Physicists and engineers have long been interested in creating new forms of matter, those that are not usually found in nature. Such materials could one day be used in, for example, new computer chips. Beyond applications, they also reveal elusive information about the fundamental workings of the universe. Recent work at MIT has both created and characterized new quantum systems demonstrating dynamic symmetry – particular types of behavior that repeat themselves periodically, like a bent and reflected form over time.
“There are two problems we had to solve,” said Changhao Li, a graduate student from the laboratory of Paola Cappellaro, professor of nuclear science and engineering. Li published the work recently in Physical examination letters, with Cappellaro and his graduate student colleague Guoqing Wang. âThe first problem was that we had to design such a system. And second, how to characterize it? How do we observe this symmetry?
Concretely, the quantum system consisted of a diamond crystal approximately one millimeter in diameter. The crystal contains many imperfections caused by a nitrogen atom next to a gap in the lattice – a so-called nitrogen gap center. Just like an electron, each center has a quantum property called spin, with two discrete energy levels. Because the system is a quantum system, the spins can be found not only in one of the levels, but also in a combination of the two energy levels, like SchrÃ¶dinger’s theoretical cat, which can be both alive and dead.
The energy level of the system is defined by its Hamiltonian, whose researchers devised periodic time dependence via microwave control. The system was said to have dynamic symmetry if its Hamiltonian was the same not only after every time period t but also after, for example, every t / 2 or t / 3, like folding a piece of paper in half or in three of so that no part sticks out. Georg Engelhardt, a post-doctoral fellow at Beijing Computational Science Research, who was not involved in this work but whose own theoretical work served as the basis, compares symmetry to guitar harmonics, in which a string can vibrate both at 100 hertz and at 50 Hz.
To induce and observe such dynamic symmetry, the MIT team first initialized the system using a laser pulse. Then they directed various selected frequencies of microwave radiation at it and allowed it to evolve, allowing it to absorb and emit energy. âWhat’s amazing is that when you add such driving, it can present some very fanciful phenomena,â Li said. âThere will be periodic shaking.â Finally, they gave him another laser pulse and measured the visible light he was fluorescing, in order to measure his condition. The measurement was only a snapshot, so they repeated the experiment several times to piece together a sort of flip book that characterized its behavior over time.
âWhat’s very impressive is that they can show they have this incredible control over the quantum system,â says Engelhardt. “It’s easy enough to solve the equation, but to do this in an experiment is quite difficult.”
Critically, the researchers observed that the dynamic symmetry of the Hamiltonian – the harmonics of the system’s energy level – dictated what transitions could occur between one state and another. âAnd the novelty of this work,â says Wang, âis also that we present a tool that can be used to characterize any quantum information platform, not just the nitrogen vacancy centers in diamonds. This is widely applicable. Li notes that their technique is simpler than the previous methods, those which require constant laser pulses to drive and measure the periodic movement of the system.
One engineering application is quantum computers, systems that manipulate qubits, bits that can be not just 0 or 1, but a combination of 0 and 1. The rotation of a diamond can encode a qubit in its two levels. of energy.
Qubits are tricky: they easily break down into a single bit, a 1, or a 0. Or the qubit can become the wrong combination of 0 and 1. âThese tools for measuring dynamic symmetries,â Engelhardt explains, âcan be used like a check that your experiment is tuned correctly – and with very high precision. âHe notes the problem of outside disturbances in quantum computers, which he likens to a detuned guitar. By adjusting the tension of the strings – by adjusting the radiation microwave – so that the harmonics meet certain theoretical requirements of symmetry, one can be sure that the experiment is perfectly calibrated.
The MIT team already has extensions to this work in view. âThe next step is to apply our method to more complex systems and study more interesting physics,â says Li. They aim for more than two energy levels – three, or 10, or more. With more energy levels, they can represent more qubits. âWhen you have more qubits, you have more complex symmetries,â Li explains. âAnd you can characterize them using our method here.â
This research was funded, in part, by the National Science Foundation.