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Ultra Cold Atomic Systems: The Investigation And Application Of Bose-Einstein Condensates

Updated: Nov 4, 2023

Author: Kian Jagtiani


Abstract


The emergence of highly effective cooling and trapping techniques for neutral atoms in the late 1990s was undeniably one of the largest scientific breakthroughs in atomic physics. The concept of Bose-Einstein condensates, first theorized by Albert Einstein and Satyendra Bose in the 1920s and later carried out experimentally in 1995, is a concept that enables us to study multitudinous phenomena, investigate the behavior of atoms at a quantum scale, make precise measurements as well as proceed with many other research opportunities that were otherwise impossible to carry out. In constant pursuit of an even colder temperature, physicists in a laboratory at JILA, a joint institute of the University of Colorado, Boulder and NIST, created the first Bose-Einstein Condensate at barely 5 nanokelvins. This paper will revolve around the fifth state of matter and will begin with a concise explanation of what it is, followed by a succinct description of how it can be attained. Subsequently, it will highlight the properties exhibited by BECs and ultimately elaborate on a few of their potential applications.


The Newest State of Matter: Bose-Einstein Condensates


Satyendra Nath Bose - an Indian physicist - sent Albert Einstein his work on the behaviour of photons. Bose’s work noted that the two classes of submicroscopic particles, bosons and fermions, react differently. As dictated by Pauli's exclusion principle, fermions naturally tend to repel/avoid each other. Bosons, on the other hand, were found to disobey the principle, and Bose cogitated that multiple bosons can share the same quantum state.


Upon receiving Bose’s Paper, Einstein built upon this and predicted that when the energy of the particles is decreased to temperatures extremely close to absolute zero (- 273 Degrees Celsius), a number of bosons can amalgamate into a single quantum body that can be described by a single wavefunction. Unfortunately, due to limitations in technology at the time, it wasn’t possible to create an environment colder than the critical temperature, the temperature below which a Bose-Einstein condensate is formed.


The critical temperature of an element is dictated by the following equation:

where:

In the 1990s, two breakthroughs in the field finally made it possible to cool substances down below their critical temperature: laser cooling and demagnetization. These discoveries won their inventors the Nobel prize and opened up a world of applications related to BECs.


As far as we know, there are no naturally occurring BECs in our solar system and as well as beyond. Although, theoretical physicists believe that they could occur naturally in close proximity to neutron stars, as the extremely high pressure could lead to dense particles gathering so close together so that they act like BECs.


Contrivance


There are two main methods that scientists use to cool a substance down by such a large magnitude: Doppler Cooling and Adiabatic Demagnetization


Doppler Cooling


Doppler Cooling is based on the idea that atoms can absorb and emit photons that are at their resonant frequency. This method consists of three pairs of orthogonal laser beams, which together cool the atoms found at their intersection.


For the sake of experimental clarity, let’s consider just one of these beams at first. If the frequency of the photons in this laser is exactly equal to the difference in the excited and ground states of an atom, then it is possible for the atom to absorb it. Once the absorption has occurred, the atom will now be in its excited state, from which it will try to return to its ground state by emitting a photon identical to the one absorbed, but in a completely random direction.


Through this process, the momentum of the atom will change; decreasing upon impact in accordance with the law of conservation of momentum. Since the temperature of a body is simply the average kinetic energy of its atoms, it is safe to say that:


Less Momentum = Less Velocity = Less Kinetic Energy = Lower Temperature


However, the process described above would only work if all the atoms are travelling directly at the laser. This means that the process will not work for gas molecules, which are known to undergo Brownian motion, as some atoms will then be sped up instead.


The Doppler effect now comes into play. If a frequency slightly less than the resonant frequency is chosen, then all atoms that are stationary or moving in the wrong direction will observe a frequency that would not enable them to absorb the proton. Whereas, atoms that are moving towards the beam, will have a higher observed frequency and will interact with the photons. The use of three orthogonal pairs of lasers ensures atoms in all directions are slowed down.


Adiabatic Demagnetization

Adiabatic Demagnetization is a process that makes use of the paramagnetic properties of certain materials and can cool them down to a few millikelvins. It is primarily meant for gases that have already been cooled down. Hence, this is the next step after Doppler Cooling in the creation of a Bose-Einstein Condensate.


