The atom laser and BE condensates

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The atom laser and BE condensates

• Vorlesung 3.2.03
• K. Kohse-Höinghaus

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Outline

• Introduction quantum mysteries, ultralarge atoms
  and frozen light
• Bose-Einstein condensates in the lab methods and
  behavior
• The atom laser
• What next?
• Literature

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Introduction Quantum mysteries?

• Maxwell 1871 assumes In a few years, all the
  great physical constants will have been
  approximately estimated and ... the only
  occupation which will then be left to the men of
  science will be to carry these measurements to
  another place of decimal.
• Rutherfords 1911 theory underpredicts the
  lifetime of hydrogen atoms by 40 orders of
  magnitude (!) - the worst quantitative failure
  in the history of physics.
• de Broglie 1923 postulates matter wave duality in
  his doctoral thesis Einstein gives a favorable
  review, thesis is accepted.
• Bose-Einstein condensation Effect predicted
  1924, observed 1995
• Mysteries superposition and decoherence (how
  quanta get classical)

Sci. Am., Feb. 2001, p. 54
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Decoherence
Sci. Am., Feb. 2001, p. 59
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Decoherence
Sci. Am., Feb. 2001, p. 59
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Introduction Ultralarge atoms?

• Can atoms behave classically?
• Formation of wave packets by superposition of
  high-level atomic states is possible with
  short-pulse lasers.
• These electronic states are not very distant in
  energy and almost equally spaced (high density of
  states)
• Such a superposition of many states is almost
  localized and behaves near the classical limit.
  Atoms swell to orders of magnitude their normal
  size. (20 ps pulses in K atoms -gt spectrally
  broad, overlap many states simultaneously, create
  a wave packet far from the nucleus.
• Orbiting of this wave packet around the nucleus
  can be followed by second (probe) laser pulse and
  is seen to follow almost planetary rules at
  least as a statistical average.

Sci. Am., June 1994, p. 24
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Wave packet
ENSEMBLE OF CLASSICAL ORBITS (left) is one way to
describe a radical wave packet. The packet
consists of a superposition of several energy
levels in effect, an electron moves
simultaneously in many orbits that surround the
nucleus. A more planetlike behavior would have
the orbits lie in one plane. Such a state, called
the elliptical stationary state, has been created
(right). The bump on the left side represents the
most likely location of the electron.
Sci. Am., June 1994, p. 28
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Introduction Frozen light

• Can one travel faster than the speed of light?
• Yes, in special cases
• Nothing travels faster than light in a vacuum,
  but even light is slowed down in many media.
  Clouds of atoms can be manipulated with lasers so
  that pulses of light travel through them with
  slower speed than highway traffic.
• Light can be frozen and be brought to a
  complete stop with ultracold clouds of atoms near
  absolute zero temperature (Bose-Einstein
  condensates)

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A benchtop guide to stopping light
Sci. Am., July 2001, p. 59
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• WAYLAYING LIGHT Before the light pulse (yellow)
  reaches the cloud of atoms (blue) that will
  freeze it, all the atoms spins (small arrows)
  are aligned and a coupling laser beam (red)
  renders the cloud transparent to the pulse (1,2).
  The cloud greatly slows and compresses the pulse
  (3), and the atoms states change in a wave that
  accompanies the slow light. When the pulse is
  fully inside the cloud (4), the coupling beam is
  turned off (5), halting the wave and the light
  at zero velocity the light vanishes. Later (6)
  the coupling beam is turned on again,
  regenerating the light pulse and setting the wave
  and the light back in motion.

Sci. Am., July 2001, p. 55
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QUANTUM WHIRLPOOLS called vortices are the only
way that a superfluid can rotate. this
theoretical simulation shows four vortices
threading through a condensate and two new
vortices forming at the edge. Colors indicate the
quantum "phase" around each vortex.
Sci. Am., Dec. 2000, p. 68.
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Bose-Einstein condensate

• Cool a gas of bosonic atoms to below a critical
  temperature then a fraction of the atoms
  condenses in the lowest quantum state.
• Atoms at temperature T and with mass m can be
  regarded as quantum mechanical wave packets that
  have a spatial extent of the order of a thermal
  de Broglie wavelength which increases with
  decreasing temperature.
• When all atoms are cooled to the point where the
  de Broglie wavelength is comparable to the
  interatomic separation, the atomic wave packets
  overlap and the gas starts to be a Bose-Einstein
  condensate.

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Bose-Einstein condensate
Left to right formation of the condensate at
about 2 µK, monitored by absorption imaging Left
TgtTcrit, middle TltTcrit, right TltltTcrit, pure
B-E condensate of about 7?105 atoms
Ketterles homepage
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Bose-Einstein condensate
Ketterles homepage
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What is an atom laser?

• An atom laser is analogous to an optical laser,
  but it emits matter waves instead of
  electromagnetic waves.
• Its output is a coherent matter wave, a beam of
  atoms which can be focused to a pinpoint or can
  be collimated to travel large distances without
  spreading. The beam is coherent, which means, for
  instance, that atom laser beams can interfere
  with each other.
• Compared to an ordinary beam of atoms, the beam
  of an atom laser is extremely bright. One can
  describe laser-like atoms as atoms "marching in
  lockstep".
• Although there is no rigorous definition for the
  atom laser (or, for that matter, an optical
  laser), all people agree that brightness and
  coherence are the essential features.

