We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the moving center acceleration. In the case of a constant acceleration, the probabilities oscillate with the oscillator frequency, so that no excitation occurs after every period. Examples of oscillating and rotating motion of the harmonic trap center are considered too. Estimations show that the effect of excitation of vibration states due to the motion of the harmonic trap center can be observed in available atomic traps.

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements in NISQ circuits; c) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30\% of a circuit's depth; d) area and volume cost metrics can misreport the resource analysis. Our findings assume that qubits are and will remain a very scarce resource. The results are applicable for both NISQ and QECC protected circuits. Our method uses multiple ways of decomposing Toffoli gates into Clifford+T gates. We illustrate our method on addition and multiplication circuits using ripple-carry. As a byproduct result we show systematically that for a practically significant range of circuit widths, ripple-carry addition circuits are more resource efficient than the carry-lookahead addition ones. The methods and circuits were implemented in the open-source QUANTIFY software.

Nuclear spins in semiconductors are leading candidates for quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their extremely long coherence lifetime. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which has enabled entanglement mediated by photonic links. The transport of quantum information by the electron itself, via controlled transfer to an adjacent centre or via the dipolar interaction, would enable even faster and smaller processors, but optical readout of arrays of such nodes presents daunting challenges due to the required sub-diffraction inter-site distances. Here, we demonstrate the electrical readout of a basic unit of such systems - a single 14N nuclear spin coupled to the NV electron. Our results provide the key ingredients for quantum gate operations and electrical readout of nuclear qubit registers, in a manner compatible with nanoscale electrode structures. This demonstration is therefore a milestone towards large-scale diamond quantum devices with semiconductor scalability.

In the context of non-relativistic quantum mechanics, we investigated Shannon's entropy of a non-Hermitian system to understand how this quantity is modified with the cyclotron frequency. Subsequently, we turn our attention to the construction of an ensemble of these spinless particles in the presence of a uniform magnetic field. Then, we study the thermodynamic properties of the model. Finally, we show how Shannon's entropy and thermodynamic properties are modified with the action of the magnetic field.

Laser cooling of matter through anti-Stokes photoluminescence, where the emitted frequency of light exceeds that of the impinging laser by virtue of absorption of thermal vibrational energy, has been successfully realized in condensed media, and in particular with rare earth doped systems achieving sub-100K solid state optical refrigeration. Studies suggest that laser cooling in semiconductors has the potential of achieving temperatures down to ~10K and that its direct integration can usher unique high-performance nanostructured semiconductor devices. While laser cooling of nanostructured II-VI semiconductors has been reported recently, laser cooling of indirect bandgap semiconductors such as group IV silicon and germanium remains a major challenge. Here we report on the anomalous observation of dominant anti-Stokes photoluminescence in germanium nanocrystals. We attribute this result to the confluence of ultra-high purity nanocrystal germanium, generation of high density of electron-hole plasma, the inherent degeneracy of longitudinal and transverse optical phonons in non-polar indirect bandgap semiconductors, and commensurate spatial confinement effects. At high laser intensities, laser cooling with lattice temperature as low as ~50K is inferred.

Entangled quantum states play an important role in quantum information science and also in quantum mechanics fundamental investigations. Implementation and characterization of techniques allowing for easy preparation of entangled states are important steps in such fields. Here we generated entangled quantum states encoded in photons transversal paths, obtained by pumping a non-linear crystal with multiple transversal Gaussian beams. Such approach allows us to generate entangled states of two qubits and two qutrits encoded in Gaussian transversal path of twin photons. We make a theoretical analyses of this source, considering the influence of the pump angular spectrum on the generated states, further characterizing those by their purity and entanglement degree. Our experimental results reveals that the generated states presents both high purity and entanglement, and the theoretical analysis elucidates how the pump beams profile can be used to manipulate such photonic states.

