Quantum oscillations without quantum coherence

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Dynamics of open quantum spin systems: An assessment of the quantum master equation approach

Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.

Decoherence-governed magnetic-moment dynamics of supported atomic objects

Due to the quantum evolution of molecular magnetic moments, the magnetic state of nanomagnets can suffer spontaneous changes. This process can be completely quenched by environment-induced decoherence. However, we show that for typical small supported atomic objects, the substrate-induced decoherence does change the magnetic-moment evolution but does not quell it. To be specific and to compare with experiment, we analyze the spontaneous switching between two equivalent magnetization states of atomic structures formed by Fe on Cu2N/Cu (1 0 0), measured by Loth et al (2012 Science 335 196-9). Due to the substrate-induced decoherence, the Rabi oscillations proper to quantum tunneling between magnetic states are replaced by an irreversible decay of long characteristic times leading to the observed stochastic magnetization switching. We show that the corresponding switching rates are small, rapidly decreasing with system's size, with a 1/T thermal behavior and in good agreement with experiments. Quantum tunneling is recovered as the switching mechanism at extremely low temperatures below the μK range for a six-Fe-atom system and exponentially lower for larger atomic systems. The unexpected conclusion of this work is that experiments could detect the switching of these supported atomic systems because their magnetization evolution is somewhere between complete decoherence-induced stability and unobservably fast quantum-tunneling switching.

Solid-state multiple quantum NMR in quantum information processing: exactly solvable models

Multiple quantum (MQ) NMR is an effective tool for the generation of a large cluster of correlated particles, which, in turn, represent a basis for quantum information processing devices. Studying the available exactly solvable models clarifies many aspects of the quantum information. In this study, we consider two exactly solvable models in the MQ NMR experiment: (i) the isolated system of two spin-1/2 particles (dimers) and (ii) the large system of equivalent spin-1/2 particles in a nanopore. The former model is used to describe the quantum correlations and their relations with the MQ NMR coherences, whereas the latter helps one to model the creation and decay of large clusters of correlated particles.

Decay of Rabi oscillations by dipolar-coupled dynamical spin environments

We study the Rabi oscillations decay of a spin decohered by a spin bath whose internal dynamics is caused by dipolar coupling between the bath spins. The form and rate of decay as a function of the intrabath coupling is obtained analytically, and confirmed numerically. The complex form of decay smoothly varies from power law to exponential, and the rate changes nonmonotonically with the intrabath coupling, decreasing for both slow and fast baths. The form and rate of Rabi oscillations decay can be used to experimentally determine the intrabath coupling strength for a broad class of solid-state systems.

Quenching spin decoherence in diamond through spin bath polarization

We experimentally demonstrate that the decoherence of a spin by a spin bath can be completely eliminated by fully polarizing the spin bath. We use electron paramagnetic resonance at 240 GHz and 8 T to study the electron-spin coherence time T2 of nitrogen-vacancy centers and nitrogen impurities in diamond from room temperature down to 1.3 K. A sharp increase of T2 is observed below the Zeeman energy (11.5 K). The data are well described by a suppression of the flip-flop induced spin bath fluctuations due to thermal electron-spin polarization. T2 saturates at approximately 250 micros below 2 K, where the polarization of the electron-spin bath exceeds 99%.

Universal phase shift and nonexponential decay of driven single-spin oscillations

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear-spin bath. Because of the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of approximately pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.

Polynomial scheme for time evolution of open and closed quantum systems

Based on the generating function of Laguerre polynomials, we propose a Laguerre polynomial expansion scheme in the calculation of the evolution of the time-dependent Schrödinger equation. Theoretical analysis and numerical tests show that the method is equally as good as the Chebyshev polynomial expansion method in efficiency and accuracy, with the additional merits that no scaling to the Hamiltonian is needed and it has wider suitability.

Numerical modeling of the central spin problem using the spin-coherent-state representation

In this work, we consider decoherence of a central spin by a spin bath. In order to study the nonperturbative decoherence regimes, we develop an efficient mean-field-based method for modeling the spin-bath decoherence, based on the representation of the central spin density matrix. The method can be applied to longitudinal and transverse relaxation at different external fields. In particular, by modeling large-size quantum systems (up to 16 000 bath spins), we make controlled predictions for the slow long-time decoherence of the central spin.

Random Lindblad equations from complex environments

In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies on the possibility of splitting the complex environment into a direct sum of subreservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different subreservoirs, characterize the average system decay dynamics. As an example, we study the anomalous irreversible behavior of a quantum tunneling system described in an effective two-level approximation. Stretched exponential and power law decay behaviors arise from the interplay between the dissipative and unitary hopping dynamics.

Quantum computation of a complex system: the kicked Harper model

The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling us to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection even for large number of qubits, whereas others are exponentially sensitive to the number of qubits. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as 7-8 qubits and can be reliably measured in presence of moderate levels of internal imperfections.