide the option of applying an axial B field to trim the position of the atoms along the axis of guide.

More images of the waveguide are shown to the right.  Two more mechanical sketches show the entire waveguide mount, which supplies current to the conductors and also acts as a heat sink.  The top sketch shows an axial view of the guide, while the bottom sketch shows a top view.  The picture to the right shows the waveguide after insertion into the vacuum chamber.  The waveguide sits in the science cell.

Once the condensate is made, we gradually ramp down the main confinement fields and ramp on the waveguide fields.  Sequential images of the condensate during this process are shown below.  The images are taken from above the chamber, so that the y direction (long axis of images) is along the axis of the waveguide.  The condensate is observed to change location, and also lengthens along the waveguide axis.  We initially believed that the position change occurred because the center of the waveguide was not precisely aligned with the center of the inital atom trap, but further investigation has suggested that this may be part of an oscillatory process.

In order to verify that our trap operated as intended, we characterized the fields.  We perturbed the cloud in an effort to induce oscillations at the resonance frequencies of the trap.   Instead of executing a smooth transfer into the waveguide, we give the atoms a sharp push.