Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is able to capture the many-body dynamics of bright, coherent pulses through these strongly interacting media. We compare our model with available experimental data in this regime and find good agreement. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

In this paper the inverse problem of the correspondence between the solutions of the Dirac equation and the electromagnetic 4-potentials, is fully solved. The Dirac solutions are classified into two classes. The first one consists of degenerate Dirac solutions corresponding to an infinite number of 4-potentials while the second one consists of non-degenerate Dirac solutions corresponding to one and only one electromagnetic 4-potential. Explicit expressions for the electromagnetic 4-potentials are provided in both cases. Further, in the case of the degenerate Dirac solutions, it is proven that at least two 4-potentials are gauge inequivalent, and consequently correspond to different electromagnetic fields. An example is provided to illustrate this case.

We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the "data-processing bound," is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper bounds, which we call the "$\varepsilon$-degradable bound" and the "$\varepsilon$-close-degradable bound," are established using the notion of approximate degradability along with energy constraints. We find a strong limitation on any potential superadditivity of the coherent information of any phase-insensitive Gaussian channel in the low-noise regime, as the data-processing bound is very near to a known lower bound in such cases. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. What remains open for several interesting channel divergences, such as the diamond norm or the Renyi channel divergence, is to determine whether, among all input states, a Gaussian state is optimal.

We obtain coincidence rates for passive optical interferometry by exploiting the permutational symmetries of partially distinguishable input photons, and our approach elucidates qualitative features of multi-photon coincidence landscapes. We treat the interferometer input as a product state of any number of photons in each input mode with photons distinguished by their arrival time. Detectors at the output of the interferometer count photons from each output mode over a long integration time. We show that coincidence rates can be elegantly expressed in terms of immanants. Immanants are functions of matrices that exhibit permutational symmetries and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our results are obtained by employing representation theory of the symmetric group to analyze systems of arbitrary number of photons in arbitrarily sized interferometers.

We study the dynamics of a one-dimensional system composed of a bosonic background and one impurity in single- and double-well trapping geometries. In the limit of strong interactions, this system can be modeled by a spin chain where the exchange coefficients are determined by the geometry of the trap. We observe non-trivial dynamics when the repulsion between the impurity and the background is dominant. In this regime, the system exhibits oscillations that resemble the dynamics of a Josephson junction. Furthermore, the double-well geometry allows for an enhancement in the tunneling as compared to the single-well case.

We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for considerable contrast and phase decay, the cavity scenario can exhibit similar behavior at much lower densities.

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.

We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born-Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit.

We present experimental observations and a study of quantum dynamics of strongly interacting electronic spins, at room temperature in the solid state. In a diamond substrate, a single nitrogen vacancy (NV) center coherently interacts with two adjacent S = 1/2 dark electron spins. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of the NV. Finally, as a demonstration of coherent control, we selectively couple and transfer polarization between the NV and the pair of electron spins. These results demonstrate a key step towards full quantum control of electronic spin registers in room temperature solids.

In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse information. We propose quantum walk neural networks (QWNN), a novel graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can then be applied to graph-structured data. We demonstrate the use of QWNNs on a variety of prediction tasks on graphs involving temperature, biological, and molecular datasets.

A new form Time Crystal has been proposed and some of its consequences have been studied. The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections. In the mini-superspace approach the scale factor undergoes the time periodic behavior, or Sisyphus dynamics, which allows us to interpret this Cosmological Time Crystal as a physically motivated toy model to simulate cyclic universe. Analyzing our model purely from Time Crystal perspective reveals many novelties such as a complex singularity structure (more complicated than the previously encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In the context of cosmology, the system can serve as a toy model in which, apart from inducing a form of cyclic universe feature, it is possible to generate an arbitrarily small positive effective Cosmological Constant. We stress that the model is purely geometrical without introduction of matter degrees of freedom.

Anticrossing behavior between magnons in a non-collinear chiral magnet Cu$_2$OSeO$_3$ and a two-mode X-band microwave resonator was studied in the temperature range 5-100 K. In the field-induced ferrimagnetic phase, we observed a strong coupling regime between magnons and two microwave cavity modes with a cooperativity reaching 3600. In the conical phase, cavity modes are dispersively coupled to a fundamental helimagnon mode, and we demonstrate that the magnetic phase diagram of Cu$_2$OSeO$_3$ can be reconstructed from the measurements of the cavity resonance frequency. In the helical phase, a normal-mode splitting between a higher-order helimagnon mode and a cavity mode was found. Our results reveal a new class of magnetic systems where strong coupling of microwave photons to non-trivial spin textures can be observed.

In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a "cosmological solution". We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a "bouncer" coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder's experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations.

We show with the examples of double- and $n$-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de Broglie-Bohm guiding equation for $N$ particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping.

