Can quantum mechanics be studied using an electromechanical system?

When a theoretical physicist is given a problem that involves quantum mechanics one of the first thing he or she is likely to do is to write the Hamiltonian of the problem. This is an operator in the quantum mechanics definition of an operator, that is, it is a mathematical object that maps one state vector (one quantum mechanical vector that describes the state of the system) into another and that is associated to a quantity in classical physics. The Hamiltonian is usually (I won’t get into what this “usually” means because this would take the whole post) associated with the total energy of the system. They are extremely important to quantum mechanics: it’s the Hamiltonian that describes how a quantum state will evolve in time!

Once a Hamiltonian is written the physicist would start looking for solutions and he/she would hope that there was an analytic solution. This means that the problem has a closed form in terms of known functions and constants. Unfortunately, the more complex the problem (and therefore, it’s Hamiltonian) the more unlikely it is that an analytic solution can be found. If that’s the case a computer can be used to find the solutions.

1_An electromechanical Ising Hamiltonian_140816_FIG1

Fig1. There are several quantum systems that cannot be solved analytically or by computer simulators. The Ising Hamiltonian for a spin glass is one of these systems.

Now there is a new problem, depending on the Hamiltonian it is possible that a classical computer would take a massive amount of time to compute the full solutions. In these situations, instead of giving up, physicist can use physical simulators. These correspond to physical system that act as computer simulators. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. Now a team of scientists from Japan have proposed that the Ising Hamiltonian could be solved using an electromechanical system.

A few questions might have come to your mind, for example: what is an Ising Hamiltonian? Well this is the Hamiltonian of the Ising model (you probably couldn’t see this coming, right?). And the Ising model is a mathematical model that describes ferromagnetism, the mechanism by which materials become permanent magnets. Its name is an homage to the physicist Erns Ising. Permanent magnets are systems that are quite easy to understand and describe, since all the spins are aligned, but not all Ising systems are like that. There are disordered materials where the the orientation of the spins does not follow a regular pattern. And these systems are hard to solve, even by a computer. However, according to the Japanese scientists, a clever way of dealing with these types of systems is to map the Ising Hamiltonian in an electromechanical system.

1_An electromechanical Ising Hamiltonian_140816_FIG2

Fig2. Scientists show that by mapping the Ising Hamiltonian into an electromechanical system it is possible to learn about the former via simulations with the later.

The scientists mapped the problem of the Ising Hamiltonian for a spin glass into an electromechanical system (a system that combines mechanical and electrical processes). They showed that it is possible to construct an electromechanical system that encodes the spin operator as well as the spin 1/2 particles and the interaction between them. This electromechanical system could be used as a physical simulator do solve the Ising Hamiltonian in a nontrivial configuration such as what is found in a spin glass. Instead of doing experiments with an Ising Hamiltonian the scientists can learn about it by running simulations in the electromechanical system.

This opens up the doors for using electromechanical systems as a versatile platform to study quantum mechanics within a macroscopic level. So brace yourselves, new discoveries in the field of quantum mechanics are coming!

Kellen Manoela Siqueira

The full paper can be found in the July 2016 issue of Science Advances.

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