Quasiparticle Approach to Molecules Interacting with Quantum Solvents

Theory of all-coupling angulon for molecules rotating in many-body environment

The formation of angulon, stemming from the rotor (molecule or impurity), rotating in the quantum many-body field, adds a new member to the quasi-particles' family and has aroused intense interest in multiple research fields. However, the analysis of the coupling strength between the rotor and its hosting environment remains a challenging task, both in theory and experiment. Here, we develop the all-coupling theory of the angulon by introducing a unitary transformation, where the renormalization of the rotational constants for different molecules in the helium nanodroplets is reproduced, getting excellent agreement with the experimental data collected during the past decades. Moreover, the strength of molecule-helium coupling and the effective radius of the solvation shell co-rotating along with the molecular rotor could be estimated qualitatively. This model not only provides significant enlightenment for analyzing the rotational spectroscopy of molecules in the phononic environment, but also provides a new method to study the transfer of the phonon angular momentum in the angulon frame.

Femtosecond Rotational Dynamics of D_{2} Molecules in Superfluid Helium Nanodroplets

Rotational dynamics of D_{2} molecules inside helium nanodroplets is induced by a moderately intense femtosecond pump pulse and measured as a function of time by recording the yield of HeD^{+} ions, created through strong-field dissociative ionization with a delayed femtosecond probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant B_{He} of the in-droplet D_{2} molecule, determined by Fourier analysis, is the same as B_{gas} for an isolated D_{2} molecule. Our observations show that the D_{2} molecules inside helium nanodroplets essentially rotate as free D_{2} molecules.

Reaction dynamics within a cluster environment

This perspective article reviews experimental and theoretical works where rare gas clusters and helium nanodroplets are used as a nanoreactor to investigate chemical dynamics in a solvent environment. A historical perspective is presented first followed by specific considerations on the mobility of reactants within these reaction media. The dynamical response of pure clusters and nanodroplets to photoexcitation is shortly reviewed before examining the role of the cluster (or nanodroplet) degrees of freedom in the photodynamics of the guest atoms and molecules.

High-resolution laser resonances of antiprotonic helium in superfluid 4He

When atoms are placed into liquids, their optical spectral lines corresponding to the electronic transitions are greatly broadened compared to those of single, isolated atoms. This linewidth increase can often reach a factor of more than a million, obscuring spectroscopic structures and preventing high-resolution spectroscopy, even when superfluid helium, which is the most transparent, cold and chemically inert liquid, is used as the host material^1–6. Here we show that when an exotic helium atom with a constituent antiproton^7–9 is embedded into superfluid helium, its visible-wavelength spectral line retains a sub-gigahertz linewidth. An abrupt reduction in the linewidth of the antiprotonic laser resonance was observed when the liquid surrounding the atom transitioned into the superfluid phase. This resolved the hyperfine structure arising from the spin–spin interaction between the electron and antiproton with a relative spectral resolution of two parts in 10⁶, even though the antiprotonic helium resided in a dense matrix of normal matter atoms. The electron shell of the antiprotonic atom retains a small radius of approximately 40 picometres during the laser excitation⁷. This implies that other helium atoms containing antinuclei, as well as negatively charged mesons and hyperons that include strange quarks formed in superfluid helium, may be studied by laser spectroscopy with a high spectral resolution, enabling the determination of the particle masses⁹. The sharp spectral lines may enable the detection of cosmic-ray antiprotons^10,11 or searches for antideuterons¹² that come to rest in liquid helium targets.

The spectral lines of antiprotonic helium atoms are shown to retain their sub-gigahertz linewidth upon submersion in a bath of superfluid helium, enabling the hyperfine structure to be resolved.

Emergence of Anyons on the Two-Sphere in Molecular Impurities

Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle.

