Researchers develop a new way to control and measure energy levels in a diamond crystal

Caption:Instrumentation setup in the Quantum Engineering Group at MIT to study dynamical symmetries with qubits in diamond crystals Credit: Guoqing Wang/MIT
Engineers and physicists have been fascinated by the creation of new types of matter. These materials could one day be used in novel computer chips. They have many applications but also provide a glimpse into the fundamental workings and nature of the universe. Recent work at MIT has created and characterized quantum systems that demonstrate dynamical symmetry. These are particular kinds of behavior that repeat repeatedly, much like a folded shape reflecting through time.

Changhao Li, a graduate students in the laboratory of Paola Cappellaro and a professor of nuclear engineering, says that there were two problems they needed to solve. Li, Cappellaro, and Guoqing Wang, a fellow graduate student, published their work in Physical Review Letters. "The first problem was how to design such a system. The second problem was how to characterize it. This symmetry can be observed in two ways.

The quantum system was a diamond crystal measuring approximately a millimeter in size. A nitrogen atom is located next to the gap in the crystal's lattice, causing many imperfections. This so-called nitrogen-vacancy centre is also present. Each center, just like an electron has a quantum property called "a spin", with two distinct energy levels. The system is a quantum system so the spins can not only be found in one level but can also be found in combination of both energy levels. This is Schrodinger's theory cat which can be alive and dead simultaneously.

The Hamiltonian is the measure of the energy level in the system. Its periodic time dependence was created by microwave control. If the Hamiltonian of the system is constant after all time periods t, but also after t/2 and t/3, then dynamical symmetry was achieved. This can be compared to folding paper in half, or in thirds, so that no piece sticks out. Georg Engelhardt was a postdoctoral researcher at Beijing Computational Science Research. Although he wasn't involved in the work, his own theoretical work served to provide a foundation. He likens the symmetry with guitar harmonics in which a string vibrates at both 100 and 50 hertz.

The MIT team initialized the system with a laser pulse to induce and observe this dynamical symmetry. They then directed microwave radiation at the system and allowed it to evolve. Li says that it can display some really fancy phenomena when you add driving. It will occasionally shake. They then shot another laser pulse at the device and measured its fluoresce. This was to determine its current state. They took a snapshot of the measurement, but it was not enough to determine its behavior over time.

A cutting-edge quantum information processing toolkit allows for the engineering and characterisation of dynamic symmetries that play an important role in physics. Credit: Image courtesy the researchers.

Engelhardt states, "What's very impressive is that the can show that they have an incredible control over quantum system." It's easy to solve the equation. However, it is difficult to prove this in an experiment.

The researchers found that the Hamiltonianthe harmonics of a system's energy level were dynamically symmetric, which meant that transitions between states could be made. Wang states that the novelty of Wang's work is that it can be used to characterize any quantum platform. It is broadly applicable. Li points out that the technique is simpler than other methods that required constant laser pulses to drive the system and measure its periodic movement.

Quantum computers are a type of engineering that allows for manipulation of qubits. These bits can be either 0 or 1 but also a combination of both 0 and 1. One qubit can be encoded in a diamond's spin by its two energy levels.

Qubits can be fragile: they break down easily into simple bits, 1 and 0. The qubit could also be confused with 0 or 1. Engelhardt states that these tools can be used to measure dynamical symmetries and are a way of ensuring that the experiment is set up correctly. Engelhardt compares the problem of quantum computers being affected by outside perturbations to a guitar that isn't tuned properly. You can calibrate the experiment by tuning the tension of strings and adjusting microwave radiation to match theoretical symmetry requirements.

Already, the MIT team is aiming for extensions to this work. Li states that the next step is to apply the method to more complex systems, and to study more interesting physics. They are looking for energy levels that exceed two, three, 10, or even more. They can represent more qubits if they have higher energy levels. Li states that more qubits means more complex symmetries. You can identify them with our method here.

Learn more How flawed diamonds can lead to flawless quantum networks

Guoqing Wang et. al., Observation of Symmetry Protected Selection Rules in Periodically Driven Quum Systems, Physical Review Letters (2021). Information from the Journal: Physical Review Letters Guoqing Wang et. al., Observation of Symmetry Protected Selection Rules in Periodically Driven Quum Systems, (2021). DOI: 10.1103/PhysRevLett.127.140604

This story is republished courtesy of MIT News (, a popular site that covers news about MIT research, innovation and teaching.