We demonstrate an all-optical thermometer based on an ensemble of silicon-vacancy centers (SiVs) in diamond by utilizing a temperature dependent shift of the SiV optical zero-phonon line transition frequency, $\Delta\lambda/\Delta T= 6.8\,\mathrm{GHz/K}$. Using SiVs in bulk diamond, we achieve $70\,\mathrm{mK}$ precision at room temperature with a sensitivity of $360\,\mathrm{mK/\sqrt{Hz}}$. Finally, we use SiVs in $200\,\mathrm{nm}$ nanodiamonds as local temperature probes with $521\,\mathrm{ mK/\sqrt{Hz}}$ sensitivity. These results open up new possibilities for nanoscale thermometry in biology, chemistry, and physics, paving the way for control of complex nanoscale systems.

The response functions of a material characterize its behavior under external stimuli, such as electromagnetic radiation. Such responses may grow linearly with the amplitude of the incident radiation, as is the case of absorption, or may be nonlinear. The latter category includes a diverse set of phenomena such as second harmonic generation (SHG), shift current, sum frequency generation, and excited state absorption, among others. Despite decades of research into nonlinear response theory, and the occasional discovery of materials with large nonlinear responses, there has been no systematic investigation into the maximum amount of nonlinear optical response attainable in solid-state materials. In this work, we present an upper bound on the second-order response functions of materials, which controls the SHG and shift current responses. We show that this bound depends on the band gap, band width, and geometrical properties of the material in question. We find that Kuzyk's bound for the maximum SHG of isolated molecules can be exceeded by conjugation or condensation of molecules to form molecular solids, and that strongly coupled systems generally have larger responses than weakly coupled or isolated ones. As a proof of principle, we perform first-principles calculations of the response tensors of a wide variety of materials, finding that the materials in our database do not yet saturate the upper bound. This suggests that new large SHG and shift current materials will likely be discovered by future materials research guided by the factors mentioned in this work.

The area theorem states that when a short optical pulse drives a quantum two-level system, it undergoes Rabi oscillations in the probability of scattering a single photon. In this work, we investigate the breakdown of the area theorem as both the pulse length becomes non-negligible and for certain pulse areas. Using simple quantum trajectories, we provide an analytic approximation to the photon emission dynamics of a two-level system. Our model provides an intuitive way to understand re-excitation, which elucidates the mechanism behind the two-photon emission events that can spoil single-photon emission. Additionally, the model clearly explains our recent results [K. Fischer and L. Hanschke, et al., Nature Physics (2017)] showing dominant two-photon emission from a two-level system for pulses with interaction areas equal to an even multiple of $\pi$.

The nuclear spin in the vicinity of a nitrogen-vacancy (NV) center possesses of long coherence time and convenient manipulation assisted by the strong hyperfine interaction with the NV center. It is suggested for the subsequent quantum information storage and processing after appropriate initialization. However, current experimental schemes are either sensitive to the inclination and magnitude of the magnetic field or require thousands of repetitions to achieve successful realization. Here, we propose polarizing a 13C nuclear spin in the vicinity of an NV center via a dark state. We demonstrate theoretically that it is robust to polarize various nuclear spins with different hyperfine couplings and noise strengths.

Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the transition probability is possible when the oscillator is highly excited, i.e. at high temperatures. Then the relative change of the excitation level of the oscillator in the course of the transition is small. The physical picture of the transition in the presence of coupling to the oscillator becomes transparent in the limiting cases of slow and fast oscillator. Slow oscillator effectively renormalizes the drive velocity. As a result, the transition probability either increases or decreases depending on the oscillator phase. The net effect is, however, the suppression of the transition probability. On the contrary, fast oscillator renormalizes the matrix element of the transition rather than the drive velocity. This renormalization makes the transition probability a non-monotonic function of the coupling amplitude.

