Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The superradiance-superabsorption interplay and a PT-symmetric harmonic oscillator with complex frequency

Rodrigo de Abreu Dourado

Published Jul 14, 2021• 0 citations
Publisher

Abstract

A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay.We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity.The mean-field approximation was used in both cases.In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method.In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically.We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model.For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss.These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser.At last, we study non-Hermitian PT -symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications.We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations.The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.

DOI
10.11606/d.76.2021.tde-09092021-120346

Related papers

Coherent many-body Rabi oscillations via superradiance and superabsorption and the mean-field approach for a superradiant laser

Rodrigo A. Dourado, M. H. Y. Moussa

The experimental success achieved in recent decades in the coherent manipulation of several Rabi cycles has led to a new stage in the physics of radiation-matter interaction. Motivated by this perspective, we propose here the engineering of coherent many-body Rabi oscillations (CMBROs) induced from the interactions of a moderately dense atomic sample with the environment and a high-finesse cavity mode. The CMBRO follows from the interplay between superradiance and superabsorption: the collective decay and absorption of the atomic sample inside the cavity. The equations we have derived for this interplay, based on the mean-field approximation, describe a two-level superradiant laser in an appropriate parameter regime, and its properties are also discussed. The control of quantum coherence according to the method presented here can be adapted to the implementation of quantum information processes as well as for the investigation of the fundamentals of quantum mechanics.

Physical Review A•Aug 17, 2021•11 citations

Deflection of mesoscopic atomic superpositions via superradiance and superabsorption

Leandro Manoel Rocha da Rocha

In this work we will deal with the effects of a coherent electromagnetic field acting on an atomic dipole gas confined to a cavity.It is known from ( 5) that in such conditions, if we a have moderately dense sample of N 2-level atoms, we can observe the presence of superradiance, i.e., the enhanced emission of a coherent pulse of intensity proportional to N 2 and, in a smaller scale, the enhanced absorption as well ( 14).When coupling this sample to a quantum electromagnetic field via Tavis-Cummings interaction we are able to enhance even more the superabsorption as well as the superemission to a lesser degree in such a way as to almost equate the intensities of both processes and give rise to interleaved oscillations between them in both field and sample resulting in the phenomenon of many-body Rabi oscillations described in (1).However, it is to expect that, due to momentum conservation, such a phenomenon would cause a deflection on the atoms of the sample in a small time interval, after which we would have a mesoscopic superposition containing all the information related to the prior state.Our main goal is the study of the deflection suffered by the atoms of such a sample and how it relates to the state before the emission.We solve the time-dependent non-linear Hamiltonian related to the superradiant emission/superabsorption via the Lewis-Riesenfeld invariant method.At the end we will show how the macroscopic states were prepared to obtain our results.

•Jan 25, 2024•0 citations

Manipulação do pulso superradiante via interações atômicas

Paulo Hisao Moriya

The superradiant phenomena is characterized by atomic dipoles ordering process in excited samples moderately denses, that occours due to the atomic induced correlations developed not directly but by the coherent radiation emitted by atoms themselves.The superradiant process evolves from a total disorder at t = 0, attain a maximum order in a time τ ∝ N -1 creating a radiation pulse whose intensity follows the sech 2 law and its peak is proportional to N 2 , thereafter the dipoles relax to a disordered equilibrium state.In this essay, we deal with the interaction between two cavity modes ω a and ω b and a classical pump with a system of N two-level atoms, whose atomic transition frequencies ω 0 .We consider a resonant interaction between atoms and mode ω a and a dispersive coupling of atoms with mode ω b , which couple the atomic sample, and the classical pump.In order to obtain how sech 2 law changes, we use the method of nonlinear small rotations to obtain effective Hamiltonian, expliciting dipolar interaction between atoms.Finally, after write the effective master equation, we use the mean-field approximation and Lewis and Riesenfeld method to obtain the mean features of this phenomena to our system.

•Feb 28, 2012•0 citations

Non-Hermitian Hamiltonian for a modulated Jaynes-Cummings model with PT symmetry

Fabio Bagarello, Margherita Lattuca, Roberto Passante +2 more

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n$-excitation subspace obey the same equations of motion that can be obtained from a static non-Hermitian Jaynes-Cummings Hamiltonian with $\mathcal{PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudobosons and pseudofermions, and discuss relevant mathematical and physical aspects.

arXiv:1503.01675•Physical Review A•Apr 30, 2015•35 citations

From Superradiance to Superabsorption: An Exact Treatment of Non-Markovian Cooperative Radiation

Ignacio González, Ángel Rivas

We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to $10^3$ emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.

quant-pharXiv:2601.05989•Quantum•Jan 12, 2026•0 citations

Theory of dynamical superradiance in organic materials

Lukas Freter, Piper Fowler-Wright, Javier Cuerda +3 more

We develop the theory of dynamical superradiance - the collective exchange of energy between an ensemble of initially excited emitters and a single-mode cavity - for organic materials where electronic states are coupled to vibrational modes. We consider two models to capture the vibrational effects: first, vibrations treated as a Markovian bath for two-level emitters, via a pure dephasing term in the Lindblad master equation for the system; second, vibrational modes directly included in the system via the Holstein-Tavis-Cummings Hamiltonian. By exploiting the permutation symmetry of the emitters and weak U(1) symmetry, we develop a numerical method capable of exactly solving the Tavis-Cummings model with local dissipation for up to 140 emitters. Using the exact method, we validate mean-field and second-order cumulant approximations and use them to describe macroscopic numbers of emitters. We analyze the dynamics of the average cavity photon number, electronic coherence, and Bloch vector length and show that the effect of vibrational mode coupling goes beyond simple dephasing. Our results show that superradiance is possible in the presence of vibrational mode coupling; for negative cavity detunings, the vibrational coupling may even enhance superradiance. We identify asymmetry of the photon number rise time as a function of the detuning of the cavity frequency as an experimentally accessible signature of such vibrationally assisted superradiance.

