A large body of conspicuous publications in recent years asserts that the high temperature approximation (HTA), a mostly tested and most widely used assumption in NMR spectroscopy and MRI technology, is invalid for concentrated samples in high magnetic fields such as for a proton COSY spectrum of water. A by product of the alleged collapse of HTA, which is equally surprising, is the existence of intermolecular multi quantum coherences (MQC) in low viscosity liquids such as water. In this work, both HTA and intermolecular MQCs in liquids will be critically examined in light of our theoretical analysis and experimental results. Our conclusions are: (1) There are no macroscopic quantum systems in conventional NMR samples such as water at room temperature. (2) At room temperature, high temperature approximation is still one of the most trustworthy approximations applicable to NMR and (3) The MQCs observed in proton COSY spectrum in, e.g., water, have nothing to do with quantum mechanical intermolecular spin interactions.
A large body of conspicuous publications in recent years asserts that the high temperature approximation (HTA), a mostly tested and most widely used assumption in NMR spectroscopy and MRI technology, is invalid for concentrated samples in high magnetic fields such as for a proton COSY spectrum of water. A by product of the alleged collapse of HTA, which is equally surprising, is the existence of intermolecular multi quantum coherences (MQC) in low viscosity liquids such as water. In this work, both HTA and intermolecular MQCs in liquids will be critically examined in light of our theoretical analysis and experimental results. Our conclusions are: (1) There are no macroscopic quantum systems in conventional NMR samples such as water at room temperature. (2) At room temperature, high temperature approximation is still one of the most trustworthy approximations applicable to NMR and (3) The MQCs observed in proton COSY spectrum in, e.g., water, have nothing to do with quantum mechanical intermolecular spin interactions.
In recent years evidence was presented that two radio frequency pulses in combination with suitably matched field gradient pulses produce cross peaks in two-dimensional NMR spectroscopy that reveal all the features of multiple-quantum/single-quantum coherence transfer signals. This experiment was termed CRAZED by Warren et al. Quite amazingly, identical signals were predicted on a purely classical basis. Thus the intriguing question arises whether this means that a classical analog to multiple-quantum coherences exists. In this study we show that this is clearly not the case. Coherence pathways of a purely single-quantum basis are excited anyway and lead independently to superimposed identical signals in parallel. Moreover, the observation of CRAZED signals per se neither disproves the adequacy of the high-temperature approximation, which was questioned in this context, nor proves a strong influence of intermolecular multiple-quantum coherences. However, the indispensable prerequisite for the description of the manifold CRAZED phenomena is that long-range dipolar interactions are taken into account either explicitly or in the continuous-limit form.
Recently, two-dimensional NMR experiments have been performed, which were likely to show that a coupling between otherwise uncoupled or equivalent spins was observable, yielding signals originating from multiple-spin multiple-quantum operators in the density matrix. According to the authors, such surprising results could be interpreted as a consequence of the radiation damping phenomenon. For this purpose, a fully quantum-mechanical frame was used, thus treating the radiation field in a quantized manner. Our analysis, based on the same theoretical grounds, as well as on new experimental arguments, lead us to diverging conclusions.
Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly on tuning system parameters. 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 the 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 were calculated using the exact solution and understood by the noise spectrum analysis in the Gaussian noise approximation. By numerical simulation, we further verify that the high-temperature quantum criticality also exists in the probe coherence measurement of spin systems with dipolar couplings. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature ( T QC ) in conventional methods and the necessary long coherence time ( t QC ) in probe decoherence measurement to observe the quantum criticality, that is, T QC ∼ 1/ t QC and much less than the interaction strength of the system. For example, probes with quantum coherence times of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that was previously known to be only observable at extremely low temperatures of nano- or pico-kelvin. This finding provides a new possibility to study quantum matters.
