A theoretical breakthrough in understanding quantum chaos could open new avenues in research into quantum information and quantum computing, many-body physics, black holes, and the still elusive transition from quantum to classical.
“By applying balanced energy gain and loss to an open quantum system, we found a way to overcome a previously held limitation that assumed interactions with the surrounding environment would reduce quantum chaos,said Avadh Saxena, a theoretical physicist at Los Alamos National Laboratory and a member of the team that published the quantum chaos paper in Physical Review Letters. “This discovery points to new directions in the study of quantum simulations and quantum information theory.”
Quantum chaos differs from the chaos theory of classical physics. The latter seeks to understand deterministic, or non-random, models and systems that are very sensitive to initial conditions. The so-called butterfly effect is the best-known example, according to which the flapping of a butterfly’s wings in Texas could, through a confusing but not random chain of cause and effect, lead to a tornado in Kansas.
On the other hand, quantum chaos describes chaotic classical dynamical systems in terms of quantum theory. Quantum chaos is responsible for the scrambling of information occurring in complex systems such as black holes. It is revealed in the energy spectra of the system, in the form of correlations between its characteristic modes and its frequencies.
It has been believed that as a quantum system loses its coherence, or “quantum character”, by coupling to the environment outside the system – the so-called quantum-to-classical transition – the signatures of quantum chaos are removed. This means that they cannot be exploited as quantum information or as a state that can be manipulated.
Turns out that’s not quite true. Saxena, physicists Aurelia Chenu and Adolfo del Campo from the University of Luxembourg and their collaborators found that the dynamic signatures of quantum chaos are actually enhanced, not suppressed, in some cases.
“Our work challenges the expectation that decoherence typically suppresses quantum chaos,” said Saxena.
The energy values in the spectra of the quantum system were previously considered to be complex numbers, i.e. numbers with an imaginary numerical component, and therefore useless in an experimental setting. But by adding the energy gain and loss at symmetrical points in the system, the research team found real values for the energy spectra, provided the strength of the gain or loss is less than a critical value.
“Balanced energy gain and loss provide a physical mechanism for performing in the laboratory the type of energy-spectral filtering that has become ubiquitous in theoretical and numerical studies of complex quantum many-body systems.” said del Campo. “Specifically, a balanced energy gain and loss in the energy phase shift leads to the optimal spectral filter. Thus, one could take advantage of balanced energy gain and loss as an experimental tool not only for probing quantum chaos, but also for studying quantum many-body systems in general.”
By modifying the decoherence, Saxena and del Campo explain, the filter allows better control of the energy distribution in the system. This can be useful in quantum information, for example.
“Decoherence limits quantum computing, so it follows that because increasing quantum chaos reduces decoherence, you can keep computing longer,” said Saxena.
The team’s paper builds on previous theoretical work by Carl Bender (of Washington University in St. Louis and former Ulam Fellow at Los Alamos) and Stefan Boettcher (formerly of Los Alamos and now at the Emory University). They found that, contrary to the paradigm accepted at the beginning of the 20th century, some quantum systems produced real energies under certain symmetries even if their Hamiltonian was not Hermitian, meaning that it satisfied certain mathematical relations. In general, these systems are called non-Hermitian Hamiltonians. A Hamiltonian defines the energy of the system.
“The prevailing understanding was that decoherence suppresses quantum chaos for Hermitian systems, with real energy values”, said Saxena. “So we thought, what if we took a non-Hermitian system-“
The research paper studied the example of pumping energy into a waveguide at a particular point; it is the gain; then pumping the energy again; the loss ; symmetrically. The waveguide is an open system, capable of exchanging energy with the environment. Instead of causing decoherence, they found, the process and interactions increase coherence and quantum chaos.