Two dimensional spectroscopy suffers from huge data acquisition times, that make it unattractive for a lot of applications. However, tailored optimization routines lead to a significant acceleration in this step. One of the most promising optimization ideas is the completion of redundant matrices from only a few of its entries. This so called matrix completion can be implemented in various algorithms. In this paper we demonstrate the application of the so called singular value thresholding algorithm to enable time efficient 2D magnetic resonance spectroscopy with Nitrogen Vacancy (NV) centers in diamond, speeding up the data acquisition by a factor of 5-10.

Magnetic resonance techniques enables a wide range of novel applications in chemistry, physics and biomedical sciences, such as powerful imaging tools which have revolutionized medicine. In the past decades, dynamical nuclear polarization (DNP) has been utilized to get orders of magnitude enhancements of nuclear magnetic resonance signals. However, current implementations of DNP require cryogenic temperatures and long times for achieving high polarization. Here we propose and analyze in detail protocols that can achieve rapid hyperpolarization of 13C nuclear spins in randomly oriented ensembles of nanodiamonds at room temperature. Our basic idea is transfer of the optical polarization of electron spins in nitrogen-vacancy centers to 13C nuclei. Severe challenges are posed by the random orientation of the nanodiamonds and their nitrogen-vacancy centers. We address these challenges by a combination of (1) an off-resonant microwave double resonance scheme in conjunction with (2) a realization of the integrated solid effect. Together with adiabatic rotations of the external magnetic fields or rotations of the nanodiamonds leads to over 10,000-fold enhancement in the 13C polarization. This high levels of hyperpolarization, together with the long nuclear-spin polarization lifetimes in nanodiamonds and the relatively high density of 13C nuclei, turn functionalized and hyperpolarized nanodiamonds into attractive MRI probes for molecular imaging both in vitro and in vivo.

Quantum phase transition describes an abrupt change in ground state properties of a quantum system upon a change of a system parameter. The phase transition is generally held to occur in a system where the number of system components is infinite, realizing the so-called thermodynamic limit. In this paper we have challenged this notion by showing that even a single two-level atom coupled to a single harmonic oscillator can undergo a quantum phase transition. It is identified that an atomic transition frequency that is much larger than an oscillator frequency in the regime of a very strong coupling strength can play the same role of the traditional thermodynamic limit achieved by the many atoms. Moreover, we have also confirmed that its adiabatic dynamics is governed by a Kibble-Zurek mechanism, which is a common trait of a critical system undergoing a phase transition.

Biological systems are very small and highly sophisticated thermodynamic engines that are operating in a regime in which quantum fluctuations are not completely negligible anymore.
In this work we are taking this viewpoint seriously and study an aspect of the energy conversion process from sunlight to chemical energy in the presence of exciton-vibrational coupling. To this end we design a prototypical quantum heat engine which defines carefully all quantities and then we proceed to demonstrate quantitatively the increase in power that is achievable due to the presence of exciton-vibrational coupling.

Trapped ions represent a promising technology for the implementation of quantum information processing. However, a wide variety of noise sources reduce the fidelity of quantum gates and require careful attention. Besides the improvement of the hardware, software solutions, that is improved protocols, represent important steps towards ion trap based quantum information processing. Each such strategy tends to have strengths and weaknesses and happy marriages of several techniques has the potential of achieving significantly improved performance. In this work we combine two approaches, continuous dynamical decoupling and decoherence free subspaces to combine their advantages. We show that this combination can be used to achieve a high fidelity quantum simulation.

Nuclear spins are exceptional candidates to store and process quantum information. Our method generates highly selective filter functions ensuring individual addressing and control of nuclear spins in realistic scenarios. In the same way, when applied to an NV center system implanted close to the diamond surface, our protocol is of relevance for the precise identification and localization of nuclear spins in large molecules located on top of the diamond. Therefore, with our work we are paving the way to the control of robust large-scale quantum platforms and the performance of magnetic resonance imaging of individual molecules.

Electronic excitations in photosynthetic membranes occur when a biomolecule (pigment) is excited by light. Many pigments constitute these membranes, which due to their mutual interaction, are able to be excited collectively. Based on Quantum Mechanics, the collective behavior results in an electronic excitation delocalized over these interacting pigments. Historically, excitonic delocalization has been observed to occur between pigments that strongly interact. A clear border that states how strong the interaction must be in order to set a size for the excitons, is still under debate. In our paper we demonstrate theoretically that the excitonic delocalization in photosynthetic membranes can extend over greater domains than previously assumed. These excitons were thought to reside over single ring-like harvesting structures in purple bacteria. As we show here, these excitons rather involve several light-harvesting rings, in a phenomenon that can be verified unambiguously through polarized absorption spectra. This work opens a way to experimentally verify how optical observables are a key tool to progress in the understanding of the interplay between classical and quantum mechanics in the biologically relevant structures for the photosynthesis of purple bacteria.

The simulation of the dynamics of a quantum system with a structured environment is a topic of longstanding interest as it has a broad range of applications ranging from the simulation of quantum technologies to the study of quantum effects in biological systems. In 2010 our group has developed a new approach, TEDOPA,  to this problem (Prior, J., Chin, A. W., Huelga, S. F., & Plenio, M. B. (2010). Efficient simulation of strong system-environment interactions. Physical review letters, 105(5), 050404) combining the theory of orthogonal polynomials with time dependent renormalisation group methods. What was missing though were rigorous error bounds on the various approximations that are made in this approach when it is implement numerically. The present work achieves this goal and establishes TEDOPA as, to our knowledge, the first method with such bounds.

