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arXiv:2103.11232 · Physical Review A

Beyond the Rabi model: Light interactions with polar atomic systems in a cavity

Giovanni Scala, Karolina Słowik, Paolo Facchi A, Saverio Pascazio, Francesco Vincenzo Pepe

Published Jul 27, 2021• 14 citations
arXivHTMLPDF

Abstract

The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.

DOI
10.1103/physreva.104.013722

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•Oct 28, 2026•0 citations
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.
A dressed-state perturbation theory beyond the rotating waveapproxi-mation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. The validity of these explicit results is discussed by comparing with the direct numerical simulation. Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED. In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.
A dressed-state perturbation theory beyond the rotating wave approximation(RWA) is presented to investigate the interaction between a two-level electronic transition of polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments(PDM) and the counter-rotating wave term(CRT) can be shown separately.The validity of these explicit results is discussed by comparison with the direct numerical simulation. Compared to the CRT coupling, PDM results in the coupling of more dressed states and the energy shift is proportional to the square of the normalized permanent dipole difference, and a greater Bloch–Siegert shift can be produced in the giant dipole molecule cavity QED. In addition, our method can also be extended to the solution of the two-level atom Rabi model Hamiltonian beyond the RWA.更多还原
A dressed-state perturbation theory beyond the rotating wave approximation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field.Analytical expressions can be explicitly derived for both the ground-and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately.The validity of these explicit results is discussed by comparing with the direct numerical simulation.Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED.In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
We address topics related to molecules coupled to quantum radiation. The formalism of light-matter interaction is different for classical and quantum fields, but some analogies remain, such as the formation of light induced crossings. We show that under particular circumstances, the molecular dynamics under quantum or classical fields produce similar results, as long as the radiation is prepared as a Fock state and far from ultra-strong coupling regimes. At this point, the choice of specific initial Fock states is irrelevant since the dynamics scales. However, in realistic multistate molecular systems, radiative scaling may fail due to the presence of simultaneous efficient non-radiative couplings in the dynamics. Polar molecules have permanent dipoles, and within the context of the full quantum Rabi model with a Pauli-Fierz Hamiltonian, they play a crucial role in the polaritonic dynamics since both permanent dipole moments and self-energy terms produce drastic changes on the undressed potential energy surfaces at high coupling strengths. We also gauge the effect of including rotational degrees of freedom in cavity molecular photodynamics. For diatomic molecules, the addition of rotation amounts to transform (both with classical or quantum fields) a light induced crossing into a light induced conical intersection. However, we show that conical intersections due to molecular rotation do not represent the standard properties of well-known efficient intrinsic conical intersections inasmuch they do not enhance the quantum transition rates.
We investigate a controlled beyond-electric-dipole extension of the quantum Rabi model in which the leading electric-dipole interaction is supplemented by an electric-quadrupole contribution. A central issue is the parity selection rule: for two exact atomic parity eigenstates of opposite parity, an electric-quadrupole transition matrix element vanishes. We therefore do not interpret the additional longitudinal coupling as an E2 transition between an opposite-parity pair. Instead, we consider an inversion-asymmetric (or parity-mixed) two-level system for which the two retained states may have different diagonal quadrupole moments. Projection of the multipolar interaction then produces a state-dependent term proportional to σz(a + a†), while the ordinary transition dipole produces the transverse term proportional to σx(a + a†). A state-independent quadrupolar contribution is removed by a bosonic displacement, leaving the effective Hamiltonian H =ωa†a+∆σz/2+gσx(a+a†)+gQσz(a+a†). This construction connects the beyond-dipole physical problem to the well-studied class of Rabi models with simultaneous transverse and longitudinal coupling, including asymmetric or biased Rabi models. We make this relation explicit by a constant spin rotation, which maps the model to a biased Rabi Hamiltonian with effective coupling κ = √g2 +g2Q and bias δ = ∆gQ/(2κ). We then derive the corresponding second-order Bargmann differential equation and solve its exceptional polynomial sector using a Zhang-type functional Bethe ansatz. The resulting Bethe equations, root-sum constraint, exceptional energy branches, and the first nontrivial parameter condition are obtained explicitly. In the limit gQ → 0, the construction continuously recovers the ordinary Rabi exceptional sector. From an experimental perspective, the connection with demonstrated quadrupolar light--matter coupling in engineered quantum systems suggests that the present framework may have relevance for spectroscopic studies of beyond-electric-dipole interactions, although a direct experimental realization of the specific effective model considered here remains to be established [20].