Miguel A. Bastarrachea-Magnani

Bio: Miguel A. Bastarrachea-Magnani is an academic researcher from Aarhus University. The author has contributed to research in topics: Quantum & Coherent states. The author has an hindex of 16, co-authored 56 publications receiving 798 citations. Previous affiliations of Miguel A. Bastarrachea-Magnani include Universidad Autónoma Metropolitana & National Autonomous University of Mexico.

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

Abstract: The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

Abstract: Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.

Comparative quantum and semiclassical analysis of atom-field systems. I. Density of states and excited-state quantum phase transitions

Abstract: We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

Comparative quantum and semiclassical analysis of atom-field systems. II. Chaos and regularity

Abstract: The nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the previous paper by focusing on the statistical properties of the quantum fluctuations in the energy spectrum and their relation with the excited-state quantum phase transitions. These properties are compared with the dynamics observed in the semiclassical versions of the models. The presence of chaos for different energies and coupling constants is exhibited, employing Poincar\'e sections and Peres lattices in the classical and quantum versions, respectively. A clear correspondence between the classical and quantum result is found for systems containing between $\mathcal{N}=80$ and 200 atoms. A measure of the Wigner character of the energy spectrum for different couplings and energy intervals is also presented employing the statistical Anderson-Darling test. It is found that in the Dicke model, for any coupling, a low-energy regime with regular states is always present. The richness of the onset of chaos is discussed both for finite quantum systems and for the semiclassical limit, which is exact when the number of atoms in the system tends to infinite.

Classical chaos in atom-field systems.

Abstract: The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is associated with ESQPTs based in the resonant case, the off-resonant cases, and a close look at the vicinity of the QPTs in resonance, show clearly that both phenomena, ESQPTs and chaos, respond to different mechanisms. The results are supported in a detailed numerical study of the dynamics of the semiclassical Hamiltonian of the Dicke model. The appearance of chaos is quantified calculating the largest Lyapunov exponent for a wide sample of initial conditions in the whole available phase space for a given energy. The percentage of the available phase space with chaotic trajectories is evaluated as a function of energy and coupling between the qubit and bosonic part, allowing us to obtain maps in the space of coupling and energy, where ergodic properties are observed in the model. Different sets of Hamiltonian parameters are considered, including resonant and off-resonant cases.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

Abstract: It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

A quantum Newton's cradle

Abstract: It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

Strong light–matter interactions: a new direction within chemistry

Abstract: It is possible to modify the chemical and physical properties of molecules, not only through chemical modifications but also by coupling molecules strongly to light. More intriguingly, strong coupling between molecules and light is possible even without the presence of a photon. The phenomenon that makes this possible is called vacuum fluctuations, which is the finite zero point energy of the quantized electromagnetic field inside an optical cavity. The light–matter coupling, which can be as large as 1 eV (100 kJ mol−1), leads to the formation of new hybrid states, called polaritons. The formed hybrid states can be viewed as a linear combination of light (vacuum field) and matter (molecules), thus completely changing the energy landscape of the system. Using vacuum fluctuations, strong light–matter interactions have for instance been used to change chemical reactivity, charge conductivity, excited state relaxation pathways and rates of chemical reactions of organic molecules. In this review a brief history of the field is given, followed by a theoretical framework, methods of analysis, and a review of accomplishments. Finally, a personal reflection on the future perspectives and applications within this field is given.