The emergence of realistic properties is a key problem in understanding the quantum-to-classical transition. In this respect, measurements represent a way to interface quantum systems with the macroscopic world: these can be driven in the weak regime, where a reduced back-action can be imparted by choosing meter states able to extract different amounts of information. Here we explore the implications of such weak measurement for the variation of realistic properties of two-level quantum systems pre- and post-measurement, and extend our investigations to the case of open systems implementing the measurements.

Quantum non-Markovianity represents memory during the system dynamics, which is typically weakened by the temperature. We here study the effects of environmental temperature on the non-Markovianity of an open quantum system by virtue of collision models. The environment is simulated by a chain of ancillary qubits that are prepared in thermal states with a finite temperature $T$. Two distinct non-Markovian mechanisms are considered via two types of collision models, one where the system $S$ consecutively interacts with the ancillas and a second where $S$ collides only with an intermediate system $S'$ which in turn interacts with the ancillas. We show that in both models the relation between non-Markovianity and temperature is non-monotonic. In particular, revivals of non-Markovianity may occur as temperature increases. We find that the physical reason behind this behavior can be revealed by examining a peculiar system-environment coherence exchange, leading to ancillary qubit coherence larger than system coherence which triggers information backflow from the environment to the system. These results provide insights on the mechanisms underlying the counterintuitive phenomenon of temperature-enhanced quantum memory effects.

We demonstrate cavity-enhanced Raman emission from a single atomic defect in a solid. Our platform is a single silicon-vacancy center in diamond coupled with a monolithic diamond photonic crystal cavity. The cavity enables an unprecedented frequency tuning range of the Raman emission (100 GHz) that significantly exceeds the spectral inhomogeneity of silicon-vacancy centers in diamond nanostructures. We also show that the cavity selectively suppresses the phonon-induced spontaneous emission that degrades the efficiency of Raman photon generation. Our results pave the way towards photon-mediated many-body interactions between solid-state quantum emitters in a nanophotonic platform.

We investigate a spatial search problem on a fractal lattice using the quantum walk. A recent study made a conjecture that the behavior of the search on a fractal lattice is determined by the spectral dimension not by the fractal dimension. However, this conjecture has so far only been discussed in connection with two- and three-dimensional Sierpinski gaskets. We tackle this problem for the two-dimensional Sierpinski carpet, and show that our simulation result supports the conjecture.

Topological insulator lasers are a newly introduced kind of lasers in which light snakes around a cavity without scattering. Like for an electron current in a topological insulator material, a topologically protected lasing mode travels along the cavity edge, steering neatly around corners and imperfections without scattering or leaking out. In a recent experiment, topological insulator lasers have been demonstrated using a square lattice of coupled semiconductor microring resonators with a synthetic magnetic field. However, laser arrays with slow population dynamics are likely to show dynamical instabilities in a wide range of parameter space corresponding to realistic experimental conditions, thus preventing stable laser operation. While topological insulator lasers provide an interesting mean for combating disorder and help collective oscillation of lasers at the edge of the lattice, it is not clear whether chiral edge states are immune to dynamical instabilities. In this work we consider a realistic model of semiconductor class-B topological insulator laser and show that chiral edge states are not immune to dynamical instabilities.

We find one-shot bounds for concentration of maximally coherent states in the so called assisted scenario. In this setting, Bob is restricted to performing incoherent operations on his quantum system, however he is assisted by Alice, who holds a purification of Bob's state and can send classical data to him. We further show that in the asymptotic limit our one-shot bounds recover the previously computed rate of asymptotic assisted concentration.

We describe an approach defining instantaneous ionization rate (IIR) as a functional derivative of the total ionization probability. The definition is based on physical quantities which are directly measurable, such as the total ionization probability and the waveform of the pulse. The definition is, therefore, unambiguous and does not suffer from gauge non-invariance. We compute IIR by solving numerically the time-dependent Schrodinger equation for the hydrogen atom in a strong laser field. We find that the IIR lags behind the electric field, but this lag is entirely due to the long tail effect of the Coulomb field. In agreement with the previous results using attoclock methodology, therefore, the IIR we define does not show measurable delay in strong field tunnel ionization.

