arXiv subjects

Pablo Martinez-Azcona

Publications and source records attributed to Pablo Martinez-Azcona.

8 recordsLinked to original sources

arXiv2026

F\"orster resonance energy transfer with transient coherent effects

We formulate the weak intramolecular coupling F\"orster resonance energy transfer theory in a form suitable for calculating ultrafast nonlinear response of molecular systems. We introduce a formally exact time-dependent factorization of the molecular statistical operator into the system and bath components. Combining this factorization with unperturbed environment evolution, we generalize the traditional F\"orster master equation for the state population probabilities into a complete master equation for the system's reduced statistical operator. The traditional F\"orster theory applies in the limit where the intermolecular coupling is weak, and the system-bath coupling is strong. Our technique of derivation explicitly leads to a time non-local F\"orster type master equation, which remains valid also in the limit of vanishing system-bath coupling. The theory predicts a rapid initial coherent evolution of populations arising from a transient initial coherence-dependent term, which induces a slippage of the initial condition that persists during subsequent rate-controlled transfer. Comparison with exact numerical results confirms the clear improvement of the present generalization over earlier formulations of the F\"orster theory and delineates its range of validity.

physics.chem-ph↗

arXiv2025

Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach

Non-stabilizerness enables universality beyond Gaussian/Clifford dynamics, yet no resource theory exists for systems combining bosonic and fermionic degrees of freedom. Using the Grassmann approach of Cahill and Glauber, we develop a phase-space framework defining hybrid magic via the $L_p$ norm of a hybrid Wigner function. We demonstrate it in the Holstein polaron, where phonon-electron coupling enhances magic growth, and in the fermionic Jaynes-Cummings model, examining dependence on atomic and cavity states. At the gate level, we define the non-stabilizer power of hybrid operations and derive a closed-form result for the conditional displacement gate. This establishes a unified quantification of non-stabilizerness in realistic hybrid systems.

quant-ph↗

arXiv2025

Magic Steady State Production: Non-Hermitian, Dissipative, and Stochastic Pathways

Universal quantum computers require entanglement and non-stabilizerness, a resource known as \textit{quantum magic}. Here, we introduce a protocol that prepares magic steady states by leveraging non-Hermitian dynamics, which, contrary to unitary dynamics, can host pure-state attractors. By studying the dissipative qubit, we find the optimal parameters to prepare $|H\rangle$ and $|T\rangle$ steady states. Interestingly, this approach does not require knowledge or preparation of a particular initial state, since all the states of the Bloch sphere converge to the engineered target steady state. We also consider the addition of classical noise in the anti-hermitian part and provide the regimes for which the noisy dynamics still converges to high magic states. We also introduce a dissipative protocol to prepare magic steady states, compare the approaches with magic state cultivation and provide a particular realization of the non-Hermitian scheme in a cat qubit.

quant-ph↗

arXiv2025

Surmise for random matrices' level spacing distributions beyond nearest-neighbors

Correlations between energy levels can help distinguish whether a many-body system is of integrable or chaotic nature. The study of short-range and long-range spectral correlations generally involves quantities which are very different, unless one uses the $k$-th nearest neighbor ($k$NN) level spacing distributions. For nearest-neighbor (NN) spectral spacings, the distribution in random matrices is well captured by the Wigner surmise. This well-known approximation, derived exactly for a 2$\times$2 matrix, is simple and satisfactorily describes the NN spacings of larger matrices. There have been attempts in the literature to generalize Wigner's surmise to further away neighbors. However, as we show, the current proposal in the literature fails to accurately capture numerical data. Using the known variance of the distributions from random matrix theory, we propose a corrected surmise for the $k$NN spectral distributions. This surmise better characterizes spectral correlations while retaining the simplicity of Wigner's surmise. We test the predictions against numerical results and show that the corrected surmise is systematically more accurate at capturing data from random matrices. Using the XXZ spin chain with random on-site disorder, we illustrate how these results can be used as a refined probe of many-body quantum chaos for both short- and long-range spectral correlations.

quant-ph↗

arXiv2024

Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians

We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an `anti-dephasing' master equation. We characterize the resulting state evolution and analyze its purity. The properties of such dynamics are illustrated in a stochastic dissipative qubit. Our analytical results show that adding noise allows for a rich control of the dynamics, stabilizing the lossy state and making state purification possible to a greater variety of steady states.

quant-ph↗

arXiv2023

Decomposing the Spectral Form Factor

Correlations between the energies of a system's spectrum are one of the defining features of quantum chaos. They can be probed using the Spectral Form Factor (SFF). We investigate how each spectral distance contributes in building this two-point correlation function. Specifically, starting from the spectral distribution of $k$-th neighbor level spacing ($k$nLS), we provide analytical expressions for the $k$-th neighbor Spectral Form Factor ($k$nSFF). We do so for the three Gaussian Random Matrix ensembles and the `Poissonian' ensemble of uncorrelated energy levels. We study the properties of the $k$nSFF, namely its minimum value and the time at which this minimum is reached, as well as the energy spacing with the deepest $k$nSFF. This allows us to quantify the contribution of each individual $k$nLS to the SFF ramp, which is a characteristic feature of quantum chaos. In particular, we show how the onset of the ramp, characterized either by the dip or the Thouless time, shifts to shorter times as contributions from longer-range spectral distance are included. Interestingly, the even and odd neighbors contribute quite distinctively, the first being the most important to built the ramp. They respectively yield a resonance or antiresonance in the ramp. All of our analytical results are tested against numerical realizations of random matrices. We complete our analysis and show how the introduced tools help characterize the spectral properties of a physical many-body system by looking at the interacting XXZ Heisenberg model with local on-site disorder that allows transitioning between the chaotic and integrable regimes.

quant-ph↗

arXiv2023

Stochastic Operator Variance: an observable to diagnose noise and scrambling

Noise is ubiquitous in nature, so it is essential to characterize its effects. Considering a fluctuating Hamiltonian, we introduce an observable, the stochastic operator variance (SOV), which measures the spread of different stochastic trajectories in the space of operators. The SOV obeys an uncertainty relation and allows finding the initial state that minimizes the spread of these trajectories. We show that the dynamics of the SOV is intimately linked to that of out-of-time-order correlators (OTOCs), which define the quantum Lyapunov exponent $λ$. Our findings are illustrated analytically and numerically in a stochastic Lipkin-Meshkov-Glick (sLMG) Hamiltonian undergoing energy dephasing.

quant-ph↗

arXiv2022

Analyticity constraints bound the decay of the spectral form factor

Quantum chaos cannot develop faster than $λ\leq 2 π/(\hbar β)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $λ$ is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponent $η$, that we introduce to characterize the early-time decay of the SFF, is bounded as $η\leq π/(2\hbarβ)$. This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.

quant-ph↗