Collective Oscillator Research Articles

Molecular Chemistry in Cavity Strong Coupling.

The coherent exchange of energy between materials and optical fields leads to strong light-matter interactions and so-called polaritonic states with intriguing properties, halfway between light and matter. Two decades ago, research on these strong light-matter interactions, using optical cavity (vacuum) fields, remained for the most part the province of the physicist, with a focus on inorganic materials requiring cryogenic temperatures and carefully fabricated, high-quality optical cavities for their study. This review explores the history and recent acceleration of interest in the application of polaritonic states to molecular properties and processes. The enormous collective oscillator strength of dense films of organic molecules, aggregates, and materials allows cavity vacuum field strong coupling to be achieved at room temperature, even in rapidly fabricated, highly lossy metallic optical cavities. This has put polaritonic states and their associated coherent phenomena at the fingertips of laboratory chemists, materials scientists, and even biochemists as a potentially new tool to control molecular chemistry. The exciting phenomena that have emerged suggest that polaritonic states are of genuine relevance within the molecular and material energy landscape.

Stability of electronic matching of macroscopic quantum objects

It is shown that water, the associated phase which possesses the properties of a collective quantum oscillator, is capable of transmitting electronic excitations to conjugate quantum objects detected by a quantum sensor based on the superconductivity of NV- centres from changes in the emission of water by the Bose-condensate of electrons. The obtained regularities of the behaviour of quantum conjugate water allow studying the state of human body systems non-locally, based on quantitative estimates of the efficiency of translation of Bose-condensate electrons excitations to quantum-conjugated objects.

Entanglement between distant macroscopic mechanical and spin systems

Entanglement is an essential property of multipartite quantum systems, characterized by the inseparability of quantum states of objects regardless of their spatial separation. Generation of entanglement between increasingly macroscopic and disparate systems is an ongoing effort in quantum science, as it enables hybrid quantum networks, quantum-enhanced sensing and probing of the fundamental limits of quantum theory. The disparity of hybrid systems and the vulnerability of quantum correlations have thus far hampered the generation of macroscopic hybrid entanglement. Here, we generate an entangled state between the motion of a macroscopic mechanical oscillator and a collective atomic spin oscillator, as witnessed by an Einstein–Podolsky–Rosen variance below the separability limit, 0.83 ± 0.02 < 1. The mechanical oscillator is a millimetre-size dielectric membrane and the spin oscillator is an ensemble of 109 atoms in a magnetic field. Light propagating through the two spatially separated systems generates entanglement because the collective spin plays the role of an effective negative-mass reference frame and provides—under ideal circumstances—a back-action-free subspace; in the experiment, quantum back-action is suppressed by 4.6 dB. Einstein–Podolsky–Rosen entanglement between a millimetre-size mechanical membrane oscillator and a collective atomic spin oscillator formed by an ensemble of caesium atoms is achieved, although the two systems are spatially separated by one metre.

Signatures of Through‐Space Charge Transfer in Two‐Photon Absorption of Paracyclophane Derivatives

Third order polarizability, (γ) taken from the collective electronic oscillator (CEO) method was used to calculate the two‐photon absorption (TPA) of tetrastyryl‐[2,2]paracyclophane derivatives with different through‐space charge transfer configurations considering various donor and acceptor combinations at the terminal styryl groups. For the virtually same linear absorption, different TPA spectra were obtained. For controlling and fine‐tuning frequency and cross‐sections of TPA the through‐space charge transfer interactions can be used. The results are explained by the electronic density matrices corresponding to governing oscillators in one‐ and two‐photon absorption and the ground state. It is indicated that for the studied systems mainly the lowest four oscillators are responsible for the TPA cross‐sections rather than a simple effective three‐state model.

Non-Markovian dynamics of fermionic and bosonic systems coupled to several heat baths.