Levitated optomechanics has great potentials in precision measurements, thermodynamics, macroscopic quantum mechanics and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell in vacuum. The linearly-polarized optical tweezer provides a restoring torque to confine the orientation of the nanodumbbell, in analog to the torsion wire which provides restoring torque for suspended lead spheres in the Cavendish torsion balance. Our calculation shows its torque detection sensitivity can exceed that of the current state-of-the-art torsion balance by several orders. The levitated nanodumbbell torsion balance provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly-polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1~GHz, which is the fastest nanomechanical rotor realized to date. Our calculations show that smaller silica nanodumbbells can sustain rotation frequency beyond 10 GHz. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

Flexible Rydberg aggregates, assemblies of few Rydberg atoms coherently sharing electronic excitations while undergoing directed atomic motion, show great promise as quantum simulation platform for nuclear motional dynamics in molecules or quantum energy transport. Here we study additional features that are enabled by the presence of more than a single electronic excitation, thus considering multi-exciton states. We describe cases where these can be decomposed into underlying single exciton states and then present dynamical scenarios with atomic motion that illustrate exciton-exciton collisions, exciton routing, and strong non-adiabatic effects in simple one-dimensional settings.

A tenet of time-resolved spectroscopy is -faster laser pulses for shorter timescales- . Here we suggest turning this paradigm around, and slow down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.

Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing error rate is inevitable. We study the influence of gate errors on simulations of the Trotterized time evolution of the quantum system with focus on the fermionic Hubbard model. Specifically, we consider the effect of stochastic over-rotations in the applied gates. Depending on the particular algorithm implemented such gate errors may lead to a time evolution that corresponds to a disordered fermionic system, or they may correspond to unphysical errors, e.g., violate particle number conservation. We substantiate our analysis by numerical simulations of model systems. In addition we establish the relation between the gate fidelity and the strength of the over-rotations in a Trotterized quantum simulation. Based on this we provide estimates for the maximum number of Trotter steps which can be performed with sufficient accuracy for a given algorithm. This in turn implies, apart from obvious limitations on the maximum time of the simulation, also limits on the system size which can be handled.

Optical control of trapped dielectric objects provides a remarkably simple, yet versatile platform for studying a plethora of intriguing problems in single molecule biophysics, thermodynamics, sensing or fundamental physics. Realizing full quantum control of trapped nanoparticles will enable new insights into quantum-enhanced precision metrology as well as into fundamental aspects of quantum physics. One of the major challenges is to efficiently transduce and manipulate the particle motion at the quantum level. Here we present a nanophotonic platform suited to solve this problem. By optically trapping a 150 nm dielectric particle in the vicinity of the near field of a photonic crystal cavity, at a distance of $\sim310$ nm from its surface, we achieve strong, tunable single-photon optomechanical coupling of up to $g_0/2\pi=9$ kHz, three orders of magnitude larger than previously reported for levitated cavity optomechanical systems. In addition, efficient collection and guiding of light through our nanophotonic structure results in a per-photon displacement sensitivity that is increased by two orders of magnitude when compared to state-of-the-art far-field detection. The demonstrated performance shows a promising route for quantum optical control of levitated nanoparticles.

The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig-Penney model within conventional and parity-time symmetric quantum mechanics (PTQM). In conventional quantum mechanics we determine the most general contact interaction compatible with self-adjointness; in PTQM we consider interactions that are symmetric under the combined transformation PT. In both cases we find that the most general interaction has four independent real parameters; depending on the parameter values the interaction can support more bound states than the conventional delta function. In the PT case the two bound state energies can be both real or a complex conjugate pair, with the transition corresponding to the breaking of PT-symmetry. The scattering states for the PT case are also found to exhibit spontaneous breaking of PT-symmetry. We investigate the energy bands when the generalized contact interactions are repeated periodically in space in one dimension. In the Hermitian case we find that the two bound states result in two narrow bands generically separated by a gap. These bands intersect at a single point in the Brillouin zone as the interaction parameters are varied. Near the intersection the bands form a massless Dirac cone. In the PT-symmetric case, as the parameters of the contact interaction are varied the two bound state bands undergo a PT-symmetry breaking transition wherein the two band energies go from being real to being a complex conjugate pair. The PT-symmetric Kronig-Penney model provides a simple soluble example of the transition which has the same form as in other models of PT-symmetric crystals.

