Quantum criticality at infinite temperature revealed by spin echo

Details Quantum criticality at infinite temperature revealed by spin echo Quantum criticality at infinite temperature revealed by spin echo

2012-02-22

arxiv.org/abs/1202.4958v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

including supplementary equations and figures

Scientific paper

Criticality occurs widely at transitions between qualitatively different states of matters. Quantum criticality due to diverging quantum fluctuations, which can be observed by varying system parameters at zero temperature, is particularly important as it indicates the emergence of new orders of quantum matters. However, at temperature higher than the system's interaction strength thermal fluctuations will dominate over the quantum fluctuations and hence conceal the quantum criticality. Extremely low temperatures are required for quantum criticality to occur in many interesting systems. For example, for nuclear spins in solids and cold atoms in optical lattices, temperatures of $10^{-9}$ or even $10^{-12}$ Kelvin are required. Here we show that quantum criticality can be observed at high or even infinite temperature by measuring the echo signal of a probe spin coupled to a quantum many-body system, because the spin echo can remove the thermal fluctuation effect and therefore reveal the quantum fluctuation effect. We also establish the correspondence between the probe coherence time and the inverse temperature required for the onset of quantum criticality. In particular, quantum criticality that would occur below $10^{-9}$ or even $10^{-12}$ Kelvin can be detected by spin echo with coherence time longer than milliseconds or seconds, respectively. This discovery provides a new route to a vast land of quantum matters, via trading long coherence time of a quantum probe for extremely low temperature.

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