arXiv subjects

D. Szilard

Publications and source records attributed to D. Szilard.

10 recordsLinked to original sources

arXiv2025

Quantum Rabi oscillations in the semiclassical limit: backreaction on the cavity field and entanglement

The goal of this chapter is to compare the predictions of the semiclassical Rabi model (SRM), which describes the interaction between a two-level system (qubit) and a classical monochromatic wave, and the quantum Rabi model (QRM), under the assumption that the cavity field is initiated in a coherent state with a large average number of photons, ranging from 5K to 40K. First, we show that for a strong atom-field coupling, when the duration of the $π$-pulse (the time interval required to completely excite or deexcite the qubit in the resonant regime) is below $100ω^{-1}$, the behaviour of the atomic excitation probability deviates significantly from the textbook sinusoidal formula derived for the SRM under the rotating-wave approximation, and we present simple analytical and semi-analytical methods to describe more accurately the dynamics. Then we show that the QRM reproduces the qubit's dynamics predicted by the SRM only for initial times, since in the QRM the qubit excitation probability exhibits a collapse behaviour even in the lossless scenario; we also notice that the qualitative behaviour of such collapses is different from the ones occurring in the dissipative SRM. In the rest of this work we study numerically the backreaction of the qubit on the cavity field and the resulting atom--field entanglement, which are disregarded in the SRM. It is shown that the atom-field entanglement increases over time and a maximally entangled state is attained for large times. Moreover, we illustrate how the Rabi oscillations continuously modify the quantum state of the cavity field, which becomes increasingly different from the original coherent state as the time increases.

quant-ph↗

arXiv2021

Probing topological phase transitions via quantum reflection in the graphene family materials

We theoretically investigate the quantum reflection of different atoms by two-dimensional (2D) materials of the graphene family (silicene, germanene, and stanene), subjected to an external electric field and circularly polarized light. By using Lifshitz theory to compute the Casimir-Polder potential, which ensures that our predictions apply to all regimes of atom-2D surface distances, we demonstrate that the quantum reflection probability exhibits distinctive, unambiguous signatures of topological phase transitions that occur in 2D materials. We also show that the quantum reflection probability can be highly tunable by these external agents, depending on the atom-surface combination, reaching a variation of 40% for Rubidium in the presence of a stanene sheet. Our findings attest that not only dispersive forces play a crucial role in quantum reflection, but also that the topological phase transitions of the graphene family materials can be comprehensively and efficiently probed via atom-surface interactions at the nanoscale.

cond-mat.mes-hall↗

arXiv2020

Tuning resonance energy transfer with magneto-optical properties of graphene

We investigate the resonance energy transfer (RET) rate between two quantum emitters near a suspended graphene sheet in vacuum under the influence of an external magnetic field. We perform the analysis for low and room temperatures and show that, due to the extraordinary magneto-optical response of graphene, it allows for an active control and tunability of the RET even in the case of room temperature. We also demonstrate that the RET rate is extremely sensitive to small variations of the applied magnetic field, and can be tuned up to a striking six orders of magnitude for quite realistic values of magnetic field. Moreover, we evidence the fundamental role played by the magnetoplasmon polaritons supported by the graphene monolayer as the dominant channel for the RET within a certain distance range. Our results suggest that magneto-optical media may take the manipulation of energy transfer between quantum emitters to a whole new level, and broaden even more its great spectrum of applications.

cond-mat.mes-hall↗

arXiv2020

Negative refraction in the relativistic electron gas

We show that a gas of relativistic electrons is a left-handed material at low frequencies by computing the effective electric permittivity and effective magnetic permeability that appear in Maxwell's equations in terms of the responses appearing in the constitutive relations, and showing that the former are both negative below the {\it same} frequency, which coincides with the zero-momentum frequency of longitudinal plasmons. We also show, by explicit computation, that the photonic mode of the electromagnetic radiation does not dissipate energy, confirming that it propagates in the gas with the speed of light in vacuum, and that the medium is transparent to it. We then combine those results to show that the gas has a negative effective index of refraction $n_{\rm eff}=-1$. We illustrate the consequences of this fact for Snell's law, and for the reflection and transmission coefficients of the gas.

