Phase transition temperature and chemical potential of the twodimensional weaklyinteracting Bosegas

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Phase transition temperature and chemical
potential of the two-dimensional
weakly-interacting Bose-gas

• Iryna Ilkiv
• IPJ, Warsaw, Roland

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Table of contents

• Brief history
• -Cooling and trapping methods
• -Bose-Einstein condensation (BEC) achievement
• Recent experiments and future
• directions of studies
• Ideal Bose-gas
• Weakly-interacting Bose-gas
• Conclusions

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Behavior of fermions and bosons at low
temperatures
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How to achieve low temperatures?

• Laser cooling
• -Doppler cooling
• -Sub-Doppler cooling
• Cooling atoms in trap
• -Evaporative cooling

The temperature scale relevant to laser cooling.
The main cooling mechanisms and their
characteristic temperatures are indicated.
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LASER COOLING of an atom makes use of the
pressure, or force, exerted by repeated photon
impacts. An atom moving against a laser beam
encounters a higher frequency than an atom moving
with the same beam. In cooling, the frequency of
the beam is adjusted so that an atom moving into
the beam scatters many more photons than an atom
moving away from the beam. The net effect is to
reduce the speed and thus cool the atom.
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EVAPORATIVE COOLING occurs in a magnetic
trap, which can be considered of as a deep bowl.
The atoms with the highest energy, escape from
the bowl. Those that remain collide with each
other frequently, apportioning out the remaining
energy. Eventually, the atoms become to move
slower
Pic.1
Pic.3
Pic.2
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Laser cooling and trapping application
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False-color images show the velocity
distribution of rubidium atoms just before the
appearance of the Bose-Einstein condensate
(left) just after its appearance (center) and in
a nearly pure condensate (right). The color
shows the number of atoms at each velocity. Atoms
at the top are essentially stationary the lower
the atom, the faster its velocity.
Velocity distribution of the trapped atoms
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Practical usage of BEC

• Properties of matter at low temperatures
• Quantum effects observation in macroscopic
  scales
• - quantum mechanical interference between two
  
  condensates
• -two-components condensates
• Creation of more precise instruments
• Explanation of unstudied phenomena in
  Astrophysics
• -condensate collapse and explosion (2000,
  85Rb)
• -acoustic black holes

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Atom lasers

• Possible applications
• Atomic clocks
• Atom lithography
• Atom interferometers
• New possibilities for nanotechnologies

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Connection with Astrophysics

• Black holes
• Supernovas

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Motivations for weakly-interacting Bose-gas
theoretical study

• To study the influence of interactions on
  Bose-gas behavior
• To compare chemical potential and phase
  transition temperature in weakly-interacting
  Bose-gas with ideal gas ones
• To study an external field influence on the
  possibility of BEC creation

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Ideal Bose-gas

• Distribution function
• Density of states
• Number of particles
• Critical temperature

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Heat capacity of ideal Bose-gas in different
space dimensions
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Weakly-interacting Bose-gas

• Energy spectrum in
• Bogoliubovs approximation

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Critical temperature and chemical potential
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Weakly-interacting Bose-gas in an external field
Ideal bose gasColoumb interactionHard sphere
interaction, b0.1Hard sphere interaction, b1.0
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Conclusions

• One of the way to study a weakly-interacting
  Bose-gas is presented.
• Results for the density of states, number of
  particles, critical temperature and chemical
  potential of weakly-interacting Bose-gas and
  their dependence of density and interacting
  parameter, are obtained.
• The influence of external field on critical
  temperature of Bose-gas is shown.
• Practical usage of BEC and future directions of
  study are discussed.
• The connection of the condensate with
  Astrophysics is shown.

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Dziekuje bardzo Thank You
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• Atom lasers are very analogous to photon lasers
  of light.
• After atoms are cooled into a BEC, they are
  ejected out of the trap in a highly collimated,
  monoenergetic beam.

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The MIT atom laser is composed of sodium atoms
(1997)The first example of a continuous atom
laser beam (rubidium atoms)(1999)The atoms fall
because of gravity, and they fall as coordinated
clumps (rubidium atoms)(1998)A
"quasi-continuous" beam, pulses of atoms so
close together that they overlap (1999).