Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.

Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.

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Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit-system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use 13 C nuclear spins as qubits and an environment of 1 H nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 µs. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum coherent dynamics of a 3D many-spin system with dipolar interactions, and determine its critical exponents. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. The resulting dynamics of the system coherence can be localized or extended, depending on the quench strength. Applying a finite-time scaling analysis to the observed time-evolution of the number of correlated spins, we extract the critical exponents ν ≈ s ≈ 0.42 around the phase transition separating a localized from a delocalized dynamical regime. These results show clearly that such nuclear-spin based quantum simulations can effectively model the non-equilibrium dynamics of complex many-body systems, such as 3D spin-networks with dipolar interactions.The complexity of many-body systems is a long standing problem in physics (1-8). As an example, quantum states of many-body systems can be localized at well defined positions in space or they can be delocalized, depending on parameters like disorder. In their localized regime, such systems may not reach a thermal state but retain information about their initial state on very long timescales (9-17). The role of the topology, dimension, long and short range interactions, and the presence of disorder is very important for the onset of these localization regimes. Much progress was achieved on the numerical and theoretical side, where these phenomena have been predicted under certain conditions. However, experimentally addressing 3D manybody systems in a controlled manner poses severe experimental problems (5,8,14,16). Non-equilibrium dynamics of many-body systems has been investigated to provide complementary information about a large variety of situations but also remains challenging (18-26). Therefore, finding different experimental situations, new approaches and techniques for controlling and observing many-body dynamics can lead to new approaches for studying manybody physics.The recent progress on the experimental control of cold atoms (6, 27, 28), trapped ions (25, 26, 29, 30), Rydberg atoms (31), polar molecules (7, 32) and nitrogen-vacancy centers in diamond (33-36) has led to promising new ways of studying the non-equilibrium dynamics and localization phenomena of many-body systems. In particular a lot of effort is focused on studying many-spin systems with dipolar interactions of the Heisenberg-type (8, 24-26, 31, 32). Here, we use nuclear magnetic resonance (NMR), which provides a natural and versatile approach for coherently controlling large numbers of spins (up to ∼ 7000) in solid state systems, where dipolar interactions are present. NMR techniques allow to quantify the number of spins that are coherently correlated, and allow control of the interact...

Phenomenological models for the antiferromagnetic (AF) vs. d-wave superconductivity competition in cuprates are studied using conventional Monte Carlo techniques. The analysis suggests that cuprates may show a variety of different behaviors in the very underdoped regime: local coexistence or first-order transitions among the competing orders, stripes, or glassy states with nanoscale superconducting (SC) puddles. The transition from AF to SC does not seem universal. In particular, the glassy state leads to the possibility of "colossal" effects in some cuprates, analog of those in manganites. Under suitable conditions, non-superconducting Cu-oxides could rapidly become superconducting by the influence of weak perturbations that align the randomly oriented phases of the SC puddles in the mixed state. Consequences of these ideas for thin-film and photoemission experiments are discussed.

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system-qubits are 13 C nuclear spins and the environment consists of a 1 H nuclear spin-bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs superior to any non-equidistant DD sequence in the presence of this kind of environmental noise.