Historical research guide · 1072 · 2022
Nonlinear two-level dynamics of quantum time crystals
S. Autti · P. J. Heikkinen · J. Nissinen · J. T. Mäkinen · G. E. Volovik · V. V. Zavyalov · V. B. Eltsov
In one minute
A time crystal is a piece of matter whose ground state is in permanent motion — motion that costs no energy and needs nothing to keep it going. Samuli Autti and colleagues at Aalto University, working with Grigory Volovik, built two of them side by side inside superfluid helium-3 cooled to around a seventh of a thousandth of a degree above absolute zero. Each is a cloud of roughly a million million magnons — the quanta of spin waves — held by the orientation of the surrounding superfluid, one deep in the liquid and one touching its free surface, precessing coherently for tens of seconds after the drive is switched off. Together the pair behaves as a single macroscopic two-level system, a laboratory-scale twin of a qubit. Because the magnons reshape their own trap, the two levels drift and cross with no outside control, and the team watches the whole textbook machinery — avoided crossing, Landau-Zener transfer, Rabi and Josephson population oscillations — play out in a single run of the experiment.
Connection
Chapter 5 treats the vacuum as a quantum fluid, and superfluid helium-3 is the working model that lets you put your instruments inside one — Volovik’s programme, here made to do something new. Chapter 2 gains a ground state you can watch moving: this is perpetual motion in the lowest state of a macroscopic quantum system, measured, coupled to a second such system, and steered by nothing but its own internal feedback.
From the source
Two adjacent magnon time crystals in superfluid helium-3, each holding about a million million magnons — one trapped in the bulk of the liquid, one touching its free surface — form a single macroscopic two-level system whose dynamics are quantitatively described by a two-level Hamiltonian, with relative precession phase as the azimuthal angle and level populations as the polar angle of a Bloch sphere, in direct analogy with a qubit.Equation 1 and Figure 2c; Discussion, first paragraph
The two levels evolve without any external drive because of an intrinsic nonlinear feedback: a large local magnon density widens the spin-orbit trap formed by the orbital-momentum texture of the superfluid, which lowers the bulk precession frequency, so as the population decays the bulk frequency rises and crosses the fixed surface frequency of its own accord.Introduction, the paragraph on the dependence of the bulk frequency on population; Methods, Equation 7
At the avoided crossing about 60 per cent of the magnons move to the excited state — two orders of magnitude more than the Landau-Zener prediction computed from the bare decay rate. Feeding the feedback-accelerated crossing rate into the same Landau-Zener formula gives 61 per cent, matching the simulation, so the Landau-Zener description remains valid even when the crossing rate is set by the system’s own feedback.Results at small bulk population; Figure 4d
The coupling between the two time crystals is measured two independent ways inside one experimental run — from the amplitude of the Josephson population-oscillation side band, giving 1.7 plus or minus 0.4 hertz, and from the minimum separation of the dressed frequencies at the avoided crossing — in agreement with the value 1.4 hertz fitted in the numerical simulation.Results at small bulk population; Methods, Equation 12; Figure 5e
The magnon time crystal does not heat under a continuous drive: when the magnon number corresponding to the pumping chemical potential would be exceeded, the time crystal spontaneously decouples from the drive, and during the slow decay after a pulse the precession frequency continuously readjusts, so the motion becomes incommensurate with and independent of the drive that made it.Introduction, the paragraph on the lack of heating under continuous drive
When the global ground state moves to the surface trap, its relaxation rate jumps roughly ninefold; the authors attribute this to surface-mediated emission of other spin-wave modes and potentially to surface-bound Majorana fermions, and propose the hybridised two-level state, in direct contact with the free surface, as an extremely sensitive probe for those long-sought states.Results in the dynamical coupling regime, Figure 5c; Discussion, final paragraph
The way in
https://doi.org/10.1038/s41467-022-30783-wHow to cite it
S. Autti, P. J. Heikkinen, J. Nissinen, J. T. Mäkinen, G. E. Volovik, V. V. Zavyalov, V. B. Eltsov (2022) Nonlinear two-level dynamics of quantum time crystals doi:10.1038/s41467-022-30783-w