The interaction between an atomic system and a few-cycle ultrafast pulse carries rich physics and a considerable application prospect in quantum-coherence control. However, theoretical understanding of its general behaviors has been hindered by the lack of an analytical description in this regime, especially with regard to the impact of the carrier-envelope phase (CEP). Here, we present an analytical theory that describes a two-level atom driven by a far-off-resonance, few-cycle square pulse. A simple, closed-form solution of the Schrodinger equation is obtained under the first-order perturbation without invoking the rotating-wave approximation or the slowly varying envelope approximation. Further investigation reveals an arithmetic relation between the final inversion of the atom and the CEP of the pulse. Despite its mathematical simplicity, the relation is able to capture some of the key features of the interaction, which prove to be robust against generalization of pulse shapes and show good agreements with numerical solutions. The theory can potentially offer a general guidance in future studies of CEP-sensitive quantum coherence.

In this work we investigate the nonperturbative decay dynamics of a quantum emitter coupled to a composite right/left handed transmission line (CRLH-TL). Our theory captures the contributions from the different spectral features of the waveguide, providing an accurate prediction beyond the weak coupling regime, and illustrating the multiple possibilities offered by the nontrivial dispersion of metamaterial waveguides. We show that the waveguide is characterized by a band-gap with two asymmetric edges: (i) a mu-near-zero (MNZ) band edge, where spontaneous emission is inhibited and an unstable pole is smoothly transformed into a bound state, and (ii) an epsilon-near-zero (ENZ) band edge, where the decay rate diverges and unstable and real (bound state) poles coexist. In both cases, branch cut singularities contribute with fractional decay dynamics whose nature depend on the properties of the band-edges.

Due to the inevitable loss in communication channels, the distance of entanglement distribution is limited to approximately 100 km on the ground. Quantum repeater can circumvent this problem by utilizing quantum memory and entanglement swapping. As the elementary functional nodes for quantum repeater, the heralded generation of two-party entanglement between two remote nodes has only been realized with built-in-type quantum memories. These schemes suffer from the trade-off between multiplexing capacity and deterministic property and hence hinder their way to efficient quantum repeaters. Here we present the first experimental demonstration of functional quantum repeater nodes using absorptive quantum memories. We build two nodes separated by 3.5 m, each contains a polarization-entangled photon-pair source and a solid-state quantum memory. A joint Bell-state measurement in the middle station heralds the successful generation of maximally-entangled states between the two quantum memories with a fidelity of (80.4$\pm$2.1)%. The quantum memories used here are compatible with deterministic entanglement sources and can support multiplexing simultaneously, which paves the way to the construction of solid-state quantum repeaters and high-speed quantum networks.

A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner's theorem. Wigner's theorem shows that every symmetry of the quantum state space must be either a unitary transformation, or a antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated to the dynamics of closed systems, and the stochastic evolution associated to quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes. We propose one such modification, wherein the evolutions are restricted to a suitable set of time symmetric operations, including both unitary evolution and the state reductions associated to projective measurements.

We examine how the presence of an excited state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

A protocol for fast and robust magnon transport in a one-dimensional spin chain is devised. Employing an approximate mapping between the chain and a single harmonically trapped particle, we exploit the known analytic control protocols for the latter and adopt them to achieve fast, high-fidelity transport in the chain. We compare the performance with finite time adiabatic protocols, establishing that the designed scheme allows for significantly faster and more stable transport. Furthermore, we show that a sharp transition exists between regions in which the protocol is effective and when it breaks down, giving rise to a heuristic speed limit for the process.

There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics. Autonomous models, which do not rely on any external time-dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations. Here, we bridge the two paradigms by constructing an autonomous model, which implements a thermodynamic cycle in a certain parameter regime. This effect is made possible by self-oscillations, realized in our model by the well studied electron shuttling mechanism. Based on experimentally realistic values, we find that a thermodynamic cycle analysis for a single-electron working fluid is {\it not} justified, but a few-electron working fluid could suffice to justify it. We also briefly discuss additional open challenges to autonomously implement the more studied Carnot and Otto cycles.

Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard technique, the production of squeezed states of the collective excitations in gases of ultracold atoms, the phonons of a Bose-Einstein condensate (BEC), is a comparably recent problem. This task is continuously gaining relevance with a growing number of proposals for BEC-based quantum metrological devices and the possibility to apply them in the detection of gravitational waves. The objective of this thesis is to find whether the recently described effect of an oscillating external potential on a uniform BEC can be exploited to generate two-mode squeezed phonon states, given present day technology. This question brings together elements of a range of fields beyond cold atoms, such as general relativity and Efimov physics. To answer it, the full transformation caused by the oscillating potential on an initially thermal phononic state is considered, allowing to find an upper bound for the magnitude of this perturbation as well as to quantify the quality of the final state with respect to its use in metrology. These findings are then applied to existing experiments to judge the feasibility of the squeezing scheme and while the results indicate that they are not well suited for it, a setup is proposed that allows for its efficient implementation and seems within experimental reach. In view of the vast parameter space leaving room for optimization, the considered mechanism could find applications not only in the gravitational wave detector that originally motivated this work, but more generally in the field of quantum metrology based on ultracold atoms.