cond-mat.quant-gas↗

arXiv2020

Efficient algebraic solution for a time-dependent quantum harmonic oscillator

Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial state. We find an iterative analytical solution given by simple recurrence relations that are very well suited for numerical calculations. We use our solution to reproduce and analyse some results from literature in order to prove the usefulness of the method and, based on these references, we discuss efficiency in squeezing, when comparing the parametric resonance modulation and the Janszky-Adam scheme.

quant-ph↗

arXiv2020

A time-dependent harmonic oscillator with two frequency jumps: an exact algebraic solution

We consider a harmonic oscillator (HO) with a time dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω_{0}, then, at t = 0, its frequency suddenly increases to ω_{1} and, after a finite time interval τ, it comes back to its original value ω_{0}. Contrary to what one could naively think, this problem is a quite non-trivial one. Using algebraic methods we obtain its exact analytical solution and show that at any time t > 0 the HO is in a squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω_{0} to ω_{1}), remaining constant after the second jump (from ω_{1} back to ω_{0}). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.

quant-ph↗

arXiv2019

Resonance energy transfer at percolation transition

We compute the resonance energy transfer (RET) in a system composed of two quantum emitters near a host dielectric matrix in which metallic inclusions are inserted until the medium undergoes a dielectric-metal transition at percolation. We show that there is no peak in the RET rate at percolation, in contrast to what happens with the spontaneous emission rate of an emitter near the same critical medium. This result suggests that RET does not strongly correlate with the local density of states.

cond-mat.mes-hall↗

arXiv2019

Quantum two-photon emission in a photonic cavity

We derive a new expression for the two-photon spontaneous emission (TPSE) rate of an excited quantum emitter in the presence of arbitrary bodies in its vicinities. After investigating the influence of a perfectly conducting plate on the TPSE spectral distribution (Purcell effect), we demonstrate the equivalence of our expression with the more usual formula written in terms of the corresponding dyadic Green's function. We establish a general and convenient relation between the TPSE spectral distribution and the corresponding Purcell factors of the system. Next, we consider an emitter close to a dielectric medium and show that, in the near field regime, the TPSE spectral distribution is substantially enhanced and changes abruptly at the resonance frequencies. Finally, motivated by the suppression that may occur in the one-photon spontaneous emission of an excited atom between two parallel conducting plates, we discuss the TPSE for this same situation and show that complete suppression can never occur for $s \rightarrow s$ transitions.

physics.optics↗

arXiv2017

Characterizing critical exponents via Purcell effect

We investigate the role of phase transitions into the spontaneous emission rate of quantum emitters embedded in a critical medium. Using a Landau-Ginzburg approach, we find that, in the broken symmetry phase, the emission rate is reduced or even suppressed due to the photon mass generated by the Higgs mechanism. Moreover, we show that the spontaneous emission presents a remarkable dependence upon the critical exponents associated to a given phase transition, allowing for an optical determination of the universality class. Our findings not only demonstrate that the Purcell effect constitutes an efficient optical probe of distinct critical phenomena, but they also unveil that a more general connection between phase transitions and spontaneous emission exist, as previous experimental and numerical evidences suggest.

quant-ph↗

arXiv2016

Purcell effect at metal-insulator transitions

We investigate the spontaneous emission rate of a two-level quantum emitter next to a composite medium made of randomly distributed metallic inclusions embedded in a dielectric host matrix. In the near-field, the Purcell factor can be enhanced by two-orders of magnitude relative to the case of an homogeneous metallic medium, and reaches its maximum precisely at the insulator-metal transition. By unveiling the role of the decay pathways on the emitter's lifetime, we demonstrate that, close to the percolation threshold, the radiation emission process is dictated by electromagnetic absorption in the heterogeneous medium. We show that our findings are robust against change in material properties, shape of inclusions, and apply for different effective medium theories as well as for a wide range of transition frequencies.

cond-mat.mes-hall↗