Employing the fermionic and bosonic Hamiltonians for the collective oscillator linearly FC-coupled with several heat baths, the analytical expressions for the collective occupation number are derived within the non-Markovian quantum Langevin approach. The master equations for the occupation number of collective subsystem are derived and discussed. In the case of Ohmic dissipation with Lorenzian cutoffs, the possibility of reduction of the system with several heat baths to the system with one heat bath is analytically demonstrated. For the fermionic and bosonic systems, a comparative analysis is performed between the collective subsystem coupled to two heat baths and the reference case of the subsystem coupled to one bath.

Multicomponent polariton superfluidity in the optical parametric oscillator regime

Superfluidity, the ability of a liquid or gas to flow with zero viscosity, is one of the most remarkable implications of collective quantum coherence. In equilibrium systems like liquid 4He and ultracold atomic gases, superfluid behaviour conjugates diverse yet related phenomena, such as persistency of metastable flow in multiply connected geometries and the existence of a critical velocity for frictionless flow when hitting a static defect. The link between these different aspects of superfluid behaviour is far less clear in driven-dissipative systems displaying collective coherence, such as microcavity polaritons, which raises important questions about their concurrency. With a joint theoretical and experimental study, we show that the scenario is particularly rich for polaritons driven in a three-fluid collective coherent regime so-called optical parametric oscillator. On the one hand, the spontaneous macroscopic coherence following the phase locking of the signal and idler fluids has been shown to be responsible for their simultaneous quantized flow metastability. On the other hand, we show here that pump, signal and idler have distinct responses when hitting a static defect; while the signal displays hardly appreciable modulations, the ones appearing in pump and idler are determined by their mutual coupling due to nonlinear and parametric processes.

Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode

We develop a quantum mechanical formalism to treat the strong coupling between an electromagnetic mode and a vibrational excitation of an ensemble of organic molecules. By employing a Bloch–Redfield–Wangsness approach, we show that the influence of dephasing-type interactions, i.e., elastic collisions with a background bath of phonons, critically depends on the nature of the bath modes. In particular, for long-range phonons corresponding to a common bath, the dynamics of the ‘bright state’ (the collective superposition of molecular vibrations coupling to the cavity mode) is effectively decoupled from other system eigenstates. For the case of independent baths (or short-range phonons), incoherent energy transfer occurs between the bright state and the uncoupled dark states. However, these processes are suppressed when the Rabi splitting is larger than the frequency range of the bath modes, as achieved in a recent experiment (Shalabney et al 2015 Nat. Commun. 6 5981). In both cases, the dynamics can thus be described through a single collective oscillator coupled to a photonic mode, making this system an ideal candidate to explore cavity optomechanics at room temperature.

Coherent Error Suppression in Multiqubit Entangling Gates

We demonstrate a simple pulse shaping technique designed to improve the fidelity of spin-dependent force operations commonly used to implement entangling gates in trapped ion systems. This extension of the Mølmer-Sørensen gate can theoretically suppress the effects of certain frequency and timing errors to any desired order and is demonstrated through Walsh modulation of a two qubit entangling gate on trapped atomic ions. The technique is applicable to any system of qubits coupled through collective harmonic oscillator modes.

Probing Ground-to-CT State Electronic Coupling for the System with No Apparent Charge Transfer Absorption Intensity by Ultrafast Visible-Pump/Mid-IR-Probe Spectroscopy