Ketterles home page
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Atomic trap

• ATOMIC TRAP cools by means of two different
  mechanisms. First, six laser beams (red) cool
  atoms, initially at room temperature, while
  corralling them toward the cen-ter of an
  evacuated glass box. Next, the laser beams are
  turned off, and the magnetic coils (copper) are
  ener-gized. Current flowing through the coils
  generates a magnetic field that further confines
  most of the atoms while allowing the energetic
  ones to escape. Thus, the average energy of the
  remaining atoms decreases, mak-ing the sample
  colder and even more closely confined to the
  center of the trap. Ultimately, many of the atoms
  attain the lowest possible energy state allowed
  by quan-tum mechanics and become a single entity
  known as a Bose-Einstein condensate.

Sci. Am., March 1998, p. 27.
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The parts of an atom laser

• A laser requires a cavity (resonator), an active
  medium, and an output coupler.
• In the MIT atom laser, the "resonator" is a
  magnetic trap in which the atoms are confined by
  "magnetic mirrors".
• The active medium is a thermal cloud of ultracold
  atoms, and the output coupler is an rf pulse
  which controls the "reflectivity" of the magnetic
  mirrors.

Ketterles homepage
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The gain process in an atom laser

• The analogy to spontaneous emission in the
  optical laser is elastic scattering of atoms
  (collisions similar to those between billiard
  balls).
• In a laser, stimulated emission of photons causes
  the radiation field to build up in a single mode.
  
• In an atom laser, the presence of a Bose-Einstein
  condensate (atoms that occupy a "single mode" of
  the system, the lowest energy state) causes
  stimulated scattering by atoms into that mode.
• More precisely, the presence of a condensate with
  N atoms enhances the probability that an atom
  will be scattered into the condensate by N1.

Ketterles homepage
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The gain process in an atom laser

• In a normal gas, atoms scatter among the many
  modes of the system. But when the critical
  temperature for Bose-Einstein condensation is
  reached, they scatter predominantly into the
  lowest energy state of the system, a single one
  of the myriad of possible quantum states. This
  abrupt process is closely analogous to the
  threshold for operating a laser, when the laser
  suddenly switches on as the supply of radiating
  atoms is increased.
• In an atom laser, the "excitation" of the "active
  medium" is done by evaporative cooling - the
  evaporation process creates a cloud which is not
  in thermal equilibrium and relaxes towards colder
  temperatures. This results in growth of the
  condensate. After equilibration, the net "gain"
  of the atom laser is zero, i.e., the condensate
  fraction remains constant until further cooling
  is applied.

Ketterles homepage
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The gain process in an atom laser

• Unlike optical lasers, which sometimes radiate
  in several modes (i.e. at several nearby
  frequencies) the matter wave laser always
  operates in a single mode. The formation of the
  Bose condensate actually involves "mode
  competition" the first excited state cannot be
  macroscopically populated because the ground
  state "eats up all the pie".

Ketterles homepage
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The output of an atom laser

• The output of an optical laser is a collimated
  beam of light. For an atom laser, it is a beam of
  atoms. Either laser can be continuous or pulsed -
  but so far, the atom laser has only been realized
  in the pulsed mode.
• Both light and atoms propagate according to a
  wave equation. Light is governed by Maxwell's
  equations, and matter is described by the
  Schroedinger equation.
• The diffraction limit in optics corresponds to
  the Heisenberg uncertainty limit for atoms. In an
  ideal case, the atom laser emits a Heisenberg
  uncertainty limited beam.

Ketterles homepage
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Optical versus atom laser differences

• Photons can be created, but not atoms. The number
  of atoms in an atom laser is not amplified. What
  is amplified is the number of atoms in the ground
  state, while the number of atoms in other states
  decreases.
• Atoms interact with each other - that creates
  additional spreading of the output beam. Unlike
  light, a matter wave cannot travel far through
  air.
• Atoms are massive particles. They are therefore
  accelerated by gravity. A matter wave beam will
  fall like a beam of ordinary atoms.
• A Bose condensates occupies the lowest mode
  (ground state) of the system, whereas lasers
  usually operate on very high modes of the laser
  resonator.
• A Bose condensed system is in thermal equilibrium
  and characterized by extremely low temperature.
  In contrast, the optical laser operates in a
  non-equilibrium situation which can be
  characterized by a negative temperature. There is
  never any population inversion in evaporative
  cooling or Bose condensation.

Ketterles homepage
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Quantum vortices in a rotating Bose-Einstein
condensate of Na atoms
Ketterle, ChemPhys Chem 2002
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Perspectives molecular condensates?
"TRILOBITE MOLECULE" of two rubidium atoms, 1,000
times larger than a typical diatomic molecule,
could be formed within a condensate by
appropriate laser excitation. Gold curves
indicate the density of the calculated electron
cloud forming the bond. The blue ball is one
atom the other is obscured under the "twin
towers". Groups have produced more ordinary
ultracold molecules in condensates by similar
laser techniques but have not yet demonstrated a
condensate of molecules.
Sci. Am., Dec. 2000, p. 75
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Literature

• Scientific American June 1994 p.24 The classical
  limit of an atom
• Scientific American Dec. 2000 p.68 The coolest
  gas in the universe
• Scientific American Feb. 2001 p.54 100 years of
  quantum mysteries
• Scientific American July 2001 p.52 Frozen light
• W. Ketterle, Atom plus atom equals ... vacuum!,
  ChemPhysChem 9/2002, 736
• Ketterles homepage http//cua.mit.edu/ketterle_g
  roup/