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In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this geometrical framework, such as the Hamiltonian and the nonlinear and affine connections, can be derived from a given metric. Several properties of this kind of spaces are demonstrated for autoparallel Hamiltonians. Moreover, we study the spacetime and momentum isometries of the metric. Finally, we discuss the possible applications of cotangent bundle geometries in quantum gravity, such as the construction of deformed relativistic kinematics and non-commutative spacetimes., Comment: 16 pages

We discuss the generation of a Schr\"odinger cat in a nanocavity created by the coupling of an electromagnetic mode with an exciton in a quantum dot considering the dispersive limit of the Jaynes-Cummings model. More than the generation itself, we focus on the effects of the environment over the bosonic state in the nanocavity, which has losses simulated by coupling with two different kind of reservoirs. In the first case, the interaction between the system with a finite reservoir shows that fragments of different sizes of the reservoir deliver the same amount of information about the physical system in the dynamics of the birth and death of the Schr\"odinger cat. The second case considers a structured reservoir, whose spectral density varies significantly with frequency. This situation becomes relevant in solid-state devices where quantum channels are embedded, as memory effects generally cannot be neglected. Under these circumstances, it is observed that the dynamics can differ substantially from the Markovian, presenting oscillations related to the average number of photons. These oscillations influence the information flow between the system and the environment, evidenced here by the measurement of non-Markovianity.

In this work, we present the technical details of the discussion presented in [J.J. Relancio, L.Santamar\'ia-Sanz (2024) arXiv:2403.18772], where we establish the basis of quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of these kind of theories. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction we are able to restrict the possible models of doubly special relativity to particular bases that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential either for an electric point-like source and a magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti de Sitter space but do for the de Sitter one in both problems., Comment: 15 pages, 5 figures

Non-local quantum field theories could be a solution to the inconsistencies arising when quantizing gravity. Doubly special relativity is regarded as a low-energy limit of a quantum gravity theory with testable predictions. We present a new formulation of quantum field theories in doubly special relativity with non-local behavior. Our construction restricts the models to those showing linear Lorentz invariance. The deformed Klein--Gordon, Dirac, and electromagnetic Lagrangians are derived. The deformed Maxwell equations and the electric potential of a point charge are discussed., Comment: 5 pages, 1 figure

We investigate the generation of an entangled electron pair emerging from a system composed of two quantum dots attached to a superconductor Cooper pair beam splitter. We take into account three processes: Crossed Andreev Reflection, cotuneling, and Coulomb interaction. Together, these processes play crucial roles in the formation of entangled electronic states, with electrons being in spatially separated quantum dots. By using perturbation theory, we derive an analytical effective model that allows a simple picture of the intricate process behind the formation of the entangled state. Several entanglement quantifiers, including quantum mutual information, negativity, and concurrence, are employed to validate our findings. Finally, we define and calculate the covariance associated with the detection of two electrons, each originating from one of the quantum dots with a specific spin value. The time evolution of this observable follows the dynamics of all entanglement quantifiers, thus suggesting that it can be a useful tool for mapping the creation of entangled electrons in future applications within quantum information protocols., Comment: To be published in Physical Review A

In this work, it is investigated the behavior of the efficiency at maximum power of a quantum dot molecule, acting as a device for photovoltaic conversion. A theoretical approach using a master equation, considering the effect of the energy offsets, and the width of the quantum barrier, identifies realistic physical conditions that enhance the photovoltaic response of the photocell. The results show the potentiality of increasing the gain in 30\% of maximum power delivered per molecule if compared with a single quantum dot. Also, the system exhibits gain when compared to the Chambadal-Novikov efficiency at maximum power, without exceeding Carnot's efficiency, as expected from the second law of thermodynamics.

In this paper we make a detailed study of the role of coherent tunneling, on the photocurrent and power delivered by a quantum dot molecule (QDM) in the presence of solar light. We focus our analysis on the coherence driven by tunneling and its impact on the photovoltaic properties of the QDM. The coherence developed by the system raises as a resource from the interplay between the strength of the tunneling coupling, the QDM band alignment, and the coupling rates with the reservoirs of thermal phonons. Our results show that a QDM can deliver up to 30% more power than a single quantum dot, and our calculations of efficiency show coherence effects, which are consistent with the Second Law of Thermodynamics.

In this paper, we present a proof-of-principle of the formation of pure maximally entangled states from the Greenberger-Horne-Zeilinger class, in the experimental context of charged quantum dots. Each qubit must be identified as a pair of quantum dots, sharing an excess electron, coupled by tunneling. The electron-electron interaction is accounted for and is responsible for the coupling between the qubits. The interplay between coherent tunneling events and many-body interaction gives rise to the formation of highly entangled states. We begin by treating the problem of encoding three-qubits in a system with three pairs of quantum dots, and the numerical analysis of the exact quantum dynamics to find the conditions for the generation of the GHZ states. An effective two-level model sheds light on the role of a high-order tunneling process behind the dynamics. The action of the main decoherence process, the charge dephasing, is quantified in the process. We then evaluate the physical requirements for the dynamical generation of GHZ states in a $N$ qubit scenario, and its challenges., Comment: To be published in Physical Review A

In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for the pressure between plates and the quantum thermal correction to the entropy. We find out that our system is thermodynamically stable for any boundary conditions, and we identify a critical temperature below which certain boundary conditions yield attractive, repulsive, and null Casimir forces., Comment: 17 pages, 14 figures. Substantial changes along the text have been introduced

The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $\delta$-$\delta^\prime$ functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case $T \to 0$ we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy., Comment: some typos have been corrected and some comments have been added to clarify certain parts of the paper Accepted for publication in Eur. Phys J. C