Process:-


Let X be the substance that has to be cooled and Y the cold liquid that helps X cool. X is first made to come in contact with Y, which is typically liquid helium, inducing a magnetic field in it. Once X and Y are in thermal equilibrium, the strength of the magnetic field is increased, which results in a more ordered system, leading to a decrease in entropy. After which, X is isolated from Y and the strength of its magnetic field is reduced. This prevents the backflow of heat and will result in X being cooler. Regular Adiabatic Demagnetization can cool substances down to approximately 0.001 Kelvin.


To obtain even lower temperatures, an extremely similar process known as Adiabatic Nuclear Demagnetization is used. The process is beyond the scope of this paper, but in essence, it makes use of nuclear dipoles rather than atomic ones, which are roughly 900 times smaller and can cool substances down 1000 times more. [ 0.001/1000 = 0.000001 Kelvin.]


Correlation to Counter-Intuitive Phenomena


Superfluids


Superfluids are fluids with the ability to flow with zero viscosity. The first superfluid to be discovered was helium-4, and it was quickly understood that superfluidity was observed due to partial Bose-Einstein condensation. Many BECs till date have been seen to exhibit superfluid-like properties, and this can be theoretically explained by the fact that BECs are effectively ‘super atoms,’ and all parts of them move in the same direction without any internal friction.


Super Solids


Scientists have observed that BECs form high density ‘droplets’ that repel each other. When placed under certain conditions, including a trap, these droplets arrange themselves in an ordered lattice. When the trap presses the droplets close together, the BEC acts as a substance known as a supersolid, which means that while maintaining the lattice structure, the droplets allow for the transfer of atoms, allowing the condensate to stay in a collective state.


Bosenovas


The self interaction of the wavefunction that the BEC is defined by can be controlled by changing the magnetic field in which the BEC is in. Adjusting the interaction to ‘repulsive’ would cause the condensate to expand at a constant rate which is theoretically expected. However, when the interaction is adjusted to ‘attractive’, rather than contracting and eventually becoming extremely small, the condensate is seen to first shrink a little bit (as expected) and then experience an explosion. The remnants of this explosion include a smaller, colder condensate surrounded by the gas of the explosion. Since this looks similar to a supernova, scientists refer to it as a ‘Bosenova’. The weird part is that the explosion is inexplicable till date and the process behind it is completely unknown.


Coherence


A property of BECs, one that has been made extremely evident throughout this paper, is that they exhibit coherence. This is a property that proves to be extremely useful, which will be discussed in the next part.


Superconductors


Superconductivity is when a circuit has zero resistance. A form of matter similar to BECs, known as Bardeen-Cooper-Shrieffers (BCSs) have been known to have atoms that are in a particular order, enabling them to facilitate the transfer of electrons easily, experiencing superconductivity.


When the two (BCSc and BECs) are overlapped, and a process called ’photoemission spectroscopy’ is used to observe electron behaviour, it can be seen that BECs exhibit superconductivity as well.


Slow/Stationary Light


Perhaps the most unusual property that BECs possess is that they can slow down light. For decades people have believed that the speed of light is constant, and that ‘c’ - the speed limit of the universe - is the speed at which light eternally travels at. However, in 1998 researchers from Harvard University slowed down light from 300,000,000 to 17 m/s . Consequently, many others have taken this further and have even completely stopped a pulse within a BEC. A simple way to understand the theoretical aspects of this would be to consider what light is made up of - photons. When they interact with atoms, they form a hybrid subatomic particle known as a polariton. These hybrid particles are greater in mass, resulting in the speed of their propagation decreasing.


A surfeit of other phenomena is observed in Bose-Einstein condensates such as swirling vortices and neutral particles that behave as if they are carrying a charge. Unfortunately, the other applications are much more complex and demand the use of equations and concepts that cannot be summarised in this paper.


Applications


Most of the work done in this field serves as a form of research known as ‘basic’ research, which means that it aids us in understanding other concepts and facilitates other fields, rather than being applicable to a specific process or form of equipment. That being said, there are multifarious examples of the latter.


Superfluids


Even now, the best lubricants in the world experience frictional losses as their molecules interact with each other to some extent. The property of superfluidity overcomes this problem and enables BECs to reduce friction by values near 100%.


