Environmental effects on the evolution of a spin system in the context of the central spin problem, have been studied for more than 60 years. With the growing complexity of quantum information processors there is a new need to better understand and control the interactions of qubits with their environment. Decoherence is an apparent loss of quantum coherence of the central spin, which is the result of the coherent evolution of the central spin and its spin environment. This evolution may be understood as the consequence of local field fluctuations induced by heteronuclear dipolar interaction between the central spin and the environment spins and homonuclear dipolar interaction of spins in the environment. A complete theoretical description for the evolution of the central spin does not exist and numerical solutions are restricted to small spin environments. \n \nAnother way of looking at the central spin problem is to study the correlations between the central spin and the environment spins. In this method the evolution of the central spin is described with the dynamics of multi-spin correlations resulting from interactions of the central spin and the environment spins. \nUsing Multiple Quantum Nuclear Magnetic Resonance (MQ NMR) techniques, we have designed experiments for the direct detection of multi-spin correlations between the central spin and environment spins. These experiments are used to observe the progress in production of correlations between the central spin and the environment. They reveal the multi-spin dynamics that underlies the decoherence process. \n \nThe central spin is initially uncorrelated with the environment and quantum information resides exclusively on it. After the interaction with the environment spins quantum information is shared in the form of correlated operators between the central spin and the environment. Using our experiments this flow of quantum information from the central spin to the environment and the quantum information content of the environment, can be quantified. Further, these experiments are used to gauge the sensitivity of correlation to perturbation in the environment, by observing the mixing dynamics of the multi-spin correlations. The Out-of-Time Correlation metric is used for the sensitivity measurements. We find that the dynamics of correlations in our system is better explained by the extent of information flow to the environment rather than the evolution time.
Environmental effects on the evolution of a spin system in the context of the central spin problem, have been studied for more than 60 years. With the growing complexity of quantum information processors there is a new need to better understand and control the interactions of qubits with their environment. Decoherence is an apparent loss of quantum coherence of the central spin, which is the result of the coherent evolution of the central spin and its spin environment. This evolution may be understood as the consequence of local field fluctuations induced by heteronuclear dipolar interaction between the central spin and the environment spins and homonuclear dipolar interaction of spins in the environment. A complete theoretical description for the evolution of the central spin does not exist and numerical solutions are restricted to small spin environments. \n \nAnother way of looking at the central spin problem is to study the correlations between the central spin and the environment spins. In this method the evolution of the central spin is described with the dynamics of multi-spin correlations resulting from interactions of the central spin and the environment spins. \nUsing Multiple Quantum Nuclear Magnetic Resonance (MQ NMR) techniques, we have designed experiments for the direct detection of multi-spin correlations between the central spin and environment spins. These experiments are used to observe the progress in production of correlations between the central spin and the environment. They reveal the multi-spin dynamics that underlies the decoherence process. \n \nThe central spin is initially uncorrelated with the environment and quantum information resides exclusively on it. After the interaction with the environment spins quantum information is shared in the form of correlated operators between the central spin and the environment. Using our experiments this flow of quantum information from the central spin to the environment and the quantum information content of the environment, can be quantified. Further, these experiments are used to gauge the sensitivity of correlation to perturbation in the environment, by observing the mixing dynamics of the multi-spin correlations. The Out-of-Time Correlation metric is used for the sensitivity measurements. We find that the dynamics of correlations in our system is better explained by the extent of information flow to the environment rather than the evolution time.
Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be manipulated and protected from decoherence. This work uses the stimulated echo experiment to track the information flow between the central spin and its environment, providing a direct measure of the sensitivity of system/environment correlations to environmental dynamics. The extent of mixing and the growth of correlations are quantified through autocorrelation functions of the noise and environmental dynamics, which also enable the estimation of nested commutators between the system/environment and environmental Hamiltonians. Complementary decoupling experiments offer a straightforward measure of the strength of the system Hamiltonians. The approach is experimentally demonstrated on a spin system.