We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support., Comment: To appear in Mod. Physics. Lett. A. Based on a talk given at the "10th ALEXANDER FRIEDMANN INTERNATIONAL SEMINAR ON GRAVITATION AND COSMOLOGY AND 4th SYMPOSIUM ON THE CASIMIR EFFECT" (St. Petersburg, Russia, June 2019)

We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite array formed by identical $\delta\text{-}\delta'$ potentials standing at the linear lattice nodes. This case will be known throughout the paper as the one-species hybrid Dirac comb. We investigate the consequences of adding the $\delta'$ interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac-$\delta$ combs and one-species hybrid Dirac combs. Secondly we study the quantum system that arises when the periodic potential is the one obtained from the superposition of two one-species hybrid Dirac combs displaced one with respect to the other and with different couplings. The latter will be known as the two-species hybrid Dirac comb. One of the most remarkable results is the appearance of a curvature change in the band spectrum when the $\delta'$ couplings are above a critical value., Comment: 25 pages, 10 figures. Mayor changes have been done in the structure of the paper

We present a proof-of-principle of how electronic transport measurements permits the observation of the Autler-Townes doublet, an optical property of nanodevices. The quantum physical system consists of one optically pumped quantum dot, a second auxiliary quantum dot, and a superconductor lead which provides an effective coupling between the dots via crossed Andreev reflection. Electrodes, working as source and drain, acts as nonequilibrium electronic reservoirs. Our calculations of the photocurrent at both, transient and stationary regimes, obtained using a density matrix formalism for open quantum systems, shows signatures of the formation of the Autler-Townes doublet, caused by the interplay between the optical pumping and the crossed Andreev reflection., Comment: 5 pages, 3 figures

In this work, we provided a proof-of-principle of efficient production of maximally entangled states using charged quantum dots coupled to vibrational modes. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electrons, initially not coupled, interact with two bosonic vibrational modes. It is demonstrated that the electron-vibrational mode coupling drives to an effective electron-electron interaction, which is the main mechanism behind the formation of maximally quantum entangled electronic states. The effect of this coupling follows a non-monotonic behavior, which is explained through an effective hamiltonian which takes into account high order transition processes., Comment: revised version, 13 pages, 7 figures

We present an alternative form of master equation, applicable on the analysis of non-equilibrium dynamics of fermionic open quantum systems. The formalism considers a general scenario, composed by a multipartite quantum system in contact with several reservoirs, each one with a specific chemical potential and in thermal equilibrium. With the help of Jordan-Wigner transformation, we perform a fermion-to-qubit mapping to derive a set of Lindblad superoperators that can be straightforwardly used on a wide range of physical setups.To illustrate our approach, we explore the effect of a charge sensor, acting as a probe, over the dynamics of electrons on coupled quantum molecules. The probe consists on a quantum dot attached to source and drain leads, that allows a current flow. The dynamics of populations, entanglement degree and purity show how the probe is behind the sudden deaths and rebirths of entanglement, at short times. Then, the evolution leads the system to an asymptotic state being a statistical mixture. Those are signatures that the probe induces dephasing, a process that destroys the coherence of the quantum system., Comment: To be published in Physical Review A

In this work we demonstrate theoretically how to use external laser field to control the population inversion of a single quantum dot exciton qubit in a nanocavity. We consider the Jaynes-Cummings model to describe the system, and the incoherent losses were take into account by using Lindblad operators. We have demonstrated how to prepare the initial state in a superposition of the exciton in the ground state and the cavity in a coherent state. The effects of exciton-cavity detuning, the laser-cavity detunings, the pulse area and losses over the qubit dynamics are analyzed. We also show how to use a continuous laser pumping in resonance with the cavity mode to sustain a coherent state inside the cavity, providing some protection to the qubit against cavity loss., Comment: Accepted for publication in Physical Review B

The entanglement of an optically generated electron-hole pair in artificial quantum dot molecules is calculated considering the effects of decoherence by interaction with environment. Since the system evolves into a mixed states and due to the complexity of energy level structure, we use the negativity as entanglement quantifier, which is well defined in $d \otimes d^\prime$ composite vector spaces. By a numerical analysis of the non-unitary dynamics of the exciton states, we establish the feasibility of producing protected entangled superpositions by an appropriate tuning of bias electric field, $F$. A stationary state with a high value of negativity (high degree of entanglement) is obtained by fine tuning of $F$ close to a resonant condition between indirect excitons. We also found that when the optical excitation is set approximately equal to the electron tunneling coupling, $\Omega/T_e \sim 1$, the entanglement reaches a maximum value. In front of the experimental feasibility of the specific condition mentioned before, our proposal becomes an useful strategy to find robust entangled states in condensed matter systems., Comment: 4 figures

In this work, we are interested on the implementation of single-qubit gates on coupled Bose-Einstein condensates (BECs). The system, a feasible candidate for a qubit, consists on condensed atoms of different hyperfine levels coupled by a two-photon transition. It is well established that the dynamics of coupled BECs can be described by the two-mode Hamiltonian which takes into account the confinement potential of the trap and the effects of collisions associated with each condensate. Other effects, as collisions between atoms belonging to different BECs and detuning are included in this approach. We demonstrate how to implement two types of quantum logic gates: \textit{transfer-population} gates (NOT, $\hat{Y}$, and Hadamard), which require inversion of population between hyperfine levels, and \textit{phase} gates ($\hat{Z}$, $\hat{S}$, and $\hat{T}$), which require self-trapping. We also discuss the experimental feasibility, checking the robustness of quantum gates against variations of physical parameters out of the ideal conditions for implementation of each quantum logic gate.