We show that a two-level atom resonantly coupled to one of the modes of a cavity field can be used as a sensitive tool to measure the proper acceleration of a combined atom-cavity system. To achieve it we investigate the relation between the transition probability of a two-level atom placed within an ideal cavity and study how it is affected by the acceleration of the whole. We indicate how to choose the position of the atom as well as its characteristic frequency in order to maximize the sensitivity to acceleration.

The dynamical decoupling (DD) based noise spectroscopy relies on achieving the regime of evolution parameters, when the measured decay rate of qubit coherence is given by environmental noise spectrum spanned on frequency comb defined by the DD pulse sequences. Using properly chosen sequences allows for inverting this relation, and thus, the reconstruction of the spectrum. Here we investigate the conditions under which this regime is achieved, and the corrections to the aforementioned relation become negligible. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian --- both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, where the spectrosopic regime can be easily achieved, it is not the case for spectral densities with finite range. Consequently, it becomes difficult (especially with limited a priori knowledge) to avoid artifacts in the reconstructed spectrum. For Gaussian line-shape of environmental spectral density, direct application of the standard DD-based spectroscopy method leads to erroneous reconstruction of long-tail behavior of the spectrum. Fortunately, with the simple extension to standard reconstruction method that exploit the general properties of the corrections, their contribution can be completely circumvented.

To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias as well as temperature differences. We observe maximal values of FDCN in moderate coupling regimes, similar to the zero-frequency cases. We find the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to a distinctive spin dynamics. We also find the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.

In order to study N-locality without inputs in long lines and in configurations with loops, e.g. the triangle, we introduce a natural joint measurement on two qubits different from the usual Bell state measurement. The resulting quantum probability $p(a_1,a_2,...,a_N)$ has interesting features. In particular the probability that all results are equal is that large, while respecting full symmetry, that it seems highly implausible that one could reproduce it with any N-local model, though - unfortunately - I have not been unable to prove it.

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.

We consider the resonant van der Waals interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes-Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the van der Waals forces, using a Lorentzian single mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position-dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones, for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.

We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis is mutually unbiased with respect to the reference basis, and together with the reference basis they form an informationally complete set of measurements. We show that, in general, any strategy capable of validating quantum coherence allows one to evaluate also the exact value of coherence. We then give an explicit construction of the optimal measurements for arbitrary dimensions. Finally, we show that the same measurement setup is also optimal for the modified task of verifying if the coherence is above or below a given threshold value.

People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for the transitions and analyze the polarization induced interference under the EIT condition. We show that such interference arises naturally under mild conditions on the optical field and atom manipulation. Its anticipated properties and its potential application of all optical switching in polarization degree of freedom are also discussed. Moreover, we construct a variation form of double-M linkage pattern where the polarization induced interference enables polarization-dependent cross-modulation between incident lights that can be effective even at the few-photon level. The theme is to gain more insight into the essential question: how can we build non-trivial optical medium where incident lights will induce polarization-dependent non-linear optical interactions, covering a wide range of the incidence intensity from the many-photon level to the few-photon level, respectively.

We analyse the linear confinement of a Majorana fermion in $\left(1+1\right)$-dimensions. We show that the Dirac equation can be solved analytically. Besides, we show that the spectrum of energy is discrete, however, the energy levels are not equally spaced.

Performing entangling gates between physical qubits is necessary for building a large-scale universal quantum computer, but in some physical implementations - for example, those that are based on linear optics or networks of ion traps - entangling gates can only be implemented probabilistically. In this work, we study the fault-tolerant performance of a topological cluster state scheme with local non-deterministic entanglement generation, where failed entangling gates (which correspond to bonds on the lattice representation of the cluster state) lead to a defective three-dimensional lattice with missing bonds. We present two approaches for dealing with missing bonds; the first is a non-adaptive scheme that requires no additional quantum processing, and the second is an adaptive scheme in which qubits can be measured in an alternative basis to effectively remove them from the lattice, hence eliminating their damaging effect and leading to better threshold performance. We find that a fault-tolerance threshold can still be observed with a bond-loss rate of 6.5% for the non-adaptive scheme, and a bond-loss rate as high as 14.5% for the adaptive scheme.