Furthermore, superfluids are known to be interrelated with superconductors to a great extent. Likewise, BECs could be used to make various superconductors and even superconductor magnets.


Like all other superfluids, they can also be used in gyroscopy, as a quantum solvent, and in a variety of other places.


Atomic Lasers


When a BEC is crafted into a beam, it acts similar to a laser. Their property of coherence ensures that every part of the beam is identical or behaves in the same way. Nonetheless, they provide multiple advantages over normal lasers as they are much more precise and also have a relatively higher energy level.


Atomic Lasers (those that contain BECs instead of photons) are expected to revolutionize atomic physics and have a positive impact on fields such as atom optics, interferometry, lithography, holographics, the measurement of the fundamental units through the enhancement of devices such as atomic clocks, etc.


Cognizance


One of the biggest problems of Quantum Mechanics and Particle Physics in general is that a lot of its principles are counter-intuitive and contradict Newtonian physics. This means that it can be quite difficult to visualise and understand a lot of the concepts.


BECs, being superatoms, provide us with a substance that acts like an atom, but with a volume that is observable by the naked eye. In fact, researchers at MIT have produced clearly visible interference patterns using sodium BECs, inherently demonstrating a micro-effect on a macro scale.

Slow/Stationary Light

The fact that light has been slowed down, especially to the point at which it is stationary, is quite remarkable. Furthermore, this leads to the possibility of the storage of light, which opens up multitudinous applications related to telecom, optical data storage and enhanced quantum computing.


Organised traffic flow in networks, single-photon switches and the spatial compression of optical energy via photonic crystals are some of the more real-world applicable solutions that are likely to be developed in the near future.


Entangled Atoms


Researchers at the Georgia Institute of Technology have observed a ‘sharp magnetically-induced quantum phase’ in a sodium BEC. They expect this to lead towards the observation of a state of entangled atomic pairs that are predicted to have applications related to computers, sensors and other technologies.


They believe that they are extremely close to observing entanglement, and have a predefined window of time in which this would be possible. Once discovered, the entangled atoms would be used to increase the sensitivity of sensors in detecting physical stimuli. It would also help enhance the speed at which quantum computers can perform a number of identified calculations.


Speculations


There are also multiple mathematical theories related to dark matter and string theory that are fundamentally based on BECs. For example, a dark matter Bose-Einstein Condensate formed from a ‘cloud’ of dark bosons is said to form something known as a ‘Bose star’ when under the effect of gravity. Scientists in Russia have conducted research at a smaller scale, and have hypothetically speculated that predicting the number of Bose stars in the universe and determining their mass in terms of ‘light dark matter’ is a key step towards solving one of the biggest questions of our time - what is dark matter? Of course, this last part is all speculatory and while it is backed to some level by experiments, quantum physics has proven itself to be too unpredictable to confidently support these theories without concrete evidence.


References


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[2] <https://www.researchgate.net/publication/303524583_Ultra-Cold_atoms_and_Bose-Einstein_co ndensates_in_Optical_Dipole_Traps> [Accessed 11 April 2021].


[3] Boulderschool.yale.edu. 2021. [online] Available at <https://boulderschool.yale.edu/sites/default/files/files/Vortices.pdf> [Accessed 11 April 2021].


[4] Hal.archives-ouvertes.fr. 2021. [online] Available at:

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<https://web.stanford.edu/~rpam/dropoff/Phys041N/lecture6-lasercooling.pdf> [Accessed 11 April 2021].


[6] NIST. 2021. Implosion and explosion of a Bose-Einstein condensate "Bosenova". [online] Available at:

<https://www.nist.gov/news-events/news/2001/03/implosion-and-explosion-bose-einstein-condensate-bosenova> [Accessed 11 April 2021].


[7] Phys.org. 2021. Physicists show coherence of Bose-Einstein condensates extends to spin state of atoms. [online] Available at:

<https://phys.org/news/2005-11-physicists-coherence-bose-einstein-condensates-state.html> [Accessed 11 April 2021].


[8] Physicscentral.com. 2021. Slow Light. [online] Available at:

<https://www.physicscentral.com/explore/action/light.cfm> [Accessed 11 April 2021].

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