We study the entanglement between a certain qubit and the remaining system in the Schr\"odinger cat state prepared on the ibmq-melbourne quantum computer. The protocol, which we use for this purpose, is based on the determination of the mean value of spin corresponding to a certain qubit. We explore the dependence of the entanglement on a parameter of the Schr\"odinger cat state which consists of different numbers of qubits. In addition, we explore the entanglement of each qubit with the remaining system in the maximum entangled Schr\"odinger cat state.

Future quantum networks will enable the distribution of entanglement between distant locations and allow applications in quantum communication, quantum sensing and distributed quantum computation. At the core of this network lies the ability of generating and storing entanglement at remote, interconnected quantum nodes. While remote physical systems of various nature have been successfully entangled, none of these realisations encompassed all of the requirements for network operation, such as telecom-compatibility and multimode operation. Here we report the demonstration of heralded entanglement between two spatially separated quantum nodes, where the entanglement is stored in multimode solid-state quantum memories. At each node a praseodymium-doped crystal stores a photon of a correlated pair, with the second photon at telecommunication wavelengths. Entanglement between quantum memories placed in different labs is heralded by the detection of a telecom photon at a rate up to 1.4 kHz and is stored in the crystals for a pre-determined storage time up to 25 microseconds. We also show that the generated entanglement is robust against loss in the heralding path, and demonstrate temporally multiplexed operation, with 62 temporal modes. Our realisation is extendable to entanglement over longer distances and provides a viable route towards field-deployed, multiplexed quantum repeaters based on solid-state resources.

By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous QMSs. Moreover we prove that, when there exists a faithful normal invariant state, N(T) has to be atomic and decoherence takes place.

Quantum phase transitions in spin systems are supposed to be accompanied by a soft collective mode, which has not been seen in experiments. Here, we directly measure the low energy excitation modes of a well-known realization of the Ising model in transverse field, LiHoF$_4$, using microwave spectroscopy techniques to probe energies well below what is accessible via neutron scattering experiments. Instead of the single excitation expected for a simple quantum Ising system, we find and characterize a remarkable array of `electronuclear' modes, arising from coupling of the spin-1/2 Ising electronic spins to a bath of spin-7/2 Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point from below and above, a softening that can be quenched with the application of a longitudinal magnetic field. The electronuclear mode structure has direct implications for the Ising systems that serve as the building blocks of adiabatic quantum computers and quantum annealers.

We investigate the onset of chaos in a periodically kicked Dicke model (KDM), using the out-of-time-order correlator (OTOC) as a diagnostic tool, in both the oscillator and the spin subspaces. In the large spin limit, the classical Hamiltonian map is constructed, which allows us to investigate the corresponding phase space dynamics and to compute the Lyapunov exponent. We show that the growth rate of the OTOC for the canonically conjugate coordinates of the oscillator is able to capture the Lyapunov exponent in the chaotic regime. The onset of chaos is further investigated using the saturation value of the OTOC, that can serve as an alternate indicator of chaos in a generic interacting quantum system. This is also supported by a system independent effective random matrix model. We further identify the quantum scars in KDM and detect their dynamical signature by using the OTOC dynamics. The relevance of the present study in the context of ongoing cold atom experiments is also discussed.

Dynamical two-particle susceptibilites are important for a wide range of different experiments in condensed-matter physics and beyond. Nevertheless, most textbooks avoid describing how to derive such response functions, perhaps because they are viewed as too complex. In the literature, most derivations work with generalized susceptibilities, which are more general, but require an even higher layer of complexity. In this work, we show a more direct derivation in the context of model Hamiltonians which can be mapped directly onto an impurity model. We also present an alternative derivation for the irreducible vertex in the context of the Falicov-Kimball model.