Quantum Criticality at High Temperature Revealed by Spin Echo

Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly with tuning a system parameter. It is an important indicator of new quantum matters emerging. In conventional methods, quantum criticality is observable only at zero or low temperature (as compared with the interaction strength in the system). We find that a quantum probe, if its coherence time is long, can detect quantum criticality of a system at high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveal the critical quantum fluctuation without requiring low temperature. We first use the exact solution of the one-dimensional transverse-field Ising model to demonstrate the possibility of detecting the quantum criticality at high temperature by spin echo. The critical behaviors have been calculated using the exact solution and understood with the noise spectrum analysis in the Gaussian noise approximation. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature (TQC) in conventional methods and the necessary long coherence time (tQC) in probe decoherence measurement to observe the quantum criticality, that is, TQC ∼ 1/tQC and much less than the interaction strength of the system. For example, probes with quantum coherence time of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that is previously known only observable at extremely low temperatures of nano- or pico-Kelvin. This finding provides a new possibility to study quantum matters.;We also designed a scheme of Faraday rotation echo spectroscopy (FRES) that can be used to study spin noise dynamics in transparent materials by measuring the fluctuation of Faraday rotation angles. The FRES suppresses the static part of the noise and reveal the quantum fluctuations at relatively high temperature, which shares the same idea of the spin echo technique in nuclear magnetic resonance (NMR). We tested our theory on a rare-earth compound LiHoF4.The quantum fluctuation obtained by FRES gives an enhanced feature at the phase boundary. The FRES can be straightforwardly generalized to more complicated configurations that correspond to more complex dynamical decoupling sequences in NMR and electron spin resonance, which may give us more extensive information on the structural and dynamical properties of magnetic materials.