Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic ordered) materials---arguably the better understood setting---has been a mystery ever since Anderson discovered disorder-induced localization. Nonetheless, together these revolutionized materials science and technology and led to new physics far beyond the solid state. We introduce a broad family of structurally complex materials---chaotic crystals---that interpolate between these organizational extremes---systematically spanning periodic structures and random disorder. Within the family one can tune the degree of disorder to sweep through an intermediate structurally disordered region between two periodic lattices. This reveals new transport and localization phenomena reflected in a rich array of energy-dependent localization degree and density of states. In particular, strong localization is observed even with a very low degree of disorder. Moreover, markedly enhanced localization and delocalization coexist in a very narrow range of energies. Most notably, beyond the simply smoothed bands found in previous disorder studies, islands of transport emerge in band gaps and sharp band boundaries persist in the presence of substantial disorder. Finally, the family of materials comes with rather direct specifications of how to assemble the requisite material organizations.

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.

Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature, although it does not satisfy the eigenstate thermalization hypothesis. In contrast, when the system size is finite and the temperature is low enough, the system may not thermalize. In this case, the steady state is well described by the generalized Gibbs ensemble constructed by using highly nonlocal conserved quantities. We also show that this model exhibits prethermalization, in which the prethermalized state is characterized by nonthermal energy eigenstates.

We study the impact of finite-size effect on continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on parameter estimation procedure. The central-limit theorem and the maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret key rate of the CV-MDI QKD protocol and should not be ignored.

We present a proof of concept for adapting the finite-difference time-domain method (FDTD) for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED). The delay term exists in both spatial and temporal directions, rendering the conventional approaches such as the method of lines inapplicable. We show that by properly designing the grid and by using the exact (partial) solution as the boundary condition, the delay PDE can be numerically solved. Our code provides a numerically exact solution to the time-dependent multi-photon scattering problem in waveguide QED. The program is written in C and open-sourced on GitHub.

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to discuss the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.

We experimentally investigate $\sigma^+$-$\sigma^-$ polarization gradient cooling~(PGC) of a single $^{87}$Rb atom in a tightly focused dipole trap and show that the cooling limit strongly depends on the polarization of the trapping field. For optimized cooling light power, the temperature of the atom reaches~$10.4(6)\,\mu$K in a linearly polarized trap, approximately five times lower than in a circularly polarized trap. The inhibition of PGC is qualitatively explained by the fictitious magnetic fields induced by the trapping field. We further demonstrate that switching the trap polarization from linear to circular after PGC induces only minor heating.

Without access to the full quantum state, modelling dissipation in an open system requires approximations. The physical soundness of such approximations relies on using realistic microscopic models of dissipation that satisfy completely positive dynamical maps. Here we present an approach based on the use of the Bohmian conditional wave function that, by construction, ensures a completely positive dynamical map for either Markovian or non-Markovian scenarios, while allowing the implementation of realistic dissipation sources. Our approach is applied to compute the current-voltage characteristic of a resonant tunnelling device with a parabolic-band structure, including electron-lattice interactions. A stochastic Schr\"odinger equation is solved for the conditional wave function of each simulated electron. We also extend our approach to (graphene-like) materials with a linear band-structure using Bohmian conditional spinors for a stochastic Dirac equation.

Feshbach resonances, which allow for tuning the interactions of ultracold atoms with an external magnetic field, have been widely used to control the properties of quantum gases. We propose a~scheme for using scattering resonances as a probe for external fields, showing that by carefully tuning the parameters it is possible to reach a $10^{-5}$G (or nT) level of precision with a single pair of atoms. We show that for our collisional setup it is possible to saturate the quantum precision bound with a simple measurement protocol.

We study the effect of action noise on state-to-state control protocols. Action noise creates dephasing in the instantaneous eigenbasis of the Hamiltonian and hampers the fidelity of the final state with respect to the target state. We find that for shorter protocols the noise more strongly influences the dynamics and degrades fidelity. We suggest improving the fidelity by inducing stronger dephasing rates along the process. The effects of action noise on the dynamics and its manipulation is described for a general Hamiltonian and is then studied by examples.

