Finding cohesion in quantum chaos

LOS ALAMOS, NM, May 26, 2022 – A theoretical breakthrough in understanding quantum chaos could open new avenues for 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 gains and losses to an open quantum system, we found a way to overcome a previously held constraint that hypothesized that interactions with the environment would reduce quantum chaos,” said Avadh Saxena, a theoretical physicist at Los Alamos National Laboratory and member of the team that published the paper on quantum chaos in physical assessment letters. “This discovery points to new directions in studying quantum simulations and quantum information theory.”

Quantum chaos differs from classical physics chaos theory. The latter tries to understand deterministic or non-random patterns and systems that are highly sensitive to initial conditions. The so-called butterfly effect is the best-known example, where the flapping of a butterfly’s wings in Texas, through an astonishingly complicated but non-random chain of cause and effect, can 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 in complex systems such as black holes. It reveals itself in the energy spectra of the system, in the form of correlations between its characteristic modes and frequencies.

It has been assumed that if a quantum system loses coherence, or its ‘quantumness’, coupling to the environment outside the system – the so-called quantum to classical transition – suppresses the features of quantum chaos. That means they cannot be exploited as quantum information or as a state that can be manipulated.

That turns out not to be entirely true. Saxena, physicists from the University of Luxembourg, Aurelia Chenu and Adolfo del Campo, and collaborators found that in some cases, the dynamic features of quantum chaos are even enhanced, not suppressed.

“Our work challenges the expectation that decoherence generally suppresses quantum chaos,” Saxena said.

The energy values ​​in the spectra of the quantum system were previously considered to be complex numbers – that is, numbers with an imaginary number component – and thus not useful in an experimental setting. But by adding energy gain and loss at symmetrical points in the system, the research team found true values ​​for the energy spectra, provided the strength of gain or loss is below a critical value.

“Balanced energy gain and loss provides a physical mechanism to achieve in the lab the kind of energy spectral filtering that has become ubiquitous in theoretical and numerical studies of complex, high-particle quantum systems,” Del Campo said. “Specifically, a balanced energy gain and loss in energy dephasing leads to the optimal spectral filter. Thus, one could use balanced energy gain and loss as an experimental tool, not just to investigate quantum chaos, but to study many-body quantum systems in general.”

By changing the decoherence, Saxena and del Campo explained, the filter allows for better control of the energy distribution in the system. This can be useful, for example, with quantum information.

“Decoherence limits quantum computing, so because increasing quantum chaos reduces decoherence, you can keep calculating for longer,” Saxena said.

The team’s paper builds on previous theoretical work by Carl Bender (of Washington University in St. Louis and former Ulam scientist at Los Alamos) and Stefan Boettcher (formerly of Los Alamos and now at Emory University). They found that, contrary to the accepted paradigm of the early twentieth century, some quantum systems yielded real energy under certain symmetries, even though their Hamiltonian was not Hermitian, meaning it satisfies certain mathematical relationships. In general, such systems are known as 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,” Saxena said. “So we thought, what if we take a non-Hermitian system?”

The research paper studied the example of pumping energy into a waveguide at one point – that is, the gain – and then pumping energy out again – the loss – symmetrically. The waveguide is an open system that can exchange energy with the environment. Rather than cause decoherence, they found that the process and interactions increase coherence and quantum chaos.

The newspaper: “Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gains and Loss: Improving Quantum Chaos,” by J. Cornelius, Z. Xu, A. Saxena, A. Chenu, and A. del Campo, in Physical Review Letters. DOI:

Funding: The work was supported by Laboratory Directed Research and Development at Los Alamos National Laboratory.


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