Quantum systems are generally subjected to noise from their environment. In many practical cases this noise has a finite width frequency spectrum, or equivalently a finite correlation time. For such noise it is possible to make use of dynamical decoupling methods that had been invented over the last 5 decades in nuclear magnetic resonance to average out the action of the noise. Recently, these methods have received considerable attention with the advent of solid state implementations of quantum information processing and they are also finding applications in trapped ion technologies. In this work we have furthered the development of these methods by introducing alternating pulse sequences that lead to tunable filter functions. This is the first of several works in this direction to emerge from this group: Robust dynamical decoupling sequences for individual-nuclear-spin addressing ; Positioning nuclear spins in interacting clusters for quantum technologies and bioimaging.

Quantum computers or quantum simulators are quantum devices that may soon outperform current classical computations for analyzing complex quantum phenomena. However, they are not yet able to perform some basic arithmetic calculations such as finding the complex conjugate. Operations involving the complex conjugate require an anti-unitary process, an impossible task if directly implemented in a quantum system restricted to unitary gates. In addition, such complex conjugate is deeply connected to the important concepts in quantum field theory like charge conjugation and time reversal. For the first time, we perform the complex conjugation and these symmetry operations in our trapped-ion quantum system through the use of enlarged spaces and the novel concept of embedding a quantum simulator. Our realization can be applied to numerous quantum calculations and simulations that require access to the implementation of unphysical operations.

The Nitrogen Vacancy (NV) center in diamond allows extremely sensitive magnetic field measurements under room temperature conditions. Implanted close to the surface, the enormous sensitivity allows for the resolution of level splittings induced by dipolar coupling in molecules attached to the surface. Exploiting correlated spectroscopy (COSY), we can read out these splittings to compute the spatial structure of the molecule and its constituents. In the strong coupling regime, the pure interaction between NV center and the molecule is sufficiently strong, to get a full contrast signal even without polarizing the nuclear spins in the molecule. We further demonstrate the speed up in data acquisition by matrix completion procedures.

The Nitrogen Vacancy (NV) center in diamond allows extremely sensitive magnetic field measurements under room temperature conditions. Implanted close to the surface, the enormous sensitivity allows for the resolution of level splittings induced by dipolar coupling in molecules attached to the surface. Exploiting correlated spectroscopy (COSY), we can read out these splittings to compute the spatial structure of the molecule and its constituents. In the strong coupling regime, the pure interaction between NV center and the molecule is sufficiently strong, to get a full contrast signal even without polarizing the nuclear spins in the molecule. We further demonstrate the speed up in data acquisition by matrix completion procedures.

Determining the state of a quantum system is a non-trivial task due to the
probabilistic nature of quantum measurements: The resulting data only allows for an estimation of the true state of the system. The same is true for characterizing a quantum process, i.e. how a complete set of states is changed e.g. by a unitary time evolution. To determine an arbitrary state of n qubits, we also have to measure a number of observables which grows exponentially with n. However, using basic linear algebra, one can find efficient representations of many many-qubit states (so-called matrix product states, MPS) and it has been shown that such states often allow for characterization with a much smaller number of observables. In our simulation, we efficiently determine an unknown quantum process of a many-qubit system by adapting existing methods for state characterization. We use a known correspondence between quantum processes on n qubits and quantum states on 2n qubits, but it turns out that this enlarged system is not necessary in an actual experiment.

Trapped ions represent one of the frontrunner technologies towards the realization of medium for large scale quantum computation. Currently the standard approach uses lasers to control and entangle the ions but some 15 years ago an alternative approach had been suggested which uses microwaves applied to ions in the presence of a magnetic field gradient to achieve spin-motion coupling and, building on that, entanglement between ions. The qubit states that were required for that are magnetically sensitive and therefore susceptible to magnetic field fluctuations. in Nature 476, 185 (2011) we proposed continuous dynamical decoupling as a means to overcome this problem and contributed to a first experimental realization. In the present work we have analysed our approach in considerable detail. We demonstrate that it is capable of delivering quantum gates of a fidelity that exceed fault tolerant thresholds and that therefore, large scale quantum computing is made possible in principle.

Trapped atomic ions have proven to be a very versatile tool for quantum information processing and the simulation of quantum dynamics. More recently, they have also become a testbed for statistical mechanics. For the study of statistical mechanical systems it is desirable to extend the toolbox of analysis techniques available with trapped ions.
In this work we show how the technique of two-dimensional (2D) spectroscopy that has been very successful in other fields, such as NMR and quantum biology, can be applied to trapped ions. It turns out that the method is particularly well-suited to study non-linear interactions in ion traps. We illustrate the usefulness of the technique with two concrete examples: one is the detection of the onset of a phase transition while the second is resonant non-linear exchange of energy between motional modes.

Ultracold quantum gases are an extremely clean realization of interacting quantum many-body systems and exhibit interesting properties such as superfluidity and quantum phase transitions. For studying these phenomena it is necessary to probe quantum gases with high accuracy while leaving their characteristic quantum features intact. In our work we suggest a scheme for measuring temperatures and excitations with a single impurity atom that is immersed in a Bose gas. The impurity is confined by a double-well potential and acts as an effective qubit coupled to phononic excitations of the quantum gas. We show how to use the detector to observe coherent density waves and to measure temperatures down to the nanokelvin regime. The scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision.