Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional ¹H zigzag spin chains in hambergite (Be₂BO₃OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long ¹H spin-lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

Information Scrambling and Loschmidt Echo

We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator-a recently suggested measure of information scrambling in quantum chaotic systems-and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it contains progressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator to monitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses how weak perturbations degrade the information encoded in these increasingly complex states. Both observables involve the implementation of a time-reversal procedure which, in practice, involves inverting the sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate the natural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile, experimental errors and strength of perturbative terms remain constant and can be quantified through the LE. For each scaling factor, information spreading occurs with a timescale, T_{2}, inversely proportional to the local second moment of the Hamiltonian. We find that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered. However, we find that the LE decay rate cannot become smaller than a critical value 1/T_{3}≈(0.15±0.02)/T_{2}, which only depends on the interactions themselves, and not on the perturbations. This result shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted from previous experiments.

Power-optimized, time-reversal pulse sequence for a robust recovery of signals from rigid segments using time domain NMR

Time domain NMR (TD-NMR) has been widely used on the analysis of liquids or liquid components in heterogeneous materials such as food, biological tissues, synthetic and bio polymers, oil-bearing rocks, biomasses and cement-based materials. The use of TD-NMR for studying solid and soft mater has been growing in number and variety of applications, mostly for organic systems where the detection of ¹H signals is highly advantageous. However, the strong ¹H-¹H dipolar interactions in solids make the ¹H FID to decay in the same order of the dead time of most commercially available NMR probe heads. Thus, solid echoes are often used for recovering signals from solid components. In this article we reinvestigate the time-reversal solid-echo pulse sequence proposed by Rhim and Kessemeier, seeking for optimal pulse power and timing conditions that maximize its efficiency on recovering ¹H signals from rigid segments. We show that under these optimized conditions, which we denote as Rhim and Kessemeier - Radiofrequency Optimized Solid-Echo (RK-ROSE), the experiment can be more efficient than its most popular counterparts Solid-Echo (SE) and mixed-Magic Sandwich Echoes (mixed-MSE). Our results also suggest that, despite the finite pulse power, with current probe technology the RK-ROSE experiment is potentially able to provide an accurate estimation of rigid components, without relying on an external calibration using multiple standard samples, as usually done in SFC analysis of the FID signal. At last, we demonstrate that RK-ROSE can be adapted as a simple filter to supress signals from mobile segments in heterogeneous materials.

Evolution of multiple quantum coherences with scaled dipolar Hamiltonian

In this article, we introduce a pulse sequence which allows the monitoring of multiple quantum coherences distribution of correlated spin states developed with scaled dipolar Hamiltonian. The pulse sequence is a modification of our previous Proportionally Refocused Loschmidt echo (PRL echo) with phase increment, in order to verify the accuracy of the weighted coherent quantum dynamics. The experiments were carried out with different scaling factors to analyze the evolution of the total magnetization, the time dependence of the multiple quantum coherence orders, and the development of correlated spins clusters. In all cases, a strong dependence between the evolution rate and the weighting factor is observed. Remarkably, all the curves appeared overlapped in a single trend when plotted against the self-time, a new time scale that includes the scaling factor into the evolution time. In other words, the spin system displayed always the same quantum evolution, slowed down as the scaling factor decreases, confirming the high performance of the new pulse sequence.

Loschmidt echo and time reversal in complex systems

Echoes are ubiquitous phenomena in several branches of physics, ranging from acoustics, optics, condensed matter and cold atoms to geophysics. They are at the base of a number of very useful experimental techniques, such as nuclear magnetic resonance, photon echo and time-reversal mirrors. Particularly interesting physical effects are obtained when the echo studies are performed on complex systems, either classically chaotic, disordered or many-body. Consequently, the term Loschmidt echo has been coined to designate and quantify the revival occurring when an imperfect time-reversal procedure is applied to a complex quantum system, or equivalently to characterize the stability of quantum evolution in the presence of perturbations. Here, we present the articles which discuss the work that has shaped the field in the past few years.