We present a dual-amplifier laser system for time-resolved multiple-probe infrared (IR) spectroscopy based on the ytterbium potassium gadolinium tungstate (Yb:KGW) laser medium. Comparisons are made between the ytterbium-based technology and titanium sapphire laser systems for time-resolved IR spectroscopy measurements. The 100 kHz probing system provides new capability in time-resolved multiple-probe experiments, as more information is obtained from samples in a single experiment through multiple-probing. This method uses the high repetition-rate probe pulses to repeatedly measure spectra at 10 µs intervals following excitation allowing extended timescales to be measured routinely along with ultrafast data. Results are presented showing the measurement of molecular dynamics over >10 orders of magnitude in timescale, out to 20 ms, with an experimental time response of <200 fs. The power of multiple-probing is explored through principal component analysis of repeating probe measurements as a novel method for removing noise and measurement artifacts.
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable in terms of the rate of decay to equilibrium. Our result shows the emergence of a Fluctuation-Dissipation theorem corresponding to a classical Brownian process, specifically, the Ornstein-Uhlenbeck process. Our predictions can be tested in quantum simulation experiments, thus helping to bridge the gap between theoretical and experimental research in quantum thermalization. We test our analytic results by exact numerical experiments in a spin-chain. We argue that our Fluctuation-Dissipation relation can be used to measure the density of states involved in the non-equilibrium dynamics of an isolated quantum system.
We derive the eigenstate thermalization hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by Deutsch (1991 Phys. Rev. A 43 2046). We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-functions that arises as a result of the orthonormality condition. This approach leads to a consistent form for off-diagonal matrix elements of observables. From there we obtain the scaling of time-averaged fluctuations of generic observables with system size for which we calculate an analytic form in terms of the inverse participation ratio. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes.
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