New π-stacked [Ru(tpy)2]2+ (T_T)-benzoquinone (Q) donor–acceptor (D–A) systems, [Ru(6-(2-cyclohexa-2′,5′-diene-1,4-dione)-2,2′:6′,2″-terpyridine)(2,2′:6′,2″-terpyridine)][PF6]2 (TQ_T), and [Ru(6-(2-cyclohexa-2′,5′-diene-1,4-dione)-2,2′:6′,2″-terpyridine)(4′-phenyl-2,2′:6′,2″-terpyridine)][PF6]2 (TQ_TPh) have been synthesized and characterized. Orthogonal alignment of Q to the tpy ligand imposes this unit juxtaposed cofacially on the central pyridyl ring in another tpy with a typical van der Waals distance. The low-energy electronic absorptions of these complexes are mainly metal-to-ligand charge transfer (MLCT) in nature, similar to that observed in T_T benchmark system, and do not exhibit distinguishable metal-to-Q charge transfer (MQCT) absorption in spite of the proximal location of the electron acceptor unit (Q) to the electron donor unit (T_T). TD-DFT calculation supports the experimental results that the collective oscillator strength of MQCT bands remains ∼0.002. Due to the negligible intensity of MQCT bands, evaluation of HDA between the ground and the lowest energy MQCT states are not available through conventional Mulliken–Hush analysis. For such systems, HDA values were successfully evaluated from the relative difference (ξ) of the carbonyl stretching frequency between the neutral Q and its one-electron radical anion, which was determined by an ultrafast visible-pump/mid-IR-probe (TrIR) spectroscopic method. TrIR results showed that the partial charge localized on the Q moiety in the MQCT state was ca. −0.97e, and the corresponding HDA was ∼1600 cm–1. This value was in good agreement with that estimated by the Mulliken population analysis of the ground-state geometry.

Nonadiabatic Excited-State Molecular Dynamics Modeling of Photoinduced Dynamics in Conjugated Molecules

Nonadiabatic dynamics generally defines the entire evolution of electronic excitations in optically active molecular materials. It is commonly associated with a number of fundamental and complex processes such as intraband relaxation, energy transfer, and light harvesting influenced by the spatial evolution of excitations and transformation of photoexcitation energy into electrical energy via charge separation (e.g., charge injection at interfaces). To treat ultrafast excited-state dynamics and exciton/charge transport we have developed a nonadiabatic excited-state molecular dynamics (NA-ESMD) framework incorporating quantum transitions. Our calculations rely on the use of the Collective Electronic Oscillator (CEO) package accounting for many-body effects and actual potential energy surfaces of the excited states combined with Tully's fewest switches algorithm for surface hopping for probing nonadiabatic processes. This method is applied to model the photoinduced dynamics of distyrylbenzene (a small oligomer of polyphenylene vinylene, PPV). Our analysis shows intricate details of photoinduced vibronic relaxation and identifies specific slow and fast nuclear motions that are strongly coupled to the electronic degrees of freedom, namely, torsion and bond length alternation, respectively. Nonadiabatic relaxation of the highly excited mA(g) state is predicted to occur on a femtosecond time scale at room temperature and on a picosecond time scale at low temperature.

Multilevel Holstein-Primakoff approximation and its application to atomic spin squeezing and ensemble quantum memories

We show that an ensemble of identical d-level atoms can be efficiently described by d-1 collective oscillator degrees of freedom in the vicinity of a product state with all atoms in the same, but otherwise arbitrary single-particle state. We apply our description to two different kinds of spin squeezing: (i) when each spin-F atom is individually squeezed without creating interatomic entanglement and (ii) when a particular collective atomic oscillator mode is squeezed via quantum non-demolition (QND) measurement and feedback. When combined in sequence, the order of the two methods is relevant in the final degree of squeezing. We also discuss the role of the two kinds of squeezing when multi-sublevel atoms are used as quantum memories for light.

Light-driven liquid-crystalline nonlinear oscillator under optical periodic forcing

An all-optically driven strategy to govern a liquid-crystalline collective molecular nonlinear oscillator is discussed. It does not require external feedback of any kind while the oscillator and a time-dependent perturbation both are sustained by incident light. Various dynamical regimes such as frequency-locked, quasiperiodic, forced, and chaotic are observed, in agreement with a theoretical approach developed in the limit of the plane-wave approximation.

Linear and third-order nonlinear optical properties for the heptamethine cyanine chromophore H-aggregates thin film

The thin film of a heptamethine cyanine chromophore HC was prepared by spin-coating technique. Its surface morphology and linear optical property were characterized by atomic force microscopy (AFM) and UV-visible absorption spectroscopy. The results show that HC molecules are arranged in a well-ordered H-aggregate type. The third-order nonlinear optical properties of the spin-coating film were also measured by degenerate four-wave mixing (DFWM) measurement. Enhanced third-order nonlinear susceptibility can be attributed to molecular aggregation effects, and the corresponding mechanism was dealt with by collective electronic oscillator (CEO) approach.

