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arXiv:1505.01559 · Physical Review A

Irreversible adiabatic decoherence of dipole-interacting nuclear-spin pairs coupled with a phonon bath

Federico D. Domínguez, Cecilia E. González, H. H. Segnorile, R. C. Zamar

Published Feb 25, 2016• 8 citations
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Abstract

We study the quantum adiabatic decoherence of a multispin array, coupled with an environment of harmonic phonons, in the framework of the theory of open quantum systems. We follow the basic formal guidelines of the well-known spin-boson model, since in this framework it is possible to derive the time dependence of the reduced density matrix in the adiabatic time scale, without resorting to coarse-graining procedures. However, instead of considering a set of uncoupled spins interacting individually with the boson field, the observed system in our model is a network of weakly interacting spin pairs; the bath corresponds to lattice phonons, and the system-environment interaction is generated by the variation of the dipole-dipole energy due to correlated shifts of the spin positions, produced by the phonons. We discuss the conditions that the model must meet in order to fit within the adiabatic regime. By identifying the coupling of the dipole-dipole spin interaction with the low-frequency acoustic modes as the source of decoherence, we calculate the decoherence function of the reduced spin density matrix in closed way, and estimate the decoherence rate of a typical element of the reduced density matrix in one- and three-dimensional models of the spin array. Using realistic values for the various parameters of the model we conclude that the dipole-phonon mechanism can be particularly efficient to degrade multispin coherences, when the number of active spins involved in a given coherence is high. The model provides insight into the microscopic irreversible spin dynamics involved in the buildup of quasiequilibrium states and in the coherence leakage during refocusing experiments in nuclear magnetic resonance of crystalline solids.

DOI
10.1103/physreva.93.022120

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We study the quantum adiabatic decoherence of a multispin array, coupled with an environment of harmonic phonons, in the framework of the theory of open quantum systems. We follow the basic formal guidelines of the well-known spin-boson model, since in this framework it is possible to derive the time dependence of the reduced density matrix in the adiabatic time scale, without resorting to coarse-graining procedures. However, instead of considering a set of uncoupled spins interacting individually with the boson field, the observed system in our model is a network of weakly interacting spin pairs; the bath corresponds to lattice phonons, and the system-environment interaction is generated by the variation of the dipole-dipole energy due to correlated shifts of the spin positions, produced by the phonons. We discuss the conditions that the model must meet in order to fit within the adiabatic regime. By identifying the coupling of the dipole-dipole spin interaction with the low-frequency acoustic modes as the source of decoherence, we calculate the decoherence function of the reduced spin density matrix in closed way, and estimate the decoherence rate of a typical element of the reduced density matrix in one- and three-dimensional models of the spin array. Using realistic values for the various parameters of the model we conclude that the dipole-phonon mechanism can be particularly efficient to degrade multispin coherences, when the number of active spins involved in a given coherence is high. The model provides insight into the microscopic irreversible spin dynamics involved in the buildup of quasiequilibrium states and in the coherence leakage during refocusing experiments in nuclear magnetic resonance of crystalline solids.
Refocalization sequences in nuclear magnetic resonance (NMR) can in principle reverse the coherent evolution under the secular dipolar Hamiltonian of a closed system. We use this experimental strategy to study the effect of irreversible decoherence on the signal amplitude attenuation in a single-crystal hydrated salt where the nuclear spin system consists of the set of hydration water proton spins having a strong coupling within each pair and a much weaker coupling with other pairs. We study the experimental response of attenuation times with temperature, crystal orientation with respect to the external magnetic field, and rf pulse amplitudes. We find that the observed attenuation of the refocalized signals can be explained by two independent mechanisms: (a) evolution under the nonsecular terms of the reversion Hamiltonian, and (b) an intrinsic mechanism having the attributes of irreversible decoherence induced by the coupling with a quantum environment. To characterize (a) we compare the experimental data with the numerical calculation of the refocalized NMR signal of an artificial, closed spin system. To describe (b) we use a model of the irreversible adiabatic decoherence of spin pairs coupled with a phonon bath which allows evaluating an upper bound for the decoherence times. This model accounts for both the observed dependence of the decoherence times on the eigenvalues of the spin-environment Hamiltonian, and the independence from the sample temperature. This result, then, supports the adiabatic decoherence induced by the dipole-phonon coupling as the explanation for the observed irreversible decay of reverted NMR signals in solids.
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.
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We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XYXYXY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XYXYXY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.
We study decoherence in an infinite range Heisenberg model (IRHM) in the two situations where the system is coupled to a bath of either local optical phonons or global optical phonons. Using a non-perturbative treatment, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under non-adiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM and thus has the same eigenstates as the IRHM. By analyzing the dynamics of the system using a quantum master equation approach, we show that the quantum states of the IRHM system do not decohere under Markovian dynamics when the spins interact with local phonons. For interactions with global phonons, the off-diagonal matrix elements of the system's reduced density matrix, obtained for non-Markovian dynamics, do not indicate decoherence only when states with the same STzS^z_TSTz​ (i.e., eigenvalue for the z-component of the total spin) are considered.
In this thesis, a scheme for calculating the dynamics of two coupled dissipative spins is developed, where each of the spins is coupled to its own boson bath. We derive analytic path sum results both in the Markov-regime and in the one-boson exchange regime. The analysis is also performed with the Bloch-Redfield method. It is shown that the two different approaches lead to identical results for the dynamics. This is not obvious a priori because both methods are based on different procedures. The path sum method gives detailed insight into the internal dynamics of two coupled spins because we consider every path sequence that contributes to the time evolution. While most studies of coupled spins are restricted to one type of coupling, e.g., Ising type, we will generalize here to linear combinations of possible couplings. Especially interesting is the occurrence of a frustration of decoherence, if the spins are interacting via a linear combination of longitudinal and transverse coupling and, when in addition, some of the eigenfrequencies become degenerate. Our analysis shows that degenerate but mutual exclusive ground states lead to increased coherence times. Maximization of coherence is one of the crucial goals of quantum state engineering. Another topic of interest is the impact of non-linear quantum environments, formed by surrounding dissipative spins. A distribution of bistable background charges is known to be responsible for 1/f1/f1/f noise in solid state devices, like the superconducting quantum interference devices. Since 1/f1/f1/f noise is seemingly the dominating source of decoherence at very low temperature, there is a profound theoretical interest in modeling it. Therefore, we analyze two interacting spins, where one of them is coupled to a boson bath and thereby represents a resonant non-linear quantum environment. We study the crossover from a non-linear to a linear bath and study the corresponding time scale for the relevant bath correlations. Interestingly, for large and increasing temperature we find a decreasing decoherence for the central spin.