Traditionally, quantum state correlation can be obtained with calculations on a state density matrix already known. Here, we propose a model with which correlations of unknown quantum states can be obtained. There are no needs of classical communication in the course of coupling, optimization and complicated calculations. All we need are weak coupling and ancillary systems. We detail the model on the state in which particles belong to the different owners. A concisely example is elaborated in the last part of this paper.

Wave-particle duality is one of the most intriguing features in quantum physics. A well-known gedanken experiment that provides evidence for this is the Wheeler's delayed-choice experiment based on a Mach-Zehnder interferometer, and many different versions of delayed-choice experiments have been conducted with both classical and quantum detecting devices. A recent proposal suggests that the delayed-choice experiment can be considered in the perspective of device-independent causal model. Here, we experimentally realize this modified delayed-choice experiment with a deterministic high purity single-photon source, which plays a key role in the Wheeler's delayed-choice experiment. We examine that any two-dimensional nonretrocausal classical model can be excluded in a device-independent manner through our experimental results based on the violation of the dimension witness inequality. We also quantify the degree of retrocausality in our experiment and the results show that the amount of violating dimension witness inequality can be connected to the degree of quantum wave-particle superposition.

The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of Quantum Mechanics. In some cases, its spectrum can be determined by combining the WKB method with resummation techniques. In this paper we point out that the deformed Hamiltonian $H=2 \cosh(p)+ V_N(x)$ is exactly solvable for any potential: an exact quantization condition, involving well-defined functions, can be written down in closed form, and determines the spectrum of bound states and resonances. In particular, no resummation techniques are needed. This Hamiltonian is obtained by quantizing the Seiberg-Witten curve of $N=2$ Yang-Mills theory, and the exact quantization condition follows from the correspondence between spectral theory and topological strings, after taking a suitable four-dimensional limit. In this formulation, conventional Quantum Mechanics emerges in a scaling limit near the Argyres-Douglas superconformal point in moduli space. Although our deformed version of Quantum Mechanics is in many respects similar to the conventional version, it also displays new phenomena, like spontaneous parity symmetry breaking.

We report on a nanoscale quantum-sensing protocol which tracks a free precession of a single nuclear spin and is capable of estimating an azimuthal angle---a parameter which standard multipulse protocols cannot determine---of the target nucleus. Our protocol combines pulsed dynamic nuclear polarization, a phase-controlled radiofrequency pulse, and a multipulse AC sensing sequence with a modified readout pulse. Using a single nitrogen-vacancy center as a solid-state quantum sensor, we experimentally demonstrate this protocol on a single 13C nuclear spin in diamond and uniquely determine the lattice site of the target nucleus. Our result paves the way for magnetic resonance imaging at the single-molecular level.

Ultrastrong-coupling between an effective two-level system and radiation offers immense potential for advancing both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the break down of the rotating-wave approximation, which applied to the quantum Rabi model yields the apparently less fundamental Jaynes-Cummings model. However, the implications of gauge-freedom for ultrastrong-coupling QED are yet to be fully recognised. Here we show that when truncating the material system to only two levels, each gauge gives a different effective description whose predictions can vary significantly for ultrastrong-coupling. Rabi models are obtained through specific gauge choices, but so too is a Jaynes-Cummings model without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this Jaynes-Cummings model is often more accurate than the Rabi model. Thus, Jaynes-Cummings physics is not restricted to light-matter coupling below the ultrastrong limit. Among the many implications of this finding is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of the ultrastrong-coupling regime.

We consider the thermoelectric response of chaotic or disordered quantum dots in the limit of phase-coherent transport, statistically described by random matrix theory. We calculate the full distribution of the thermoelectric coefficients (Seebeck $S$ and Peltier $\Pi$), and the thermoelectric figure of merit $ZT$, for large open dots at arbitrary temperature and external magnetic field, when the number of lead modes $N$ is large. Our results show that the thermoelectric coefficients and $ZT$ are maximal when the temperature is half the Thouless energy, and the magnetic field is negligible. We find that the thermoelectric coefficients and $ZT$ are small, but they exhibit a type of universality, in the sense that they do not depend on the asymmetry between the left and right leads.

We unveil the stable $(d+1)$-dimensional topological structures underlying the quench dynamics for all the Altland-Zirnbauer classes in $d=1$ dimension, and propose to detect such dynamical topology from the time evolution of entanglement spectra. Focusing on systems in classes BDI and D, we find crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The entanglement-spectrum crossings are shown to be stable against symmetry-preserving disorder and faithfully reflect both $\mathbb{Z}$ (class BDI) and $\mathbb{Z}_2$ (class D) topological characterizations. As a byproduct, we unravel the topological origin of the global degeneracies emerging temporarily in the many-body entanglement spectrum in the quench dynamics of the transverse-field Ising model. These findings can experimentally be tested in ultracold atoms and trapped ions with the help of cutting-edge tomography for quantum many-body states. Our work paves the way towards a systematic understanding of the role of topology in quench dynamics.