arXiv subjects

Gonzalo Ordonez

Publications and source records attributed to Gonzalo Ordonez.

At least 19 recordsLinked to original sources

arXiv2026

Operator-frame geometry of non-compact quantum systems with frame-vacuum phase transitions

We formulate the geometric structure of non-compact bosonic quantum systems in regimes where vacuum instability renders the relevant quantum states non-normalizable, causing conventional state-space quantum geometry -- described by the Berry connection, curvature, and quantum metric -- to become ill-defined. To overcome this breakdown, we develop a formulation of quantum geometry at the level of canonical operator frames, allowing for complexified Bogoliubov-Valatin transformations that lift the requirement that creation operators be Hermitian conjugates of annihilation operators. Canonical operator frames are defined as choices of bosonic creation and annihilation operators realizing the canonical commutation relations. A natural equivalence relation among such frames generalizes the phase ambiguity of quantum states and determines a parameter space that analytically extends the stable-regime parameter space. The space of canonical operator frames forms a principal bundle over parameter space -- the operator-frame bundle -- equipped with a natural Ehresmann connection that defines parallel transport while preserving the canonical commutation relations. In the stable regime, this construction reduces to the Berry connection, while more generally it yields a well-defined operator-space quantum geometric tensor (QGT) that remains valid across vacuum instabilities. Using the framework of rigged Hilbert spaces, we define a notion of quantum frame vacuum and obtain a consistent state-space QGT. Focusing on a single bosonic mode, we demonstrate analyticity of the QGT across the quantum frame-vacuum phase transition and present the corresponding phase diagram on the complexified squeezing-parameter plane. We further introduce a realistic physical setting that allows continuous paths connecting stable and unstable regimes, along which the QGT evolves smoothly across Stokes lines.

quant-ph↗

arXiv2026

Non-Hermitian Quantum Mechanics of Open Quantum Systems: Revisiting The One-Body Problem

We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve the problem completely, making it easier to see the structures of problems involving open quantum systems. We show that this results in the discovery of a new complete set, which is one of the main topics of the present article. Another reason for focusing on the one-body problem is that the theory permits the strong coupling between the system and the environment. In the current research landscape, it is valuable to revisit the one-body problem for open quantum systems, which can be solved accurately for arbitrary strengths of the system-environment couplings. A rigorous understanding of the problem structures in the present approach will be helpful when we tackle problems with many-body interactions. First, we consider potential scattering and directly define the resonant state as an eigenstate of the Schrödinger equation under the Siegert outgoing boundary condition. We show that the resonant eigenstate can have a complex energy eigenvalue, even though the Hamiltonian is seemingly Hermitian. Second, we introduce the Feshbach formalism, which eliminates the infinite degrees of freedom of the environment and represents its effect as a complex potential. The resulting effective Hamiltonian is explicitly non-Hermitian. By unifying these two ways of defining resonant states, we obtain a new complete set of bases for the scattering problem that contains all discrete eigenstates, including resonant states. We finally mention the non-Markovian dynamics of open quantum systems. We emphasize the time-reversal symmetry of the dynamics that continuously connects the past and the future. We can capture it using the new complete set that we develop here.

quant-ph↗

arXiv2025

Weak-coupling bound states in semi-infinite topological waveguide QED

A striking feature of cavity quantum electrodynamics is the existence of atom-photon bound states, which typically form when the coupling between the atom and its environment are strong enough that after de-excitation the atom can ``grab'' an emitted photon and re-absorb it, resulting in a virtual cloud surrounding the atom. Here we will demonstrate the existence of bound states that instead form in the case of weak coupling. Specifically, we show that when a quantum emitter is weakly coupled to a structured reservoir exhibiting topologically-protected surface states, hybridizations between these states and the emitter can form, resulting in mid-gap bound states. We illustrate this using a semi-infinite extension of the Su-Schrieffer-Heeger (SSH) model as our reservoir. First, we diagonalize the bare semi-infinite SSH chain and reveal a winding number that predicts only the edge state on the finite side of the chain survives the semi-infinite extension. Then, after coupling the quantum emitter to this end of the chain, we analyze the modified emitter spectrum and reveal the existence of bound states in three parameter regions. Two of these represent the usual strong-coupling bound states, while the third gives the weak-coupling bound states with eigenvalue appearing in the SSH band gap and which exhibit partial sublattice localization. We demonstrate that oscillations between the weak-coupling bound states can be used to transfer the particle from the emitter into the lattice in a predictable and reversible manner.

