arXiv subjects

Jorge G. Hirsch

Publications and source records attributed to Jorge G. Hirsch.

At least 37 records · Page 2Linked to original sources

arXiv2022

Identification of quantum scars via phase-space localization measures

There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the $α$-moments of the Husimi function and is known as the Rényi occupation of order $α$. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the Rényi occupations with $α>1$ are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments ($α>1$) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.

quant-ph↗

arXiv2021

Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).

quant-ph↗

arXiv2021

The violation of Bell-CHSH inequalities leads to different conclusions depending on the description used

Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained assuming that the hidden variables do not exist at all, or that they exist but their values cannot be simultaneously assigned, or that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program.

quant-ph↗

arXiv2021

Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

quant-ph↗

arXiv2021

Quantum scarring in a spin-boson system: fundamental families of periodic orbits

As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom-photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

cond-mat.stat-mech↗

arXiv2021

Ubiquitous quantum scarring does not prevent ergodicity

In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite of that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.

cond-mat.stat-mech↗

arXiv2020

Influence of pairing and deformation on charge exchange transitions

We describe the importance of charge-exchange reactions, and in particular Gamow-Teller transitions, in astrophysical processes and double beta decay, and in understanding of nuclear structure. We first provide an overview of the central role played by the isovector pairing and the quadrupole-quadrupole channels in the description of energy spectra and in the manifestation of collective modes, some associated with deformation of the nuclear shape. We then turned our focus to Gamow-Teller (GT) transitions in relatively light nuclei, especially in the 2p1f shell, where isoscalar pairing may be playing a role in competition with the isovector pairing that dominates in heavier regions. Following a summary of the progress made in recent years on this subject, we report a systematic shell model study aimed at providing further clarification as to how these pairing modes compete. In this study, we use a schematic Hamiltonian that contains a quadrupole-quadrupole interaction as well as both isoscalar and isovector pairing interactions. We first find an optimal set of Hamiltonian parameters for the model, to provide a starting point from which to vary the relevant pairing strengths and thus assess how this impacts the behavior of GT transitions and the corresponding energy spectra and rotational properties of the various nuclei involved in the decays. The analysis includes as an important theme a comparison with experimental data. The need to suppress the isoscalar pairing mode when treating nuclei with a neutron excess to avoid producing spurious results for the ground state spin and parity with the simplified Hamiltonian is highlighted. Varying the strength parameters for the two pairing modes is found to exhibit different but systematic effects on GT transition properties and on the corresponding energy spectra, which are detailed. (abridged)

nucl-th↗

arXiv2020

Quantum chaos in a system with high degree of symmetries

We study dynamical signatures of quantum chaos in one of the most relevant models in many-body quantum mechanics, the Bose-Hubbard model, whose high degree of symmetries yields a large number of invariant subspaces and degenerate energy levels. While the standard procedure to reveal signatures of quantum chaos requires classifying the energy levels according to their symmetries, we show that this classification is not necessary to obtain manifestation of spectral correlations in the temporal evolution of the survival probability. Our findings exhibit the survival probability as a powerful tool to detect the presence of quantum chaos, avoiding the experimental and theoretical challenges associated with the determination of a complete set of energy eigenstates and their symmetry classification.

quant-ph↗

arXiv2020

Experimental realization of the classical Dicke model

We report the experimental implementation of the Dicke model in the semiclassical approximation, which describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is managed by making use of two non-linearly coupled active, synthetic LC circuits, implemented by means of analog electrical components. The simplicity and versatility of our platform allows us not only to experimentally explore the coexistence of regular and chaotic trajectories in the Dicke model but also to directly observe the so-called ground-state and excited-state ``quantum'' phase transitions. In this analysis, the trajectories in phase space, Lyapunov exponents and the recently introduced Out-of-Time-Order-Correlator (OTOC) are used to identify the different operating regimes of our electronic device. Exhaustive numerical simulations are performed to show the quantitative and qualitative agreement between theory and experiment.

quant-ph↗

arXiv2020

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

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.

cond-mat.stat-mech↗

arXiv2019

Influence of isoscalar and isovector pairing on Gamow-Teller transitions for nuclei in the 2p1f shell: A schematic shell model study

