In this work, a classical/quantum correspondence for a pseudo-hermitian system with finite energy levels is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed.

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking robustness of quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any knowledge about the nature of the imperfections.

Using the platform of a trapped-atom clock on a chip, we have generated spin-squeezed states with up to 8.1(9) dB of metrological squeezing in a cloud of $2\times 10^4$ ultracold alkali atoms by quantum nondemolition (QND) measurement in a fiber Fabry-Perot microcavity. Observing the time evolution of the squeezed state on unprecedented timescales of more than one second reveals a surprising measurement amplification effect in the final measurement of the spin state. It results from a subtle interplay between the spin dynamics of interacting indistinguishable particles and energy-dependent cavity coupling and leads to an increased cavity shift per spin, and thus to a higher signal per photon read out. Metrological spin squeezing is preserved for 1 s. Both results open up encouraging perspectives for squeezing-enhanced atomic clocks in a metrologically relevant stability regime.

Fault-tolerant quantum computation is the only known route to large-scale, accurate quantum computers. Fault tolerance schemes prescribe how, by investing more physical resources and scaling up the size of the computer, we can keep the computational errors in check and carry out more and more accurate calculations. Underlying all such schemes is the assumption that the error per physical gate is independent of the size of the quantum computer. This, unfortunately, is not reflective of current quantum computing experiments. Here, we examine the general consequences on fault-tolerant quantum computation when constraints on physical resources, such as limited energy input, result in physical error rates that grow as the computer grows. In this case, fault tolerance schemes can no longer reduce computational error to an arbitrarily small number, even if one starts below the so-called fault tolerance noise threshold. Instead, there is a minimum attainable computational error, beyond which further growth of the computer in an attempt to reduce the error becomes counter-productive. We discuss simple, but rather generic, situations in which this effect can arise, and highlight the areas of future developments needed for experiments to overcome this limitation.

We demonstrate a quantum key distribution implementation over deployed dark telecom fibers with polarisation-entangled photons generated at the O-band. One of the photons in the pairs are propagated through 10km of deployed fiber while the others are detected locally. Polarisation drifts experienced by the photons propagating through the fibers are compensated with liquid crystal variable retarders. This ensures continuous and stable QKD operation with an average QBER of 6.4% and a final key rate of 109 bits/s.

A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that such defined measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.

Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state. Furthermore, we carry out experimental verification of this information-theoretical bound by means of a single spin embedded in an ultracold trapped $^{40}$Ca$^{+}$ ion. Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.

Several theoretical studies have recently predicted that the Majorana phases could be realized as quantized plateaus in the magnetoconductance of the artificially engineered hybrid junctions based on two-dimensional electron gases (2DEG) under fully out-of-plane magnetic fields. The large transverse Rashba spin-orbit interaction in 2DEG together with a strong orbital effect due to magnetic fields yield topological phase transitions to nontrivial phases hosting Majorana modes. Such Majorana modes are formed at the ends of 2DEG-based wires with a hybrid superconductor-semiconductor integrity. Here, we report on the experimental observation of such topological phases in hybrid junctions on an In0.75Ga0.25As 2DEG platform by sweeping small out-of-plane magnetic fields (B< 100 mT) and probing the conductance to highlight the characteristic quantized magnetoconductance plateaus. The observed signature of topological phases in small out-of-plane magnetic fields in planar hybrid junctions suggests that In0.75Ga0.25As heterostructure affords a promising material platform for the realization of scalable topological circuits for the applications in quantum technologies.

We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest set-up of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (\PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The $\mathcal{PT}$ phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find a negative relative magnetoresistance effect of approximately $ -B^{2} $ dependence when a hyperplane is cut through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by extending an artificial dimension in 3D optical lattices. Moreover, we show that the quantum metric tensor can be detected by applying an external drive in the optical lattices.

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring and how wedge disclination influences different quantum transport quantities.

In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega(t)$ varies during evolution so to display either a non harmonic hole or barrier. To this scope we focus on the case where $\omega(t)^2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,\omega^2)$ plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, that is known to be the very fundamental dynamical object entering the description of both classical and quantum dynamics of time-dependent quadratic systems. Once such quantity is determined and its significant characteristics highlighted, we provide a more refined insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.

We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg-Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables, and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. Following a quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase-separation between the impurities and their surrounding for strong repulsions. For attractive post-quench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

The existence of non--vanishing Bohm potentials, in the Madelung--Bohm version of the Schr\"odinger equation, allows for the construction of particular solutions for states of quantum particles interacting with non--trivial external potentials whose propagation is equivalent to the one for classical free particles.

A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. The potential function defines the amplitude and the phase of any wavefunction which solves the one--dimensional Schr\"odinger equation. This new approach allows us to recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions that have vanishing and non--vanishing Bohm potentials. For most of the potentials, no solutions to the Schr\"odinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some unexpected and surprising quantum results which seem to (but do not) violate the correspondence principle such as accelerated Airy wavefunctions which solve the free Schr\"odinger equation, are due to the presence of non--vanishing Bohm potentials. New examples of this kind are found and discussed. The relation of these results to some of the unusual solutions to other wave equations is briefly discussed.

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks require large energy dissipation. For periodic clocks, operating on a limit cycle, this is a consequence of phase diffusion. It is also true for non periodic clocks (for example, radio carbon dating) but due to telegraph noise not to phase diffusion. In this case a key role is played by accurate measurements that decrease entropy, thereby raising the free energy of the clock, and requires access to a low entropy reservoir. In the quantum case, for which thermal noise is replaced by quantum noise (spontaneous emission or tunnelling), measurement plays an essential role for both periodic and non periodic clocks. The paper concludes with a discussion of the Tolman relations and Rovelli's thermal time hypothesis in terms of clock thermodynamics.

Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and the superfluid phases at integer fillings. Here we present an approach for the robust preparation of many-body ground states of polaritons in a finite-sized JC lattice by optimized nonlinear ramping. In the deep Mott-insulating and deep superfluid regimes, polaritons can be pumped into a JC lattice and be prepared in the ground state with high accuracy via engineered pulse sequences. Using such states as initial state and employing optimized nonlinear ramping, we demonstrate that many-body ground states in the intermediate regimes of the parameter space can be generated with high fidelity. We exploit a Landau-Zener-type of estimation on this finite-sized system and derive an optimal ramping index for selected ramping trajectories, which greatly improves the fidelity of the prepared states. With numerical simulation of the ramping process, we further show that by choosing an appropriate trajectory, the fidelity can remain close to unity in almost the entire parameter space. This method is general and can be applied to many other systems.