quant-ph↗

arXiv2024

Manipulating quasi-bound states in a photonic crystal with periodic impurities to store quantum information

We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It turns out that when there are more impurities in our designed system then there exists a wider range of wavenumber where particles become essentially trapped. A perturbative-based explanation is shown to verify this phenomenon quantitatively. Due to this window of wavenumbers quantum information could be encoded in our system by constructing differently shaped wave packets that are bound by the tuning of parameters in our system.

quant-ph↗

arXiv2023

Wave function propagation in a two-dimensional paramagnetic semiconductor from an impurity

We simulated modifications to a model of a two-dimensional paramagnetic semiconductor called the half-BHZ model, also known as the QWZ model, and simulated a modified full BHZ model, where a time reversal pair is introduced. Our modifications to the models include adding single and multiple impurities connected to the lattices or as a connection between the time-reversal pairs. We employed the Julia programming language to show how to speed up calculations for time evolutions. By simulating the time evolutions, we could observe the differences in the effects of these modifications. Our simulations showed the presence of scattering behavior associated with the infinite QWZ model topological states. Moreover, we observed scattering and absorption behavior related to the parameters and placements of impurities and Hamiltonian imaginary component's symmetry or anti-symmetry. These tools and early results lay the foundations for developing electronic devices that use the models' unique scattering and absorption behaviors and explore more complex and physically accurate modifications to the models.

cond-mat.mes-hall↗

arXiv2021

Characteristic influence of exceptional points in quantum dynamics

We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open quantum systems, which are described by an outwardly Hermitian Hamiltonian that gives rise to a non-Hermitian effective description after one projects out the environmental component of the system. We classify the exceptional points into two categories: those at which two or more resonance states coalesce and those at which at least one resonance and the partnering anti-resonance coalesce (possibly including virtual states as well), and we introduce several simple models to explore the dynamics for both of these types. In the latter case of coalescing resonance and anti-resonance states, we show that the presence of the continuum threshold plays a strong role in shaping the dynamics, in addition to the exceptional point itself. We also briefly discuss the special case in which the exceptional point appears directly at the threshold.

quant-ph↗

arXiv2021

Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems

For a system consisting of a quantum emitter coupled near threshold (band edge) to a one-dimensional continuum with a van Hove singularity in the density of states, we demonstrate general conditions such that a characteristic triple level convergence occurs directly on the threshold as the coupling $g$ is shut off. For small $g$ values the eigenvalue and norm of each of these states can be expanded in a Puiseux expansion in terms of powers of $g^{2/3}$, which suggests the influence of a third-order exceptional point. However, in the actual $g \rightarrow 0$ limit, only two discrete states in fact coalesce as the system can be reduced to a $2 \times 2$ Jordan block; the third state instead merges with the continuum. Moreover, the decay width of the resonance state involved in this convergence is significantly enhanced compared to the usual Fermi golden rule, which is consistent with the Purcell effect. However, non-Markovian dynamics due to the branch-point effect are also enhanced near the threshold. Applying a perturbative analysis in terms of the Puiseux expansion that takes into account the threshold influence, we show that the combination of these effects results in quantum emitter decay of the unusual form $1 - C t^{3/2}$ on the key timescale during which most of the decay occurs. We then present two conditions that must be satisfied at the threshold for the anomalous exceptional point to occur: the density of states must contain an inverse square-root divergence and the potential must be non-singular. We further show that when the energy of the quantum emitter is detuned from threshold, the anomalous exceptional point splits into three ordinary exceptional points, two of which appear in the complex-extended parameter space. These results provide deeper insight into a well-known problem in spontaneous decay at a photonic band edge.