We perform a systematic study of Gamow-Teller (GT) transitions in the 2p1f shell, using the nuclear shell model with two schematic Hamiltonians. The use of the shell model provides flexibility to analyze the role of different proton-neutron pairing modes in the presence of nuclear deformation. The schematic Hamiltonians that are used contain a quadrupole-quadrupole interaction as well as isoscalar (T=0) and isovector (T=1) pairing interactions, but differ in the single particle energies. The objective of the work is to observe the behavior of GT transitions in different isoscalar and isovector pairing scenarios, together with the corresponding energy spectra and rotational properties of the parent and daughter nuclei (42Ca -> 42Sc, 44Ca -> 44Sc, 46Ti -> 46V, 48Ti -> 48V). We also treat the rotational properties of 44Ti and 48Cr. All results are compared with experimental data. The results obtained from our models depend on the different scenarios that arise, whether for N = Z or N neq Z nuclei. In the latter case, the presence of an attractive isoscalar pairing interaction imposes a 1+ ground state in odd-odd nuclei, contrary to observations for some of the nuclei considered, and it is necessary to suppress that pairing mode when considering such nuclei. The effect of varying the strength parameters for the two pairing modes is found to exhibit different but systematic effects on energy spectra and on GT transition properties.

nucl-th↗

arXiv2019

Algorithmic measurement procedures

Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we draw some limitations for measurement procedures: procedures that verify if a quantity is measured cannot work in every case.

cs.OH↗

arXiv2019

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

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.

cond-mat.stat-mech↗

arXiv2019

Analytical description of the survival probability of coherent states in regular regimes

Using coherent states as initial states, we investigate the quantum dynamics of the Lipkin-Meshkov-Glick (LMG) and Dicke models in the semi-classical limit. They are representative models of bounded systems with one- and two-degrees of freedom, respectively. The first model is integrable, while the second one has both regular and chaotic regimes. Our analysis is based on the survival probability. Within the regular regime, the energy distribution of the initial coherent states consists of quasi-harmonic sub-sequences of energies with Gaussian weights. This allows for the derivation of analytical expressions that accurately describe the entire evolution of the survival probability, from $t=0$ to the saturation of the dynamics. The evolution shows decaying oscillations with a rate that depends on the anharmonicity of the spectrum and, in the case of the Dicke model, on interference terms coming from the simultaneous excitation of its two-degrees of freedom. As we move away from the regular regime, the complexity of the survival probability is shown to be closely connected with the properties of the corresponding classical phase space. Our approach has broad applicability, since its central assumptions are not particular of the studied models.

quant-ph↗

arXiv2018

Testing Randomness in Quantum Mechanics

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.

quant-ph↗

arXiv2017

Improving randomness characterization through Bayesian model selection

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We have applied our method to an experimental device based on the process of spontaneous parametric downconversion, implemented in our laboratory, to confirm that it behaves as a genuine quantum random number generator (QRNG). As our approach relies on Bayesian inference, which entails model generalizability, our scheme transcends individual sequence analysis, leading to a characterization of the source of the random sequences itself.

physics.data-an↗

arXiv2017

$^{35,37,39}$S isotopes in $sd-pf$ space : Shell-model interpretation

The structure of $^{35,37,39}$S isotopes is described by performing comprehensive shell model calculations with SDPF-U and SDPFMW interactions. Protons and neutrons are restricted to the $sd$-shell for $N < 20$, neutrons start to fill the $pf$-shell for $N > 20$. Natural parity states are described by only in-shell mixing, unnatural parity states with 1p-1h inter-shell neutron excitations. With SDPF-U interaction, reported are the results for natural parity states only because this interaction is not suitable for cross shell excitations. Calculated energy levels, electromagnetic properties and spectroscopic factors are in good agreement with the recently available experimental data.

nucl-th↗

arXiv2016

Systematic afterpulsing-estimation algorithms for gated avalanche photodiodes

We present a method designed to efficiently extract optical signals from InGaAs avalanche photodiodes (APDs) operated in gated mode. In particular, our method permits an estimation of the fraction of counts which actually results from the signal being measured, as opposed to being produced by noise mechanisms, specifically by afterpulsing. Our method in principle allows the use of InGaAs APDs at high detection efficiencies, with the full operation bandwidth, either with or without resorting to the application of a dead time. As we show below, our method can be used in configurations where afterpulsing exceeds the genuine signal by orders of magnitude, even near saturation. The algorithms which we have developed are suitable to be used either in real-time processing of raw detection probabilities or in post-processing applications, after a calibration step has been performed. The algorithms which we propose here can complement technologies designed for the reduction of afterpulsing.

physics.ins-det↗