The quantum Ising chain in a transverse magnetic field is $t\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e$ paradigm of a quantum phase transition, displaying universal quantum criticality at low temperatures. Insights from this model have informed studies of quantum criticality in numerous modern correlated-electron materials. There have been a number of experimental studies of the quantum Ising chain, most notably in the material CoNb2O6. It has recently become clear that there was a surprising discrepancy between the observations: the energy gap in the quantum disordered regime as measured by nuclear magnetic resonance was approximately twice that measured by other methods. Here, the authors show via careful analysis of the low-temperature excitations that this is not a discrepancy, rather, it is in fact to be expected from the subtle interactions between the excitations. Although the underlying spin excitations are bosonic, their interactions transmute them into fermions, and this is a key ingredient in understanding the experiments.
Explanation of decoherence and quasi-equilibrium in systems with few degrees of freedom demands a deep theoretical analysis that considers the observed system as an open quantum system. In this work, we study the problem of decoherence of an observed system of quantum interacting particles, coupled to a quantum lattice. Our strategy is based on treating the environment and the system-environment Hamiltonians fully quantum mechanically, which yields a representation of the time evolution operator useful for disentangling the different time scales underlying in the observed system dynamics. To describe the possible different stages of the dynamics of the observed system, we introduce quantum mechanical definitions of essentially isolated, essentially adiabatic, and thermal-contact system-environment interactions. This general approach is then applied to the study of decoherence and quasi-equilibrium in proton nuclear magnetic resonance ((1)H NMR) of nematic liquid crystals. A summary of the original results of this work is as follows. We calculate the decoherence function and apply it to describe the evolution of a coherent spin state, induced by the coupling with the molecular environment, in absence of spin-lattice relaxation. By assuming quantum energy conserving or non-demolition interactions, we identify an intermediate time scale, between those controlled by self-interactions and thermalization, where coherence decays irreversibly. This treatment is also adequate for explaining the buildup of quasi-equilibrium of the proton spin system, via the process we called eigen-selectivity. By analyzing a hypothetical time reversal experiment, we identify two sources of coherence loss which are of a very different nature and give rise to distinct time scales of the spin dynamics: (a) reversible or adiabatic quantum decoherence and (b) irreversible or essentially adiabatic quantum decoherence. Local irreversibility arises as a consequence of the uncertainty introduced by the coupling with an infinite quantum environment. The reversible part can be represented by a semiclassical model, similar to standard line-shape adiabatic models. By exploiting the separation existing between the time scales of the spin coherences and the irreversible decoherence, we present a novel technique to obtain the orientational molecular distribution function for a nematic liquid crystal. The procedure is based on the comparison of the observed coherence time evolution and numerical calculation under the adiabatic quantum decoherence approach. As an example, it is used the experimental free induction decay from a nematic PAA(d6) sample to extract such an orientational distribution. This is the first theoretical description of the experimental liquid crystal NMR signal in the time domain. On the contrary, the irreversible decoherence is intrinsically full-quantum mechanical, as it is governed by the commutation properties of the environment and the spin-lattice Hamiltonians. Consistently, it depends on the molecular correlation in a decisive way, since it vanishes under a mean-field model for the molecular dynamics. The results of this work can contribute to the understanding of the open question of the applicability of the spin-temperature concept in spin systems with few degrees of freedom.
Nonclassicality Analysis and Entanglement Witnessing in Spin-1/2 NMR Systems
We investigate quantum features and non-classical nature of two-spin-1/2 NMR systems at thermal equilibrium under external magnetic fields. More specifically, using suitable quantifiers, we analyze quantum coherence, mixedness, and entanglement in NMR systems and examine their features within the system. We derive closed-form analytical expressions for the quantum elements and show how they depend on temperature and magnetic field strength. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measures of coherence, and a sharp peak in mixedness. Moreover, we analyze the entanglement of the system using a suitable entanglement witness. This provides an experimentally friendly setting for testing entanglement in NMR systems. In other words, the witness links the entanglement in the system to quantum observables, making it directly provable in NMR experiments. We establish a connection between quantum information quantifiers and experimentally accessible NMR spectra of the system, enabling the quantification of entanglement, coherence, and mixedness through NMR signal processing.