1 What is Bose-Einstein condensation?
“A very remarkable effect occurs in a gas of noninteracting bosons at a certain
transition temperature, below which a substantial fraction of the total number
of particles in the system will occupy the single orbital of lowest energy, called
the ground orbital. … The total occupancy of all orbitals will always be equal
to the specified number of particles in the system. The ground-orbital effect is
called the Einstein condensation. ” [2]
I begin this blog with the quotation above as from my research it most succinctly
explains the complex phenomenon of Bose-Einstein condensation, a very inter-
esting and relevant region of physics to this day. Bose-Einstein condensation
is relevant in the fields of statistical physics, statistical thermodynamics and
condensed matter physics, in which gasses of bosons of low densities are cooled
to close to that of absolute zero. As an undergraduate of theoretical physics at
trinity college Dublin undertaking these modules I feel equipped to discuss this
matter. Low temperatures and density of Bose gases are only two of the many
conditions required for Bose-Einstein condensation to occur and depending on
the frame work we picture the system is in these conditions will change. Often
graphs that represent Bose-Einstein condensation are hard to interpret however
the two I have selected to display below demonstrate its physical occurrence.
This is quite significant as this quantum phenomenon is a great example of the-
oretical physics postulate making they’re way from theory to the forefront of
experimental physics.
transition temperature, below which a substantial fraction of the total number
of particles in the system will occupy the single orbital of lowest energy, called
the ground orbital. … The total occupancy of all orbitals will always be equal
to the specified number of particles in the system. The ground-orbital effect is
called the Einstein condensation. ” [2]
I begin this blog with the quotation above as from my research it most succinctly
explains the complex phenomenon of Bose-Einstein condensation, a very inter-
esting and relevant region of physics to this day. Bose-Einstein condensation
is relevant in the fields of statistical physics, statistical thermodynamics and
condensed matter physics, in which gasses of bosons of low densities are cooled
to close to that of absolute zero. As an undergraduate of theoretical physics at
trinity college Dublin undertaking these modules I feel equipped to discuss this
matter. Low temperatures and density of Bose gases are only two of the many
conditions required for Bose-Einstein condensation to occur and depending on
the frame work we picture the system is in these conditions will change. Often
graphs that represent Bose-Einstein condensation are hard to interpret however
the two I have selected to display below demonstrate its physical occurrence.
This is quite significant as this quantum phenomenon is a great example of the-
oretical physics postulate making they’re way from theory to the forefront of
experimental physics.
Figure 1
Figure 2
Figure 1 is a “direct observation of BEC of magnetically trapped sodium
atoms by dispersive light scattering. The clouds have condensate fractions that
increase form close to 0%(left) to almost 100% (right). The dense core is the
condensate, and the more diffuse cloud is the normal component. The signal for
the normal component is rather weak and appears patchy due to interference
with laser stray light” [1]
Figure 2 displays “The density of the atomic cloud is shown, with temperature
decreasing from left to right. The high peak, the Bose-Einstein condensate,
emerges above the other atoms. The picture is from the JILA laboratory” [4]
Depending on the Bosonic gas the temperature for which BEC occurs may
differ, this is called the critical temperature. In the Canonical ensemble for fixed
partial number the critical temperature is defined by the equation
$ T_c = (\frac{n}{\zeta(3/2)})^{3/2} \frac{2 \pi \hbar ^2 }{mK_b}$
mKb where n is the partial density, m is the mass per boson ̄h is
planks reduced constant, k_b is Boltzman’s constant and ζ is the Riemann zeta
function. [3]
condensate, and the more diffuse cloud is the normal component. The signal for
the normal component is rather weak and appears patchy due to interference
with laser stray light” [1]
Figure 2 displays “The density of the atomic cloud is shown, with temperature
decreasing from left to right. The high peak, the Bose-Einstein condensate,
emerges above the other atoms. The picture is from the JILA laboratory” [4]
Depending on the Bosonic gas the temperature for which BEC occurs may
differ, this is called the critical temperature. In the Canonical ensemble for fixed
partial number the critical temperature is defined by the equation
$ T_c = (\frac{n}{\zeta(3/2)})^{3/2} \frac{2 \pi \hbar ^2 }{mK_b}$
mKb where n is the partial density, m is the mass per boson ̄h is
planks reduced constant, k_b is Boltzman’s constant and ζ is the Riemann zeta
function. [3]
2 Why is it important
Research into the field of Bose statistics has improved our understanding of
quantum mechanics as, in essence, these bosons act as a single quantum state
after undergoing Bose-Einstein condensation. What does this mean? “Quantum
mechanics, elementary particles of the same type are considered identical. For
example, an electron in an atom could be replaced by another electron and
the atom would behave in exactly the same way.” [1] This is significant as
our classical approximations of physics do not yield these results under any
circumstances and as such this is is to be discussed in a quantum regime .
“Cornell, Ketterle and Wieman shared the 2001 Nobel Prize in physics for their
accomplishment” [4] They individually achieved creating Bose-Einstein gasses
in laboratory setting, with some claiming this to be considered the fifth state of
matter. This field of Bose statistics is one hundred years old as of the writing
of this blog, initiated by the postulates of Satyendra Bose on how a photon gas
acts at low temperatures in the 1920’s and achieved 75 years later.
3 Applications
“‘In 1997, MIT researchers developed an atom laser based on BECs that was
able to drip single atoms downward from a micro spout, and in February 1999,
a team at Harvard University used a BEC to slow down light to just 38 MPH
by shining a laser beam through the condensate. ” [4]. From this quotation we
can see some interesting science being undertaken, the former application of this
phenomenon is apparent in the field of condensed matter and the creation of
semiconductors in which the placement of dopants is crucial to the properties of
the technology and precision is crucial. The latter application is fascinating as
typically to “slow down ” light we beam it through a substance of high refractive
index and density, but as discussed earlier Bose gasses have a low density. This
is all to demonstrate the unique applications and properties of BEC and that
a team at Harvard University used a BEC to slow down light to just 38 MPH
by shining a laser beam through the condensate. ” [4]. From this quotation we
can see some interesting science being undertaken, the former application of this
phenomenon is apparent in the field of condensed matter and the creation of
semiconductors in which the placement of dopants is crucial to the properties of
the technology and precision is crucial. The latter application is fascinating as
typically to “slow down ” light we beam it through a substance of high refractive
index and density, but as discussed earlier Bose gasses have a low density. This
is all to demonstrate the unique applications and properties of BEC and that
its still undergoing research to this day.
References
[1] John Doyle. “Bose–Einstein condensation”. In: Proceedings of the National
Academy of Sciences 94.7 (1997), pp. 2774–2775. doi: 10.1073/pnas.94.
7.2774. eprint: https://www.pnas.org/doi/pdf/10.1073/pnas.94.7.
2774. url: https://www.pnas.org/doi/abs/10.1073/pnas.94.7.2774.
[2] C. Kittel and H. Kroemer. Thermal Physics. W. H. Freeman, 1980. isbn:
9780716710882. url: https://books.google.ie/books?id=c0R79nyOoNMC.
[3] Prof. Manuela Kulaxizi. “Statistical physics II” Semester 2 Hilary term
Trinity College Dublin
[4] AMERICAN PHYSICAL SOCIETY “ This Month in Physics History
Making Superatoms First Bose Einstein Condensate June 5, 1995: First Bose
Einstein Condensate ” June 2004 url: https://www.aps.org/publications/apsnews/
200406/upload/jun04.pdf
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