Domain percolation in a quenched ferromagnetic spinor condensate
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| Number of Parts | 40 | |
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/38447 (DOI) | |
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Transcript: English(auto-generated)
00:09
Kia ora, I'm Nanako, and this is Shreya. In this work, we theoretically explore the geometrical statistical properties of the spin domains that form an equine spinor Bose-Einstein condensate.
00:21
A spinor Bose-Einstein condensate is an ultracold gas of bosonic atoms in which each atom has access to several different spin states. In our case, we study a spin-one system with three accessible spin levels. The atoms in the condensate we consider also have ferromagnetic interactions, which means that these interactions favour the
00:41
system magnetising. We consider the system prepared in an initial state that is unmagnetised. The quench is implemented by suddenly changing the quadratic Zeeman energy to a value at which this condensate is unstable, so that it forms easy-axis magnetic domains. That is, spin domains that are aligned with or against the direction set by the Zeeman field.
01:03
In this simulation, we show the dynamics of a small quasi-two-dimensional condensate undergoing this evolution. Starting from the unmagnetised state, you will notice that small domains form. Then, as time progresses, these domains tend to grow larger. We analyse the structure of these domains once they form. To do this, we have applied
01:25
the ideas of percolation theory. Notably, we focus our attention on the positive or upward-pointing spin domains. We can make a binary image by setting all positive domains to be white. We examine if any of these domains percolate across the system. Here
01:41
is an example of a percolating domain that connects from the lower boundary to the top boundary. This domain also happens to connect the left and right boundaries. In order to explore percolation characteristics, we need to change the relative portion of atoms in the positive domain and see how this affects the probability of a percolating domain occurring. In this work, we varied the positive domain populations using a coherent
02:05
spin rotation, a standard technique of atomic physics experimental toolbox. We find that the probability of finding a percolating domain varies smoothly as a portion of positive atoms is varied, thus identifying a smooth percolation transition. Conducting
02:22
a finite size analysis, we examine how this probability changes as the system size increases. This allows us to extrapolate to the thermodynamic limit where the transition is discontinuous, and hence identify the percolation threshold and the correlation length critical exponent. In addition to showing that spin domain formation can be described by percolation
02:43
theory, we also examine the feasibility of studying this behavior in experiments. That is, we examine factors such as the time dependence of domain growth and the continuous nature of the spin density on the percolation analysis. We also suggest a way to minimize heating from the quench by preparing a sociable initial stage.
03:03
We hope that this work will inspire experiments to make the first studies of percolation in an ultra-cold atomic gas.