The control of open quantum systems has a fundamental relevance for fields ranging from quantum information processing to nanotechnology. Typically, the system whose coherent dynamics one wants to manipulate, interacts with an environment that smoothly degrades its quantum dynamics. Thus, a precise understanding of the inner mechanisms of this process, called "decoherence", is critical to develop strategies to control the quantum dynamics. In this thesis we solved the generalized Liouville-von Neumann quantum master equation to obtain the dynamics of many-spin systems interacting with a spin bath. We also solve the spin dynamics within the Keldysh formalism. Both methods lead to identical solutions and together gave us the possibility to obtain numerous physical predictions that contrast well with Nuclear Magnetic Resonance experiments. We applied these tools for molecular characterizations, development of new numerical methodologies and the control of quantum dynamics in experimental implementations. But, more important, these results contributed to fundamental physical interpretations of how quantum dynamics behaves in open systems. In particular, we found a manifestation of an environmentally induced quantum dynamical phase transition.
During the last decade the field of quantum information has seen considerable progress both
theoretically and experimentally. The building block of this theory is the so-called qubit,
the quantum counterpart of the classical bit. It turns out that spin degrees of freedom
of quantum particles are among the most promising candidates for quantum information
processing and computation. Thus, a deep understanding of the different processes that
govern the dynamics of these objects is of fundamental importance. For instance, the decoherence
process, caused the coupling of the qubits to their surrounding environment, is
the main obstacle to quantum information processing: it leads them to lose their quantum
coherence and thus behave classically. In addition, quantum systems exhibit correlations
that have no classical counterpart. This phenomenon is called entanglement and is the
vital resource for quantum teleportation and quantum computing. Decoherence and entanglement
dynamics were extensively studied within the framework of the Markovian
approximation using the master equation approach. However, due to the non-commuting
character of quantum observables, only few models are known to be exactly solvable.
Moreover, many spin systems display a strongly non-Markovian behavior. This thesis is
devoted to the development of new techniques for deriving the exact dynamics of spin
qubits, coupled through Heisenberg and/or Ising interactions to spin environments that
have internal dynamics. The basic idea behind these techniques is to use the underlying
symmetries exhibited by the Hamitonian operators of the composite systems. This allows
for the study of problems related to decoherence and entanglement.
Entanglement and decoherence arguably define the central issues of concern in present day quantum information theory. Decoherence occurs when a system interacts with its environment in an irreversible way; this prevents the quantum superposition of the system + environment's wavefunction from interfering with each other. A better understanding of environment-induced destruction of coherent superposition states is needed, as well as a clear description of the degree of entanglement between the quantum system and its environment. We quantitatively establish a correspondence between entanglement, decoherence, and spin dynamics for a two-state system coupled to a bath of harmonic oscillators, resulting in the celebrated spin-boson model. Applications to solid-state and cold atomic systems are also discussed.
We consider here the problem of a "central spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with nuclear spins and with any surrounding paramagnetic electronic spins. It has also been used to describe Si:P near the metal-insulator transition, and quantum spin glasses. In this paper we consider the possible coherent motion of the central spin. We reduce the model to an effective low-energy Hamiltonian, and then calculate the correlation function using instanton methods. The general solution is given for the unbiased case, for all relevant values of the couplings. Under certain conditions, nuclear spin diffusion also plays a role. The results are then used to calculate the spectral absorption for 2 experimental systems, viz., TbFe3 grains, and ferritin molecules. Our results have general implications for the observation of mesoscopic and macroscopic quantum coherence, and for the foundations of quantum mechanics. They show that a spin environment usually has a very destructive effect on coherence, which cannot be understood using the conventional "oscillator bath" models of quantum environments.
We present a theoretical discussion of various aspects of the dynamics of information in quantum systems of qubits. We begin by reviewing ideas about entanglement and information in systems of qubits, different models for realistic qubits coupled to an external environment, how this causes the loss of information stored in qubits, and some practical designs for qubits that have been created. Then we study how the state of many-body systems can be decomposed in terms of its different subsystems and derived a hierarchy of equations describing the motion of these different parts. We show that in a qubit system, the central objects in this hierarchy are correlators between different components of different qubits. Systems where the environment coupled to a central qubit is a "spin bath'' of environmental qubits are then considered in detail and we find that information lost by the central qubit is transferred via a cascade to higher and higher order correlations with the environment. We discuses this process in the realistic example of an "Fe₈'' magnetic molecule qubit. Finally we discuss simple models of the dynamics of many entangled qubits.