We analyze the quantum dynamics of a two-level emitter in a resonant microcavity with optical feedback provided by a distant mirror (i.e., a half-cavity) with a focus on stabilizing the emitter-microcavity subsystem. Our treatment is fully carried out in the framework of cavity quantum electrodynamics. Specifically, we focus on the dynamics of a perturbed dark state of the emitter to ascertain its stability (existence of time oscillatory solutions around the candidate state) or lack thereof. In particular, we find conditions under which multiple feedback modes of the half cavity contribute to the stability, showing certain analogies with the Lang-Kobayashi equations, which describe a laser diode subject to classical optical feedback.

The assumption that physical systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies. These have been studied for systems with a few degrees of freedom only. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationary dynamics typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

We propose a unique way how to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator becomes self-adjoint. Our construction is based on minimising a 'Hilbert-Schmidt distance' to the original inner product among the entire class of admissible inner products. We prove that either the minimiser exists and is unique, or it does not exist at all. In the former case we derive a system of Euler-Lagrange equations by which the optimal inner product is determined. A sufficient condition for the existence of the unique minimally anisotropic metric is obtained. The abstract results are supplied by examples in which the optimal inner product does not coincide with the most popular choice fixed through a charge-like symmetry.

Cavity-QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, and investigate its sensitivity to realistic sources of experimental noise and imperfections.

Preparation uncertainty relations establish a trade-off in the statistical spread of incompatible observables. However, the Heisenberg-Robertson (or Schroedinger's) uncertainty relations are expressed in terms of the product of variances, which is null whenever the system is in an eigenstate of one of the observables. So, in this case the relation becomes trivial and in the other cases it must be expressed in terms of a state-dependent bound. Uncertainty relations based on the sum of variances do not suffer from this drawback, as the sum cannot be null if the observables are incompatible, and hence they can capture fully the concept of quantum incompatibility. General procedures to construct generic sum-uncertainty relations are not known. Here we present one such procedure, based on Lie algebraic properties of observables that produces state-independent bounds. We illustrate our result for the cases of the Weyl-Heisenberg algebra, special unitary algebras up to rank 4, and any semisimple compact algebra.

Improving the temporal resolution of single photon detectors has an impact on many applications, such as increased data rates and transmission distances for both classical and quantum optical communication systems, higher spatial resolution in laser ranging and observation of shorter-lived fluorophores in biomedical imaging. In recent years, superconducting nanowire single-photon detectors (SNSPDs) have emerged as the highest efficiency time-resolving single-photon counting detectors available in the near infrared. As the detection mechanism in SNSPDs occurs on picosecond time scales, SNSPDs have been demonstrated with exquisite temporal resolution below 15 ps. We reduce this value to 2.7$\pm$0.2 ps at 400 nm and 4.6$\pm$0.2 ps at 1550 nm, using a specialized niobium nitride (NbN) SNSPD. The observed photon-energy dependence of the temporal resolution and detection latency suggests that intrinsic effects make a significant contribution.

In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is introduced there. Next, we define the concept of system of measurement correlations and that of measuring process. The former is the exact counterpart of instrument in the (generalized) Heisenberg picture. In quantum mechanical systems, we then show a one-to-one correspondence between systems of measurement correlations and measuring processes up to complete equivalence. This is nothing but a unitary dilation theorem of systems of measurement correlations. Furthermore, from the viewpoint of the statistical approach to quantum measurement theory, we focus on the extendability of instruments to systems of measurement correlations. It is shown that all completely positive (CP) instruments are extended into systems of measurement correlations. Lastly, we study the approximate realizability of CP instruments by measuring processes within arbitrarily given error limits.