Electronic Excitations in a Ladder Type Fluoranthenopyracylene in its Neutral and Charged States: A Theoretical and Experimental Study

This work reports on theoretical and spectroelectrochemical studies of a thermally and chemically stable fluoranthenopyracylene ladder type molecule 7,10,17,20 tetra-p-dodecylphenyl(bisfluorantheno[8,9-a,c]) pyracylene. Optimal geometries were evaluated for neutral and positively/negatively charged states performing density functional theory (DFT) calculations. Absorption spectral line frequencies as well as oscillator strengths were calculated using the time-dependent DFT and collective electronic oscillator (CEO) methods. The calculated optical spectra are in good agreement with the experimental measurements in solution. The difference of charged states produced by reduction and/or oxidation versus the electronic neutral forms on the vertical excitation energies and CEO electronic density matrix distribution has been characterized and compared to the geometrical changes of the molecular fragments. The localization of excitation in the optical transition of the charged states shows that the excitation is less separated and shows larger electronic coherence in comparison to the neutral form.

Solid state cavity QED: Strong coupling in organic thin films

We review our research efforts to develop solid state integrated devices that operate in the strong coupling limit of cavity quantum electrodynamics (QED) for eventual application in high speed optical switching, optical computing, and quantum computing. Our devices contain J-aggregates of (organic) cyanine dyes which, by virtue of their molecular arrangement and strong dipolar coupling, exhibit a collective narrow linewidth high oscillator strength optical transition. Using J-aggregates, the strong coupling limit can be reached at room temperature with large coupling strengths (Rabi-splitting >250 meV) in exciton–polariton microcavity structures. We demonstrate that high quality nanoscale thick J-aggregate films can be uniformly deposited over macroscopic substrates, engineered at the molecular level, and patterned into single or multi-dimensional photonic bandgap structures. Our unique methods for depositing J-aggregates enabled us to structure light emitting devices that demonstrated the first ever electrically pumped polariton emission, uniquely accomplished in room temperature operation. Additionally, we demonstrated critically coupled resonators that concentrate nearly all of the incident light into 5 nm thick J-aggregate films, yielding a record high effective absorption constant of 6.8 · 10 6 cm � 1 for films with thickness that is less than 1% of the incident light wavelength. Such remarkable optical properties, enabled by scalable deposition techniques, suggest that J-aggregates are a unique materials platform on which to demonstrate integrated exciton–polariton devices with the far reaching properties of polaritons in the optical domain. � 2007 Elsevier B.V. All rights reserved. PACS: 71.36.+c; 71.35.Aa; 85.60.Jb; 78.40.Me

Density Matrix Analysis, Simulation, and Measurements of Electronic Absorption and Fluorescence Spectra of Spirobifluorenes

The linear absorption and fluorescence spectra as well as the oscillator strengths of 2,2',7,7'-tetraphenyl-9,9'-spirobifluorene (A), 2,2',7,7'-tetrakis(biphenyl-4-yl)-9,9'-spirobifluorene (B), and 2,2',7,7'-tetrakis(9,9'-spirobifluoren-2-yl)-9,9'-spirobifluorene (C) are calculated on the basis of the collective electronic oscillator (CEO) approach of Mukamel et al. (see, e.g., Chem. Rev. 2002, 102, 3171). The graphical visualization and quantitative characterization of CEO modes allows one to extract the real-space distribution of electronic excitations of the molecules under study. Effects of the lengthening and branching of the oligophenylene segments have been analyzed. The influence of the lowest excited (S1) vs ground-state (S0) geometry changes on the CEO modes is investigated and related to the geometry changes of the molecular parts. The obtained theoretical results are in good agreement with experimental trends observed in absorption and fluorescence data.

