We study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the
reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in the asymptotic Rydberg levels $n^{2}S_j$ and $n^{2}D_j$, for $n=20-80$. We predict atom-molecule binding energies in the range $10-10^3$ kHz for the first vibrational state below threshold. The average trimer formation rate is order $10^8, {rm s}^{-1}$ at 1.0 $mu$K, and depends weakly on the principal quantum number $n$. Our results set the foundations for a broader understanding of exotic long range collisions of dilute molecules in ultracold atomic Rydberg reservoirs.
Strong coupling with single molecules in plasmonic picocavities has emerged as a resource for room-temperature quantum control with nanoscale light. Tip-based nanoprobes can measure the local dynamics of individual molecular picocavities, but the ove
rhead associated with sampling an inhomogeneous picocavity distribution can be challenging for scalability. We propose a macroscopic approach in which an ensemble of molecular picocavities acts as a nonlinear plasmonic metamaterial. Using a quantum optics perspective, we study theoretical performance limits for optical cross-phase modulation in the system, taking into account realistic distributions of picocavity volumes and molecular transition frequencies. The medium nonlinearity is mediated by local strong coupling with the lowest vibronic emission sideband of individual organic chomophores. The local vacua change the refractive index of the medium at the frequency of a weak probe field $omega_p$, set to drive the bare zero-phonon absorption band. Refractive index variations $Delta n/n$ of a few percent, relative to a molecule-free scenario, are feasible with dilute ensembles. The probe phase evolution can be switched off in the presence of a signal field at a higher frequency $omega_s$, for intensities as low as 10 kW/cm$^2$. The mechanism for optical switching involves a novel ($omega_p+omega_s$) two-photon absorption channel, assisted by local vacuum fields. Our work paves the way for future studies of plasmonic metamaterials that exploit strong light-molecule interactions, for applications in optical state preparation and control.
For most complex 9-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $geq 1$, only the characteristically nilpotent ones should be considered.
We develop a fully quantum mechanical methodology to describe the static properties and the dynamics of a single anharmonic vibrational mode interacting with a quantized infrared cavity field in the strong and ultrastrong coupling regimes. By compari
ng multiconfiguration time-dependent Hartree (MCTDH) simulations for a Morse oscillator in a cavity, with an equivalent formulation of the problem in Hilbert space, we describe for the first time the essential role of permanent dipole moments in the femtosecond dynamics of vibrational polariton wavepackets. We show that depending on the shape of the electric dipole function $d_e(q)$ along the vibrational mode coordinate $q$, molecules can be classified into three general families. For molecules that are polar and have a positive slope of the dipole function at equilibrium, we show that an initial diabatic light-matter product state without vibrational or cavity excitations can evolve into a polariton wavepacket with a large number of intracavity photons, for interaction strengths at the onset of ultrastrong coupling. This build up of intracavity photon amplitude is accompanied by an effective $lengthening$ of the vibrational mode of nearly $10%$, comparable with a laser-induced vibrational excitation in free space. In contrast, molecules that are also polar at equilibrium but have a negative slope of the dipole function, experience an effective mode $shortening$ under equivalent coupling conditions. Our model predictions are numerically validated using realistic $ab$-$initio$ potentials and dipole functions for HF and CO$_2$ molecules in their ground electronic states. We finally propose a non-adiabatic state preparation scheme to generate vibrational polaritons using nanoscale infrared antennas and UV-vis photochemistry or electron tunneling, to enable the far-field detection of spontaneously generated infrared quantum light.
We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2L_j$; $Lleq 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^1Sigma^+$; $v=0$, $J=0$). We compute the associated $C_6$ d
ispersion coefficients of atom-molecule pairs involving $^{133}$Cs and $^{85}$Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O(n^7)$ over the range of principal quantum numbers $40leq nleq 150$. For all atom-molecule pairs considered, Rydberg states $n^2S_j$ and $n^2P_j$ result in attractive $1/R^6$ potentials. In contrast, $n^2D_j$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as $n^{-5}$ for $n>40$. For intermediate values of $nlesssim40$, both repulsive and attractive interaction energies in the order of $ 10-100 ,mu$K can be achieved with specific atomic and molecular species. The accuracy of the reported $C_6$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $Delta C_6/C_6$ estimated to be no greater than 1% on average.