Laser spectroscopy of helium solvated molecules: probing the inertial response

Helium is the only solvent within which molecules can "freely" rotate, albeit with an increased moment of inertia relative to the gas phase. Evidence for this can be obtained by performing infrared laser spectroscopy on molecules embedded large helium clusters (nanodroplets), which often reveals rotationally resolved lines that are more closely spaced than in vacuo. The additional rotational inertia results from coupling of the helium to the molecule (rotor), and decreases in going from heavy (e.g., SF₆) to light (e.g., CH₄) rotors due to a partial breakdown in the adiabatic (following) approximation; faster (lighter) rotors cannot couple as well to helium since their effective interaction with helium is less anisotropic. In addition to this "mass" dependence to the coupling, there is also a time dependence to it, which shows up in the IR spectra as an asymmetry in the rovibrational lineshapes; this results from a delay in the response of helium to the change in rotational speed of the solvated molecule (when ΔJ = ±1). In this perspective we discuss the coupling between various probe molecules and helium that have been investigated by infrared laser spectroscopy in the frequency domain.

Rotation of CH3+ Cations in Helium Droplets

Observation of the free rotation of molecules in helium droplets enabled microscopic study of interaction of quantum rotors with a superfluid environment at T = 0.4 K. This work extends studies of rotation in helium to molecular cations, such as methenium, CH₃⁺. The spectrum of the v₃ band of CH₃⁺ around 3130 cm^-1 has three prominent peaks assigned to the rotational structure of the band. While the free CH₃⁺ is an oblate top, in helium it behaves as a prolate top. This effect is ascribed to the strong binding of two He atoms along the figure axis of the ion. Our results indicate that the other He atoms within the first solvation shell remain fluxional and in disparity with the widely accepted model of a rigid He "snowball" surrounding ions.

Molecular Impurities as a Realization of Anyons on the Two-Sphere

Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.

Intermolecular forces and correlations mediated by a phonon bath

Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born-Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.

Anthracene-Argon Clusters Generated in Superfluid Helium Nanodroplets: New Aspects on Cluster Formation and Microsolvation

About two decades after extensive studies on anthracene-Ar_n clusters in the gas phase, we report corresponding studies in superfluid helium droplets. With AN as a small fluorophore and spectroscopic data from the gas phase and helium droplets, both the formation of clusters and the microsolvation in superfluid helium droplets can be studied. As expected for helium droplets, a significantly higher number of isomeric variants of the respective cluster sizes are obtained, because metastable variants are stabilized by the low temperature and the surrounding helium. Moreover, spectroscopic data recorded in helium droplets reveal cluster configurations with Ar atoms shielded by a helium solvation layer. Surprisingly, AN-Ar_n clusters with more than four Ar atoms do not appear to form rigid configurations. The helium droplet data in combination with the gas phase spectra may serve as a suitable reference for further theoretical investigations on solvation and cluster formation in superfluid helium droplets.

Direct detection of polar structure formation in helium nanodroplets by beam deflection measurements

Long-range intermolecular forces are able to steer polar molecules submerged in superfluid helium nanodroplets into highly polar metastable configurations. We demonstrate that the presence of such special structures can be identified, in a direct and determinative way, by electrostatic deflection of the doped nanodroplet beam. The measurement also establishes the structures' electric dipole moments. In consequence, the introduced approach is complementary to spectroscopic studies of low-temperature molecular assembly reactions. It is enabled by the fact that within the cold superfluid matrix the molecular dipoles become nearly completely oriented by the applied electric field. As a result, the massive (tens of thousands of helium atoms) nanodroplets undergo significant deflections. The method is illustrated here by an application to dimers and trimers of dimethyl sulfoxide (DMSO) molecules. We interpret the experimental results with ab initio theory, mapping the potential energy surface of DMSO complexes and simulating their low temperature aggregation dynamics.

Quantum Microsolvation of Protonated Methane with ^{4}He: Large-Amplitude Motion Heavily Influences Bosonic Exchange

Quantum simulations of small CH_{5}^{+}·^{4}He_{n} complexes disclose significant and antagonistic impact of small-amplitude local vibrational motion vs large-amplitude global fluxional motion within the CH_{5}^{+} impurity on helium in real and permutation space. While the former significantly enhances bosonic exchange in the surrounding ^{4}He microsolvation shell compared to the rigid-body reference, the latter greatly suppresses long permutation cycles, which is traced back to the different nature of these quantum fluctuations. Therefore, it is expected that the resulting impact on local superfluidity is generic for fluctuating impurities in bosonic environments.

