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Nt1310 Unit 1 Research Paper

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\caption{Images of the velocity distributions for the trapped rubidium atoms taken from \cite{JILA}. On the left is the distribution for the thermal cloud, taken when the system is at a larger temperature $\sim400\,\,\textrm{nK}$ than the critical temperature for BECs, the center frame is a point in between that is part condensate and part thermal, $\sim200\,\,\textrm{nK}$, and the final image is purely condensate within the density peak when temperature $\sim50\,\,\textrm{nK}$. The physical size of each image is $\sim200\,\,\mu\textrm{m}\times270\,\,\mu\textrm{m}$ and is taken after a period of about 0.04s. The color represents density, with red as low density and white as high density and the lower the peak the more the atoms have moved …show more content…

70 years later%
\footnote{Historical note:- World\textquoteright{}s first BEC was consisted of about 2000 $^{87}\text{Rb}$ atoms and achieved at 10:54 AM on
June 5, 1995 in a laboratory at JILA (Boulder, USA) as shown in Fig.~\ref{C1Fig1}
\cite{Making2004}.%
}, atomic BEC was created experimentally in dilute vapors of $^{87}\text{Rb}$
\cite{Anderson14071995}, basically, which triggered an explosion of related research activities. In the BEC state, all atoms in the bosonic gas fall into a single quantum-mechanical ground state. The transition to the BEC occurs if the atomic density \textbf{$n$}, and the deBroglie wavelength $\lambda$, corresponding to the characteristic velocity of the thermal motion of the atoms, satisfy the following condition \cite{Pethick02}:

\begin{alignat}{1} & n\lambda_{\text{th}}^{3}\approx2.61,\label{eq:C1e1}
\end{alignat}
here, $\lambda_{\text{th}}=\sqrt{\hbar^{2}/3mk_{\text{B}}T}$ is the thermal deBroglie wavelength%
\footnote{The deBroglie wavelength connects classical particle physics and quantum mechanical wave physics as $\lambda_{\text{th}}=\frac{\hbar}{mv}$.
We can easily determine the mean velocity of a particle in a gas …show more content…

In order to observe quantum mechanical effects in a gas, we have to reduce the temperature drastically. Roughly, we can calculate this temperature by demanding that the thermal deBroglie wavelength has to become equal to the mean particle distance $\lambda\approx10\,\,\textrm{nm}$
$\Rightarrow T=\frac{\hbar^{2}}{3mk_{\text{B}}\left(10\,\,\textrm{nm}\right)^{2}}\approx0.002\,\,\textrm{K}$. %
}, hence, as a matter of fact, the atomic BECs are the coldest objects existing in labs. BEC's creation became only possible after the development of appropriate experimental techniques needed to reach the necessary ultra-low temperatures. Mainly, we can divide the cooling procedure of atoms into main steps, \textbf{First}:- the method of laser cooling is applied to the gas loaded into a magneto-optical trap, this method was rewarded with the Nobel Prize in Physics for 1997 \cite{RevModPhys.70.685,RevModPhys.70.707,RevModPhys.70.721}, this method makes it possible to create a moderately cool state, at temperature $\sim100\,\,\mu\textrm{K}$. \textbf{Second}:- this step undergoes forced evaporative cooling, losing $\sim90\%$ of atoms, and the remaining atomic cloud spontaneously forms the

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