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Physical Review A

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

Published Aug 17, 2021• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.104.023708

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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.
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.
We present a protocol based on the interplay between superradiance and superabsorption to achieve the coherent deflection of an atomic sample due to the momentum transfer from the atoms to a cavity field. The coherent character of this momentum transfer, causing the atomic sample to deflect as a whole, follows from the collective nature of the atomic superradiant pulse and its superabsorption by the cavity field. The protocol is then used for the construction of positional mesoscopic atomic superpositions in cavity quantum electrodynamics.
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 study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction can promote cooperative radiative relaxation. For small number of atoms this results in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation. Above superradiance threshold increase in delay time and enhancement of superradiance is occurred. In the case of strong interaction (as compared to excitation energy of an atom) transition to the regime of multiphoton relaxation occurs, which we discuss using a simple model of two atoms in a high-Q single mode cavity. It is shown that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed as well.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.