quant-ph↗

arXiv2020

Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in a doped polyacetylene

Spin-dependent charge transfer decay in an alkali atom doped polyacetylene is studied in terms of the complex spectral analysis, revealing the single-spin Zeeman splitting influenced by the spin-orbit interaction. Nonhermitian effective Hamiltonian has been derived from the total system hermitian Hamiltonian using Brillouin-Wigner-Feshbach projection method, where the microscopic spin-dependent dissipation effect is correctly incorporated in the energy-dependent self-energy. Since the present method maintains the dynamical and chiral symmetries of the total system, we discovered two types of exceptional point (EP) singularities in a unified perspective: the EP surface and EP ring are attributed to the dynamical and chiral symmetry breaking, respectively. We have revealed that the coherent single-spin electron resonance (SSESR) spectrum reflects the complex eigenenergy spectrum of the system. We have formulated the SSESR spectrum in terms of the nonlinear response function in the Liouville-space pathway approach, where we have constructed the Liouville space basis using the complex eigenstates of the total Hamiltonian. We have calculated the one- and two-dimensional Fourier transform SSESR (1DFT and 2DFT) spectra reflecting the spin-relaxation dynamics at the donor site. While the 1DFT SSESR spectrum reflects the complex eigenenergy spectrum, the 2DFT gives detailed information on the quantum coherence in the spin-relaxation dynamics as a cross-correlation between the two frequencies. We found a giant response of the coherent SSESR around the EP ring singularity due to the vanishing normalization factors at the EP ring and the resonance effect. We have discovered that the giant response is much larger in magnitudes in the 2DFT spectrum than in the 1DFT spectrum, which promises the 2DFT SSESR a useful tool to observe the single-spin response in a molecule.

physics.optics↗

arXiv2019

Resonant-State Expansion of the Fano Peak in Open Quantum Systems

We describe the Fano asymmetry by expanding the transmission amplitude with respect to states with point spectra (discrete eigenstates), including not only bound states but also resonant states with complex eigenvalues. We first introduce a novel complete set that spans the Hilbert space of the central part of an open quantum-dot system. This complete set contains all states of point spectra, but does not contain any states of continuous spectra. We thereby analytically expand the conductance of the dot in terms of all discrete states without any background integrals. This expansion implies that the resonant states produce the main contributions to the electron transmission. We then explain the Fano peak as an interference effect involving resonant states. We find that there are three types of Fano asymmetry according to their origins: the interference between a resonant state and an anti-resonant state, that between a resonant state and a bound state, and that between two resonant states. We derive microscopic expressions of the Fano parameters that describe the three types of Fano asymmetry. We show that the last two types display the asymmetric energy dependence given by Fano, but the first one shows a slightly different form.

cond-mat.mes-hall↗

arXiv2019

Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems

It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called "unphysical," they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for $t>0$; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamics ending at a time-reversal symmetric final state is dominated by the anti-resonant states for $t<0$.

quant-ph↗

arXiv2019

Non-Markovian dynamics revealed at the bound state in continuum

We propose a methodical approach to controlling and enhancing deviations from exponential decay in quantum and optical systems by exploiting recent progress surrounding another subtle effect: the bound states in continuum, which have been observed in optical waveguide array experiments within this past decade. Specifically, we show that by populating an initial state orthogonal to that of the bound state in continuum, it is possible to engineer system parameters for which the usual exponential decay process is suppressed in favor of inverse power law dynamics and coherent effects that typically would be extremely difficult to detect in experiment. We demonstrate our method using a model based on an optical waveguide array experiment, and further show that the method is robust even in the face of significant detuning from the precise location of the bound state in continuum.

