|
|
| Fig. 1: Experimental Schematic showing individually trapped atoms, and transverse Rydberg lasers interacting with all atoms. (Source: A. Periwal) |
Many talks on quantum simulation open with the same Feynman quote, and this paper is no different.
"Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy."
Unfortunately for Feynman, and perhaps all of us, making a quantum mechanical simulation is challenging, because quantum mechanical objects are hard to control. In this paper, I will discuss how individual atoms are trapped and made to interact to simulation a simple 1D Hamiltonian, and then I will discuss how some of the effects observed in this system lead to new theoretical insights. [1,2]
There are many different possibilities for quantum mechanical simulation and computing. Perhaps the most famous is the superconducting qubit, used in Google's demonstration of quantum supremacy. [3] The experiment described here, however, used individual neutral Rubidium atoms trapped and arranged in a 1D lattice. [1]
Neutral atoms have weak interactions by default, but stronger interactions can be mediated by exciting the atoms into a high-lying Rydberg state, which make the atom radius dramatically larger, creating Van der Waals interactions between nearby atoms. These interactions are mediated by lasers, and so by tuning laser frequencies and powers, the scales of different terms in the Hamiltonian can be changed. The ground state and the Rydberg state can be used as effective spin states, and each atom can be imaged directly. Slow adiabatic ramps can be used to probe the phase space of the 1D Hamiltonian, and sudden changes in laser frequency/power can be used to study dynamics after a quench.
A quench of one particular low energy state (an alternating ground, Rydberg state), showed coherent oscillations and a lack of thermalization that was not immediately understood. Shortly after these experimental results were published, a paper on quantum scars, explaining these results was published.
Physicists have known for decades that classically chaotic systems can still have special periodic orbits. The analog in a quantum mechanical system are scars, where eigenfunctions of the Hamiltonian are sometimes concentrated on the trajectory of one of these special orbits. However, in this experiment we are dealing with a many-body trajectory.
The paper on quantum scars showed dynamics in a L = 32 system that were consistent with the experimental results. [2] We should note that the Rydberg simulator was able to have up to 51 qubits! The Hamiltonian describing the time evolution of the system does not have any subtle symmetries, and the level statistics bear this out. However, by looking at the overlap of the alternating ground/Rydberg state with the Hamiltonian eigenfunctions, Turner et al. found a set of eigenfunctions with especially strong overlap to the initial state. [2] These eigenstates are concentrated on a periodic many-body trajectory, and explain the oscillations observed in the initial experiment.
© Avikar Periwal. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] H. Bernien et al., "Probing Many-Body Dynamics on a 51-Atom Quantum Simulator," Nature 551, 579 (2017).
[2] C. J. Turner et al., "Weak Ergodicity Breaking from Quantum Many-Body Scars," Nat. Phys. 14, 745 (2018).
[3] Arute, Frank et al. "Quantum supremacy using a programmable superconducting processor." Nature 574, 505 (2019).