Simulating quantum mechanics

Emerging technological advances in laboratory methods have made it possible for scientists to directly observe the fragile quantum state.

The laws of quantum mechanics are often considered mysterious and counter-intuitive where many elusive phenomena predicted by quantum physics have not been directly observable. Fortunately in the last couple of decades impressive progress in the control of single atoms and quanta of light has opened up the fundamental laws of nature to direct experimental study. This offers a promising future where we can employ “quantum technology” to perform tasks not achievable by other means.

Examples include quantum cryptography for secure communication or quantum computing for breaking cryptog-raphy schemes. The interest in the experimental progress in this field was brought to light when the Nobel prize in physics in 2012 was given to Serge Haroche and David J. Wineland, for their groundbreaking experiments in the manipulation of single atoms and single light particles.

Researching the interaction of light with matter

My research interest within quantum mechanics involves studying the interaction of light with matter on the most fundamental level. Progress in high performance computing (HPC) has helped me simulate the laws of quantum mechanics.

Figures 1a & 1b show the cavity mirrors in white blocks and the cloud of atoms in red. The strength of the interaction between the atoms and the cavity is controlled by the strength of a laser pump shown in blue.

Figure 1a - Below threshold: Here the coupling strength is weak and the atoms act independently of each other.

Figure 1b - Above threshold: Here the coupling strength is strong, and the atoms self-organise into a lattice, and cooperate to generate light at high intensity; the so-called super-radiant phase. The atoms and the light are now entangled to make up a new type of matter that is more than just the sum of its parts.

This is a very numerically demanding task due to how the size of a quantum system “scales” with the number of particles it consists of. It is therefore necessary to use high performance computer clusters to simulate quantum systems of even moderate size. Such simulations are of great value as outcomes can be used to guide the experimental efforts in the lab and also because simulations offer access to information that is hard or impossible to retrieve by measurement. In this way one can study many elusive phenomenon, such as quantum entanglement, in detail.

At the University of Auckland my co-workers and I have recently made an effort in this direction by simulating a large number of atoms interacting with the electromagnetic field on the NeSI Pan high performance computing cluster. We assume that the atoms are trapped inside a cavity, consisting of highly reflective mirrors, which increases the strength of the interaction between the electromagnetic field and the atoms. This system has a fascinating property, first predicted theoretically in the 1950s, but not witnessed in experiment until 2010; namely, if the interaction strength between the atoms and electromagnetic field becomes sufficiently strong, the system enters a so-called “super-radiant phase” emitting light at high intensity higher than what one would expect just by adding up the rate of emission from each atom.

In the presence of this “collective effect”, where the atoms cooperate to generate light, the atoms and the photons present inside the cavity can no longer be viewed as individual constituents, but are entangled in such a way that they create a fundamentally new type of matter. By simulating this transition from “normal phase” where the atoms and photons act on an individual basis to the “super-radiant phase” where they collectively cooperate on a computer cluster, we can gain insight into this entangling of light and matter. Our goal is to capture a genuinely quantum phenomenon of entanglement between atoms and an electromagnetic field.

Simulation design

Simulations for a quantum state was represented by 720 × 720 complex numbers.

Figures 2 & 3 show a visualisation of the quantum state of the electromagnetic field inside the cavity.

Figure 2 - This is what the EM field looks like below threshold. It is in the “vacuum” state (zero photons) which is the same state it would be in if there were no atoms present. Interestingly, due to quantum mechanical fluctuations, even the vacuum state has an interesting structure.

Figure 3 - The EM field above threshold; the superradiant phase. The two-peak structure with concentrations away from the origin (0,0) is a quantum state with a large number of photons.

We applied a matrix to the quantum state viewed as a vector which involved a matrix size of (720 × 720) × (720 × 720). To do one run approximately 90 GB of RAM was needed which is largely available on the NeSI Pan cluster.

One hundred simulations were run in parallel which quickly mapped out the behaviour of the system over a large range of model parameters. By looking at the numerical results for the quantum state, one can witness the system going through several transitional regions of different behaviour as we vary the model parameters. Qualitatively, these different behaviours of the quantum state are different phases of the “quantum matter” inside the cavity.

Figures 2 and 3 show visualisation of the quantum state of the electromagnetic field in the cavity, in two different phases for the quantum matter, inferred from our numerical simulations

Collaboration with international researchers

Parallel to our numerical simulations, we are now in collaboration with a group of researchers at the National University of Singapore (NUS) who are implementing laboratory experiments to realize the same model. In drawing upon our results, these simulations can provide a useful guide to the researchers at NUS and help them understand the dynamics. We also believe that through the collaboration, we can anticipate novel experimental results and probe deeper into the quantum nature of the interaction of light and matter.

My research efforts in Auckland, and the collaboration my co-workers and I now have with Singapore, would not have been feasible without access to the NeSI computing cluster and the help received from the technical staff in setting up our simulations. The staff stand out for how they understand the needs of the scientists, and the effort they make to streamline the use of the cluster for us on an individual basis.


This case study has been adapted from the original produced by the Centre for eResearch at the University of Auckland.


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