quant-ph↗

arXiv2017

The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry

Open quantum systems are often represented by non-Hermitian effective Hamiltonians that have complex eigenvalues associated with resonances. In previous work we showed that the evolution of tight-binding open systems can be represented by an explicitly time-reversal symmetric expansion involving all the discrete eigenstates of the effective Hamiltonian. These eigenstates include complex-conjugate pairs of resonant and anti-resonant states. An initially time-reversal-symmetric state contains equal contributions from the resonant and anti-resonant states. Here we show that as the state evolves in time, the symmetry between the resonant and anti-resonant states is automatically broken, with resonant states becoming dominant for $t>0$ and anti-resonant states becoming dominant for $t<0$. Further, we show that there is a time-scale for this symmetry-breaking, which we associate with the "Zeno time." We also compare the time-reversal symmetric expansion with an asymmetric expansion used previously by several researchers. We show how the present time-reversal symmetric expansion bypasses the non-Hilbert nature of the resonant and anti-resonant states, which previously introduced exponential divergences into the asymmetric expansion.

quant-ph↗

arXiv2017

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

It has been reported in the literature that the survival probability $P(t)$ near an exceptional point where two eigenstates coalesce should generally exhibit an evolution $P(t) \sim t^2 e^{-Γt}$, in which $Γ$ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz, et al, Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify the survival probability exhibits the previously reported modified exponential decay on intermediate timescales, but this is replaced with an inverse power law on very long timescales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all timescales and the heuristic approach fails completely. When the EP2A appears very near the threshold we obtain the novel evolution $P(t) \sim 1 - C_1 \sqrt{t} + D_1 t$ on intermediate timescales, while further away the parabolic decay (Zeno dynamics) on short timescales is enhanced. We also discuss the parametric encirclement of the EP2A in an appendix.

quant-ph↗

arXiv2017

Impurity-directed Transport within a Finite Disordered Lattice

We consider a finite, disordered 1D quantum lattice with a side-attached impurity. We study theoretically the transport of a single electron from the impurity into the lattice, at zero temperature. The transport is dominated by Anderson localization and, in general, the electron motion has a random character due to the lattice disorder. However, we show that by adjusting the impurity energy the electron can attain quasi-periodic motions, oscillating between the impurity and a small region of the lattice. This region corresponds to the center of a localized state in the lattice with an energy matched by that of the impurity. By precisely tuning the impurity energy, the electron can be set to oscillate between the impurity and a region far from the impurity, even distances larger than the Anderson localization length. The electron oscillations result from the interference of hybridized states, which have some resemblance to Pendry's necklace states [J. B. Pendry, J. Phys. C: Solid State Phys. 20, 733-742 (1987)]. The dependence of the electron motion on the impurity energy gives a potential mechanism for selectively routing an electron towards different regions of a 1D disordered lattice.

cond-mat.mes-hall↗

arXiv2015

Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula

We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads asymmetrically. We exactly construct many-electron scattering eigenstates for the two-lead system, where two-body bound states appear as a consequence of one-body resonances and the Coulomb interactions. By using an extension of the Landauer formula, we calculate the average electric current for the system under bias voltages in the first order of the interaction parameters. Through a renormalization-group technique, we arrive at the universal electric current, where we observe the suppression of the electric current for large bias voltages, i.e., negative differential conductance. We find that the suppressed electric current is restored by the asymmetry of the system parameters.

cond-mat.mes-hall↗

arXiv2014

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green's function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schroedinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly the exponential decays due to the resonance poles.

quant-ph↗

arXiv2013

Tunable Bound States in Continuum by Optical Frequency

We demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities induced by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.

quant-ph↗

arXiv2011

The quantum Bernoulli map

The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of decaying eigenfunctions. We introduce the quantum version of the Bernoulli map. We define it as a projection of the quantum baker map. We construct a quantum analogue of the generalized spectral representation, yielding quantum decaying states represented by density matrices. The quantum decaying states develop a quasi-fractal shape limited by the quantum uncertainty.

quant-ph↗