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Results in Physics

Double dressing by both the number of atoms and the number of photons inside cavity

Gennady A. Koganov, R. Shuker

Published Apr 22, 2023• 1 citation
Publisher

Abstract

We study a system of N two-level atoms interacting with a coherent field a resonant cavity in a self-consistent manner. No direct correlation between the atoms, such as induced by dipole–dipole interaction, is included. Initially all atoms are not exited, and there are n0 photons in the cavity. We show that the system reveals collective-like behavior, which stems from mutual influence of the atoms and coherent field in the cavity. In distinction from conventional dressing of atomic states by strong electromagnetic field, the system of N two-level atoms in a resonant cavity is actually dressed by both the number of photons and the number of atoms N. This double dressing results in both N and n0-dependent oscillation frequency, ω(n0,N). At N>>n0 the spectral density contains, apart from the main peak at the collective atomic frequency gN, additional features at odd sub-harmonics. There is interference signature at the double dressing spectrum which has half-peaks and half-dips that is a synchronization among the frequencies of photon and the atomic dressings. It is a beautiful manifestation of quantum interference in the present novel double dressing by the number n of photons and by the number N of atoms.

DOI
10.1016/j.rinp.2023.106447

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Nanosystems Physics Chemistry Mathematics•Oct 27, 2017•1 citation
We study a system of N two-level atoms interacting with a coherent field a resonant cavity in a self-consistent manner. No direct correlation between the atoms, such as induced by dipole–dipole interaction, is included. Initially all atoms are not exited, and there are n0 photons in the cavity. We show that the system reveals collective-like behavior, which stems from mutual influence of the atoms and coherent field in the cavity. In distinction from conventional dressing of atomic states by strong electromagnetic field, the system of N two-level atoms in a resonant cavity is actually dressed by both the number of photons and the number of atoms N. This double dressing results in both N and n0-dependent oscillation frequency, ω(n0,N). At N>>n0 the spectral density contains, apart from the main peak at the collective atomic frequency gN, additional features at odd sub-harmonics. There is interference signature at the double dressing spectrum which has half-peaks and half-dips that is a synchronization among the frequencies of photon and the atomic dressings. It is a beautiful manifestation of quantum interference in the present novel double dressing by the number n of photons and by the number N of atoms.
The excitation spectrum arising from photon density-density correlations has been considered in a system of two interacting identical atoms. The two-level atoms are pumped near resonance by a strong electromagnetic field while they interact through their dipole-dipole interaction and radiate to each other as well. In such a system the photon density-density correlations arise from the interference spectrum due to the beating of the frequency of the pump field and the atomic transition frequency, as well as from the spectrum induced by the dipole-dipole and radiative interactions between the atoms. The spectral function of this system has been calculated in the limit of high photon densities. It consists of four terms describing four bands which are similar to those appearing in the two-atom resonance fluorescence spectrum for the symmetric modes when the central peak is missing. The collective behavior as well as the dynamics of the system are discussed in detail. By using the spectral function, an expression for the photon density-density correlation function at different times has been derived where thermal effects have been also included.
The damped and coherently-driven JaynesndashndashndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.
We consider the effect of quantum interference on population distribution and photon statistics of a cavity field interacting with dressed states of a strongly driven three-level atom. We analyse three coupling configurations of the cavity field to the driven atom, with the cavity frequency tuned to the outer Rabi sideband, the inner Rabi sideband and the central frequency of the 'singly dressed' three-level atom. The quantum doubly dressed states for each configuration are identified and the population distribution and photon statistics are interpreted in terms of transitions among these dressed states and their populations. We find that the population distribution depends strongly on quantum interference and the cavity damping. For the cavity field tuned to the outer or inner Rabi sidebands the cavity damping induces transitions between the dressed states which are forbidden for the ordinary spontaneous emission. Moreover, we find that in the case of the cavity field coupled to the inner Rabi sideband the population distribution is almost Poissonian with a large average number of photons that can be controlled by quantum interference. This system can be considered as a one-atom dressed-state laser with controlled intensity.
Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.
Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
The spectral properties of a photon spontaneously emitted by a material two-level system, modelling an atom or ion, in a parabolic cavity are investigated.In particular, we concentrate on the special case of a motionless two-level system positioned exactly at the focus of a parabolic cavity with a dipole moment oriented along the symmetry axis of this cavity.Treating the corresponding atom-field coupling in the dipoleand rotating wave approximation, it is demonstrated that inside the parabolic cavity the position and frequency dependence of the spectrum of the spontaneously emitted photon exhibits interesting interference patterns.These patterns are explored in detail with the help of a photon path representation of the first-order electric field correlation function.In the radiation, zone the spatial behavior of the spectrum reveals strong interference in particular at distances from the two-level system of the order of the focal length of the parabola.With increasing distances, these interference patterns decay except for an undepleted component surrounding the symmetry axis at an almost constant radius.Furthermore, the maximum of the frequency dependence of the spectrum exhibits a position-dependent frequency shift with respect to the atomic resonance frequency.