Quasiparticle Approach to Molecules Interacting with Quantum Solvents

Abstract

Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently-predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)]. Most important, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian. The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species. These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle. Among its many peculiar properties, superfluid4 He is quite averse to mixing with impurities which could serve as a microscopic probe of the superfluid phase. As a result, for several decades after the discovery of superfluidity by Allen, Misener, and Kapitza [1,2], only macroscopic -hydrodynamic -properties of superfluid helium have been studied in the laboratory. In the 1990's, however, it was demonstrated that atoms and molecules can be trapped in superfluid helium if the latter forms little droplets containing on the order of a thousand helium atoms [3][4][5][6][7]. Over the following years, trapping atoms, molecules, and ions inside superfluid helium nanodroplets -sometimes called 'nanocryostats' -emerged as an important tool of molecular spectroscopy [6][7][8][9][10][11][12]. Such nanodroplets allow to trap single molecules in a cold environment (∼ 0.4 Kelvin), thereby isolating them from external perturbations. This allows to record spectra free of collisional and Doppler broadening, as well as to study species that are unstable in the gas phase, such as free radicals.While superfluid helium does not cause a substantial broadening of molecular spectral lines, it affects molecular rotation. In particular, molecules in superfluid helium nanodroplets acquire an effective moment of inertia, that is larger compared to its gas-phase value [6,9]. The relative magnitude of the effect increases from lighter to heavier species and is somewhat similar to renormalization of the effective mass for electrons interacting with a crystalline lattice [13][14][15][16].Semiclassically, molecular rotation in helium can be rationalized within the 'adiabatic following' model [6,7,[17][18][19][20][21][22]. There, it is assumed that the molecule induces a local density deformation (a 'non superfluid shell') of helium which co-rotates along with the molecule, thereby increasing its moment of inertia. However, such a classical approach does not allow to get insight into the intriguing aspects of the problem arising from quantum many-body physics. Helium, on the other hand, represents a dense, strongly-interactin...

Fingerprints of angulon instabilities in the spectra of matrix-isolated molecules

“…In order to derive the simplest possible model, we take into account only the isotropic term, λ = ξ = 0, as well as the leading anisotropic term, λ = ξ = 3. It has been previously shown [22,24] that the effects of helium can be parametrized by a few characteristic properties of the molecule-helium potential, such as the PES anisotropy and the depth of its minima, which renders the fine details of the PES irrelevant. Therefore, in order to further simplify the model, we choose effective potentials characterized by the Gaussian form-factors, f λξ (r) = u λξ (2π) −3/2 e − r 2 2r 2 λξ , such that their magnitude, u λξ , and range, r λξ , reproduce known properties of the moleculehelium interaction.…”

“…Recently, it was predicted that a superfluid can acquire angular momentum via a different, microscopic route, which takes effect in the presence of rotating impurities, such as molecules [6][7][8][9][10][11][12][13]. In particular, it was demonstrated that a rotating impurity immersed in a superfluid forms the 'angulon' quasiparticle, which can be thought of as a rigid rotor dressed by a cloud of superfluid excitations carrying angular momentum [14-21].The angulon theory was able to describe, in good agreement with experiment, renormalization of rotational constants [22,23] and laser-induced dynamics [24,25] of molecules in superfluid helium nanodroplets. One of the key predictions of the angulon theory are the socalled 'angulon instabilities ' [14-16] that occur at some critical value of the molecule-superfluid coupling where the angulon quasiparticle becomes unstable and one or a few quanta of angular momentum are resonantly transferred from the impurity to the superfluid.…”

“…(1) becomes quantitatively accurate for a symmetrictop molecule immersed in a weakly-interacting BoseEinstein Condensate [14,16]. It has been demonstrated, however, that one can develop a phenomenological theory based on the angulon Hamiltonian that describes rotations of molecules in superfluid 4 He in good agreement with experiment [22,24]. Here we pursue a similar route, i.e., we fix the interaction parameters, v λξ (q), based on ab inito PES's [68,[84][85][86][87][88][89] in such a way that the depth of the trapping potential (mean-field energy shift) for the molecule is reproduced [6].…”

“…Let us proceed with calculating the spectrum of a symmetric-top impurity in 4 He in the weakly-interacting regime, applicable to both CH 3 and NH 3 [22]. We start from constructing a variational ansatz based on singleboson excitations, analogous to that used in Ref.…”

Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment

“…Recently, it was shown that interaction of such orbital impurities with a many-particle environment can be rationalized by using the concept of the angulon quasiparticle [52][53][54][55][56][57][58]. While in the case of polarons the bath degrees of freedom couple to the impurity's translational motion, in angulons the orbital angular momentum is redistributed between the impurity and the many-particle environment.…”