arXiv:2509.03067•Nanophotonics•Dec 1, 2025•1 citation
A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay.We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity.The mean-field approximation was used in both cases.In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method.In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically.We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model.For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss.These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser.At last, we study non-Hermitian PT -symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications.We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations.The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.
The experimental success achieved in recent decades in the coherent manipulation of several Rabi cycles has led to a new stage in the physics of radiation-matter interaction. Motivated by this perspective, we propose here the engineering of coherent many-body Rabi oscillations (CMBROs) induced from the interactions of a moderately dense atomic sample with the environment and a high-finesse cavity mode. The CMBRO follows from the interplay between superradiance and superabsorption: the collective decay and absorption of the atomic sample inside the cavity. The equations we have derived for this interplay, based on the mean-field approximation, describe a two-level superradiant laser in an appropriate parameter regime, and its properties are also discussed. The control of quantum coherence according to the method presented here can be adapted to the implementation of quantum information processes as well as for the investigation of the fundamentals of quantum mechanics.
In this work we will deal with the effects of a coherent electromagnetic field acting on an atomic dipole gas confined to a cavity.It is known from ( 5) that in such conditions, if we a have moderately dense sample of N 2-level atoms, we can observe the presence of superradiance, i.e., the enhanced emission of a coherent pulse of intensity proportional to N 2 and, in a smaller scale, the enhanced absorption as well ( 14).When coupling this sample to a quantum electromagnetic field via Tavis-Cummings interaction we are able to enhance even more the superabsorption as well as the superemission to a lesser degree in such a way as to almost equate the intensities of both processes and give rise to interleaved oscillations between them in both field and sample resulting in the phenomenon of many-body Rabi oscillations described in (1).However, it is to expect that, due to momentum conservation, such a phenomenon would cause a deflection on the atoms of the sample in a small time interval, after which we would have a mesoscopic superposition containing all the information related to the prior state.Our main goal is the study of the deflection suffered by the atoms of such a sample and how it relates to the state before the emission.We solve the time-dependent non-linear Hamiltonian related to the superradiant emission/superabsorption via the Lewis-Riesenfeld invariant method.At the end we will show how the macroscopic states were prepared to obtain our results.
The superradiant phenomena is characterized by atomic dipoles ordering process in excited samples moderately denses, that occours due to the atomic induced correlations developed not directly but by the coherent radiation emitted by atoms themselves.The superradiant process evolves from a total disorder at t = 0, attain a maximum order in a time τ ∝ N -1 creating a radiation pulse whose intensity follows the sech 2 law and its peak is proportional to N 2 , thereafter the dipoles relax to a disordered equilibrium state.In this essay, we deal with the interaction between two cavity modes ω a and ω b and a classical pump with a system of N two-level atoms, whose atomic transition frequencies ω 0 .We consider a resonant interaction between atoms and mode ω a and a dispersive coupling of atoms with mode ω b , which couple the atomic sample, and the classical pump.In order to obtain how sech 2 law changes, we use the method of nonlinear small rotations to obtain effective Hamiltonian, expliciting dipolar interaction between atoms.Finally, after write the effective master equation, we use the mean-field approximation and Lewis and Riesenfeld method to obtain the mean features of this phenomena to our system.
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic nnn-excitation subspace obey the same equations of motion that can be obtained from a static non-Hermitian Jaynes-Cummings Hamiltonian with PT\mathcal{PT}PT symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of PT\mathcal{PT}PT symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudobosons and pseudofermions, and discuss relevant mathematical and physical aspects.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
We develop the theory of dynamical superradiance - the collective exchange of energy between an ensemble of initially excited emitters and a single-mode cavity - for organic materials where electronic states are coupled to vibrational modes. We consider two models to capture the vibrational effects: first, vibrations treated as a Markovian bath for two-level emitters, via a pure dephasing term in the Lindblad master equation for the system; second, vibrational modes directly included in the system via the Holstein-Tavis-Cummings Hamiltonian. By exploiting the permutation symmetry of the emitters and weak U(1) symmetry, we develop a numerical method capable of exactly solving the Tavis-Cummings model with local dissipation for up to 140 emitters. Using the exact method, we validate mean-field and second-order cumulant approximations and use them to describe macroscopic numbers of emitters. We analyze the dynamics of the average cavity photon number, electronic coherence, and Bloch vector length and show that the effect of vibrational mode coupling goes beyond simple dephasing. Our results show that superradiance is possible in the presence of vibrational mode coupling; for negative cavity detunings, the vibrational coupling may even enhance superradiance. We identify asymmetry of the photon number rise time as a function of the detuning of the cavity frequency as an experimentally accessible signature of such vibrationally assisted superradiance.