We propose a strategy to measure weak static magnetic fields with nitrogen-vacancy color center in diamond. Inspired by avian magnetoreception models, we consider the feasibility of utilizing quantum coherence phenomena to measure weak static magnetic fields. Nitrogen-vacancy (NV) color centers are regarded as the ideal platform to study quantum sciences as a result of its long coherence time up to a millisecond timescale. In high-purity diamond, hyperfine interaction with 13C nuclear spins dominates the decoherence process. In this paper, we numerically simulate the decoherence process between 0 and +1 of the individual NV color center spin in 13C nuclear baths with various of magnitudes of external magnetic fields. By applying Hahn echo into the system, we obtain the coherence of NV color center spin as a function of total evolution time and magnetic field. Furthermore we obtain the high-accuracy relationship between the three decoherence-characteristic timescales, i.e. T_W, T_R, T_2, and magnetic field B. And we draw a conclusion that T_R has the highest sensitivity about magnetic field among the three time-scales. Thus, for a certain NV color center, T_R can be the scale for the magnitude of magnetic field, or rather, the component along the NV electronic spin axis. When measuring an unknown magnetic field, we adjust the NV axis to three mutually orthogonal directions respectively. By this means, we obtain the three components of the magnetic field and thus the magnitude and direction of the actual magnetic field. The accuracy could reach 60 nT/Hz^{1/2},and could be greatly improved by using an ensemble of NV color centers or diamond crystals purified with 12C atoms.

We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, and yielding the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes our proposal suitable for devices for rapid and robust generation of Bell states.

Recently it was proposed to use cavity-optomechanical systems to test for quantum gravity corrections to quantum canonical commutation relations [Nat. Phys. 8, 393-397 (2012)]. Improving the achievable precision of such devices represents a major challenge that we address with our present work. More specifically, we develop sophisticated paths in phase-space of such optomechanical system to obtain feasible accuracy and precision under shot noise and contributions from higher-order corrections to the optomechanical Hamiltonian. Furthermore, we propose a method to increase precision by using squeezed states of light. Finally, we demonstrate the robustness of our scheme to experimental imperfection, thereby improving our prospects of carrying out tests of quantum gravity with near-future optomechanical technology.

Proposing a system of two rotatable nanoparticles (NPs) in the presence of electromagnetic vacuum fluctuations, using the framework of canonical quantization, the electromagnetic and matter fields have been quantized. The non-contact frictional torque, affecting the rotation of NPs due to the presence of electromagnetic vacuum fluctuations and also by the matter field fluctuations have been derived. Considering the distance between NPs less than 100 nm in the near-field, we observe the rotations are phase locked. It has been shown that the electromagnetic vacuum fluctuations play the role of noises to break down the synchronization. Also surprisingly, we find the frictional torque between NPs in the near-field is much bigger than the popular contact friction between them where it causes a robust synchronization in the near-field.

We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ drastically for either classical or quantum projective measurement, and we explore the peculiarities brought by the combination of the two.

We put forward a proper formalism for the evaluation of the distributions of measurement outcomes. We compute and discuss the statistics in idealized and experimentally relevant setups. We demonstrate the visibility and manifestations of the interference between initial and final states in the statistics of measurement outcomes for both variables in various regimes.

We analytically predict the peculiarities at the circle ${\cal O}^2_1+{\cal O}^2_2=1$ in the distribution of measurement outcomes in the limit of short measurement times and confirm this by numerical calculation at longer measurement times. We demonstrate analytically anomalously large values of the time-integrated output cumulants in the limit of short measurement times(sudden jump) and zero overlap between initial and final states, and give the detailed distributions. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the conditioned measurement can be accurately predicted even if they are small.