Oriented Polar Molecules Trapped in Cold Helium Nanodropets: Electrostatic Deflection, Size Separation, and Charge Migration

Helium nanodroplets doped with polar molecules are studied by electrostatic deflection. This broadly applicable method allows even polyatomic molecules to attain subkelvin temperatures and nearly full orientation in the field. The resulting intense force from the field gradient strongly deflects even droplets with tens of thousands of atoms, the most massive neutral systems studied by beam "deflectometry." We use the deflections to extract droplet size distributions. Moreover, since each host droplet deflects according to its mass, spatial filtering of the deflected beam translates into size filtering of neutral fragile nanodroplets. As an example, we measure the dopant ionization probability as a function of droplet radius and determine the mean free path for charge hopping through the helium matrix. The technique will enable separation of doped and neat nanodroplets and size-dependent spectroscopic studies.

Imaging Quantum Vortices in Superfluid Helium Droplets

Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.

Microsolvation of porphine molecules in superfluid helium nanodroplets as revealed by optical line shape at the electronic origin

We investigate the line shape at the electronic origin of single porphine molecules doped into superfluid helium droplets as a function of the droplet size. Helium droplets comprised of less than 10⁵ atoms are generated from an expansion of gaseous helium, while droplets with more than 10⁵ atoms originate from liquid helium. In contrast to our recent study on phthalocyanine, porphine is found to exhibit a solvent shift to the blue with respect to the gas-phase resonance frequency as well as a multiplet splitting. A comparison of the helium-induced features of phthalocyanine and porphine with those obtained in similar studies on tetracene and pentacene reveals that these occur chiefly as two kinds of excitations distinguished by their linewidths and their dependence on the droplet size. Moreover, at quasi-bulk conditions achieved with droplets in excess of 10⁶ helium atoms, none of these four dopant species yields an optical spectrum that can be assigned to a plausible rotational band structure.

Quantum Groups as Hidden Symmetries of Quantum Impurities

We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, G_{q}. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. We exemplify our approach by considering a quantum rotor interacting with a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbative regime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength, in good agreement with nonperturbative calculations. Furthermore, the value of the deformation parameter allows one to predict at which coupling strengths rotor-bath interactions result in a formation of a stable quasiparticle. The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, but also provides valuable insights into hidden symmetries of interacting many-particle systems.

Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems

We introduce a diagrammatic Monte Carlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.

Impulsive alignment of 4He-CH3I: A theoretical study

We simulate the non-adiabatic laser alignment of the weakly bound ⁴He-CH₃I complex based on a quantum mechanical wave packet calculation for a model He-CH₃I interaction potential. Two different regimes are found depending on the laser intensity. At intensities typical of non-adiabatic alignment experiments, the rotational dynamics resembles that of the isolated molecule. This is attributed to the fact that after the initial prompt alignment peak the complex rapidly dissociates. The subsequent revival pattern is due to the free rotation of the molecule detached from the helium atom. It is superimposed to a flat background corresponding to ∼20% of the wave packet which remains bound, containing lower rotational excitation. At lower intensities, dissociation is avoided but the rotational excitation is not high enough to provide an efficient alignment and a broad non-regular structure is observed. Besides, the interaction of the He atom with the molecule quenches any possible alignment. These interpretations are based on the calculation of different observables related to the rotational motion. We compare our findings with recent experimental and theoretical results of non-adiabatic alignment of linear molecules solvated in helium nanodroplets or weakly interacting with one helium atom.

Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem

Recently, it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles [Phys. Rev. Lett. 118, 095301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.095301]. Here, we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a two-sphere interacting with a gauge field of a non-Abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole Abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.

Laser-Induced Rotation of Iodine Molecules in Helium Nanodroplets: Revivals and Breaking Free

Rotation of molecules embedded in helium nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective rotation lasting long enough to form revivals. With increasing fluence, however, the revivals disappear-instead, rotational dynamics as rapid as for an isolated molecule is observed during the first few picoseconds. Classical calculations trace this phenomenon to transient decoupling of the molecule from its helium shell. Our results open novel opportunities for studying nonequilibrium solute-solvent dynamics and quantum thermalization.