All existing quantum gravity proposals share the same deep problem. Their predictions are extremely hard to test in practice. Quantum effects in the gravitational field are exceptionally small, unlike those in the electromagnetic field. The fundamental reason is that the gravitational coupling constant is about 43 orders of magnitude smaller than the fine structure constant, which governs light-matter interactions. For example, the detection of gravitons -- the hypothetical quanta of energy of the gravitational field predicted by certain quantum-gravity proposals -- is deemed to be practically impossible. In this letter we adopt a radically different, quantum-information-theoretic approach which circumvents the problem that quantum gravity is hard to test. We propose an experiment to witness quantum-like features in the gravitational field, by probing it with two masses each in a superposition of two locations. First, we prove the fact that any system (e.g. a field) capable of mediating entanglement between two quantum systems must itself be quantum. This argument is general and does not rely on any specific dynamics. Then, we propose an experiment to detect the entanglement generated between two masses via gravitational interaction. By our argument, the degree of entanglement between the masses is an indirect witness of the quantisation of the field mediating the interaction. Remarkably, this experiment does not require any quantum control over gravity itself. It is also closer to realisation than other proposals, such as detecting gravitons or detecting quantum gravitational vacuum fluctuations.

The identification of an unknown quantum gate is a significant issue in quantum technology. In this paper, we propose a quantum gate identification method within the framework of quantum process tomography. In this method, a series of pure states are inputted to the gate and then a fast state tomography on the output states is performed and the data are used to reconstruct the quantum gate. Our algorithm has computational complexity $O(d^3)$ with the system dimension $d$. The algorithm is compared with maximum likelihood estimation method for the running time, which shows the efficiency advantage of our method. An error upper bound is established for the identification algorithm and the robustness of the algorithm against the purity of input states is also tested. We perform quantum optical experiment on single-qubit Hadamard gate to verify the effectiveness of the identification algorithm.

Uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. Recently, many uncertainty relations have been proposed with improved lower bounds and are capable of incorporating multiple observables. Here we report an experimental verification of seven uncertainty relations of this type with single-photon measurements. The results, while confirm these uncertainty relations, show as well the relative stringency of various uncertainty lower bounds.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

In this article, we proposed an simple and efficient one-out-of-two quantum oblivious transfer (QOT) protocol based on nonorthogonal states. This property makes the quantum immune some operations to accomplish irreversible goal. In addition, the property can also avoid entangled cheat from illegal agent. Therefore, it can build QOT protocol on the quantum resource directly instead of two level structure, i.e. first create two classical key using the quantum resource (all-or-nothing QOT) then build one-out-of-two up to it. Furthermore, our protocol can allow legal agents to authenticate each other through the reorder and dummy message technique, and discuss the relationship with the no-go theorem in detail. The security analysis showed our protocol does not belong to no-go theorem of norms and against external and internal attack. In addition, the efficacy analysis showed our protocol is more efficient than other two level structure.

In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local asymptotic mixed normality of the underlying statistical model and the consistency of the maximum likelihood estimator. Furthermore, we prove the asymptotic optimality of this estimator as it saturates the usual Cram\'er Rao bound.

WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Treating the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm.

The appearance of topological effects in systems exhibiting non-trivial topological band structures strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic random walk version of the Su-Schrieffer-Heeger model with no relation to coherent wave dynamics. We explain that the commonly used topological invariant in the momentum space translates into an invariant in a counting field space. This quantization gives rise to clear signatures of the topological phase in an associated waiting time distribution.

The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common cause, and each of these causal mechanisms can be coherent or not. Furthermore, one can combine these mechanisms in different ways: by probabilistically realizing either one or the other or by having both act simultaneously (termed a physical mixture). In the latter case, it is possible for the two mechanisms to be combined quantum-coherently. Previous work has shown how to experimentally realize one example of each class of possible causal relations. Here, we make a theoretical and experimental study of the transitions between these classes. In particular, for each of the two distinct types of coherence that can exist in mixtures of common-cause and cause-effect relations--coherence in the individual causal pathways and coherence in the way the causal relations are combined--we determine how it degrades under noise and we confirm these expectations in a quantum-optical experiment.

We predict a spin pure dephasing channel in a spin-preserving electron tunneling between quantum dots in external magnetic field. The dephasing does not rely on any spin-environment coupling and is caused by a mismatch in $g$-factors in the two dots leading to distinguishability of phonon packets emitted during tunneling with opposite spins. Combining multiband $\boldsymbol{k}\cdot\boldsymbol{p}$ modeling and dynamical simulations via a Master equation we show that this fundamental effect of spin measurement effected by the phonon bath may be controlled by size and composition of the dots or by external fields. By comparing the numerically simulated degree of dephasing with the predictions of general theory based on distinguishability of environment states we show that the proposed mechanism is the dominating spin dephasing channel in the system.