This is a tutorial-style introduction to the field of molecular polaritons. We describe the basic physical principles and consequences of strong light-matter coupling common to molecular ensembles embedded in UV-visible or infrared cavities. Using a
microscopic quantum electrodynamics formulation, we discuss the competition between the collective cooperative dipolar response of a molecular ensemble and local dynamical processes that molecules typically undergo, including chemical reactions. We highlight some of the observable consequences of this competition between local and collective effects in linear transmission spectroscopy, including the formal equivalence between quantum mechanical theory and the classical transfer matrix method, under specific conditions of molecular density and indistinguishability. We also overview recent experimental and theoretical developments on strong and ultrastrong coupling with electronic and vibrational transitions, with a special focus on cavity-modified chemistry and infrared spectroscopy under vibrational strong coupling. We finally suggest several opportunities for further studies that may lead to novel applications in chemical and electromagnetic sensing, energy conversion, optoelectronics, quantum control and quantum technology.
We propose a cavity QED approach to describe light-matter interaction between an individual anharmonic molecular vibration and an infrared cavity field. Starting from a generic Morse oscillator with quantized nuclear motion, we derive a multi-level q
uantum Rabi model to study vibrational polaritons beyond the rotating-wave approximation. We analyze the spectrum of vibrational polaritons in detail and compare with available experiments. For high excitation energies, the spectrum exhibits a dense manifold of true and avoided level crossings as the light-matter coupling strength and cavity frequency are tuned. These crossings are governed by a pseudo parity selection rule imposed by the cavity field. We also analyze polariton eigenstates in nuclear coordinate space. We show that the bond length of a vibrational polariton at a given energy is never greater than the bond length of a bare Morse oscillator with the same energy. This type of bond hardening of vibrational polaritons occurs at the expense of the creation of virtual infrared cavity photons, and may have implications in chemical reactivity.
We propose a cavity QED scheme to enable cross-phase modulation between two arbitrarily weak classical fields in the optical domain, using organic molecular photoswitches as a disordered intracavity nonlinear medium. We show that a long-lived vibrati
onal Raman coherence between the $cis$ and $trans$ isomer states of the photoswitch can be exploited to establish the phenomenon of vacuum-induced transparency (VIT) in high-quality microcavities. We exploit this result to derive an expression for the cross-phase modulation signal and demonstrate that it is possible to surpass the detection limit imposed by absorption losses, even in the presence of strong natural energetic and orientational disorder in the medium. Possible applications of the scheme include the development of organic nanophotonic devices for all-optical switching with low photon numbers.
We exhibit an example of a filiform (complex) Lie algebra of dimension 13 with all its ideals of codimension 1 being characteristically nilpotent, and we construct a non trivial filiform deformation of it.
The interaction of organic molecules and molecular aggregates with electromagnetic fields that are strongly confined inside optical cavities within nanoscale volumes, has allowed the observation of exotic quantum regimes of light-matter interaction a
t room temperature, for a wide variety of cavity materials and geometries. Understanding the universal features of such organic cavities represents a significant challenge for theoretical modelling, as experiments show that these systems are characterized by an intricate competition between coherent and dissipative processes involving entangled nuclear, electronic and photonic degrees of freedom. In this review, we discuss a new theoretical framework that can successfully describe organic cavities under strong light-matter coupling. The theory combines standard concepts in chemical physics and quantum optics to provide a microscopic description of vibronic organic polaritons that is fully consistent with available experiments, and yet is profoundly different from the common view of organic polaritons. We show that by introducing a new class of vibronic polariton wave functions with a photonic component that is dressed by intramolecular vibrations, the new theory can offer a consistent solution to some of the long-standing puzzles in the interpretation of organic cavity photoluminescence. Throughout this review, we confront the predictions of the model with spectroscopic observations, and describe the conditions under which the theory reduces to previous approaches. We finally discuss possible extensions of the theory to account for realistic complexities of organic cavities such spatial inhomogeneities and the multi-mode nature of confined electromagnetic fields.