Interchain interactions in charged diacetylenic oligomers carrying bulk substituents revisited

We are studying how the electronic properties of an aggregate, built with conjugated oligomers carrying bulk substituents, are affected by intermolecular interactions. In this paper we apply the CEO (Collective Electronic Oscillator) method, on the basis of the semiempirical INDO/S Hamiltonian, to compute the electronic density matrix modifications following the photon absorption in a doubly charged cluster of two units of a fully carbazolyl-substituted oligodiacetylene tetramer, taken as a model system. The picture that had emerged from our previous calculations based on the less sophisticated CIS (Configuration Interaction including Singles) approach is seen to be confirmed. Despite the large separation between the backbones, a through-space charge transfer occurs between the two oligomers due to the fact that the excess charge, contrary to what is generally believed, is not localized on the conjugated backbone, but is spread out over the carbazolyl moieties of the charged molecule. Consideration of this kind of interaction improves the theoretical results obtained for the isolated charged oligomer chain, and aids in better explaining some features of the experimental photoinduced spectra of the corresponding polymer.

Nonlinear Infrared and Optical Responses of a Holstein−Peirls−Hubbard Dimer

A simple model based on the Holstein-Peierls-Hubbard Hamiltonian has been used to calculate the nonlinear responses at infrared and optical frequencies. The model is applied to a molecular ion radical dimer in order to account for the contribution to the nonlinear responses arising from the intermolecular charge transfer excitations and from their coupling to both intramolecular and intermolecular phonons. A similar calculation has been performed on a model quadrupolar conjugated molecule characterized by intramolecular charge transfer excitations. The calculations are performed according to a collective electronic oscillator scheme by solving the Liouville equation for the bielectronic density matrix. Such a choice allows us to retain the ability, inherent in the Hubbard type models, to fully account for the on-site electron correlation effects. Calculated spectra are reported for one-photon and two-photon absorption (the latter in the form of the imaginary part of the Kerr susceptibility) and for third harmonic generation. Narrow resonances are observed in the infrared, related mostly to the coupling with intramolecular modes. The off-resonant contribution to the nonlinear susceptibility arising from the electron-phonon interactions appears to be marginal (in the order of 1%) in all cases.

Influence of Interchain Interactions on the Electronic Properties of Neutral and Charged Oligodiacetylenes Carrying Bulk Substituents

We discuss the effect of the interchain interactions on the electronic properties of a "dimer", named (CHD(4))(2), built from two molecules of a fully carbazolyl-substituted oligodiacetylene containing four repeating units. Each carbazolyl moiety is connected to its respective backbone through a methylene spacer, and the excitations of the neutral and doubly positively charged dimer are obtained using the CIS (configuration interaction including singles) and CEO (collective electronic oscillator) models. The separation distance between the backbones is fixed to a value that could possibly imply a very weak, if any, interchain interaction between the oligomers. In the charged dimer, where we have not been able to perform CEO calculations, it can be expected from previous results that the CIS method will behave satisfactorily. Contrary to the neutral case and surprisingly enough, the simulated photoinduced absorption (PA) spectra indicate a substituent-induced strong interaction between the oligomers, due to the very large amount of excess charge on the distorted oligomer which is spread over its carbazolyl moieties. Broadening of the lowest energy band due to the latter interaction improves the agreement between the theoretical and the experimental PA spectrum for the corresponding polymer. The through-space charge transfer directly connecting the charged with the neutral molecule could supply an efficient channel for charge transport in substituted polydiacetylenes.

Non-Markovian dynamics of quantum systems. I. Formalism and transport coefficients

Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of general and linear couplings in the coordinate and momentum between the collective harmonic oscillator and heat bath. The long-time tails of correlation functions are investigated in the low- and high-temperature regimes of dissipation for different couplings. The Onsager's regression hypothesis is discussed for the non-Markovian dynamics. The Lindblad theory is justified on the basis of the microscopical model.