Microscopic molecular superfluid response: theory and simulations

Onset of Rotational Decoupling for a Molecular Ion Solvated in Helium: From Tags to Rings and Shells

Little is known about how rotating molecular ions interact with multiple ^{4}He atoms and how this relates to microscopic superfluidity. Here, we use infrared spectroscopy to investigate ^{4}He_{N}⋯H_{3}O^{+} complexes and find that H_{3}O^{+} undergoes dramatic changes in rotational behavior as ^{4}He atoms are added. We present evidence of clear rotational decoupling of the ion core from the surrounding helium for N>3, with sudden changes in rotational constants at N=6 and 12. In sharp contrast to studies on small neutral molecules microsolvated in helium, accompanying path integral simulations show that an incipient superfluid effect is not needed to account for these findings.

Real-time hydrogen molecular dynamics satisfying the nuclear spin statistics of a quantum rotor

Apparent presence of the nuclear-spin species of a hydrogen molecule, para-hydrogen and ortho-hydrogen, associated with the quantum rotation is a manifestation of the nuclear quantum nature of hydrogen, governing not only molecular structures but also physical and chemical properties of hydrogen molecules. It has been a great challenge to observe and calculate real-time dynamics of such molecularized fermions. Here, we developed the non-empirical quantum molecular dynamics method that enables real-time molecular dynamics simulations of hydrogen molecules satisfying the nuclear spin statistics of the quantum rotor. While reproducing the species-dependent quantum rotational energy, population ratio, specific heat, and H-H bond length and frequency, we found that their translational, orientational and vibrational dynamics becomes accelerated with the higher rotational excitation, concluding that the nuclear quantum rotation stemmed from the nuclear spin statistics can induce various kinds of dynamics and reactions intrinsic to each hydrogen species.

Neural network interaction potentials for para-hydrogen with flexible molecules

The study of molecular impurities in para-hydrogen ( pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions, including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with only one or very few pH2, the microsolvation regime for intermediate particle numbers, and matrix isolation with many solvent molecules. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can, in principle, provide the necessary atomistic insight, but they require very accurate descriptions of the involved interactions. Here, we present a data-driven approach for the generation of impurity⋯ pH2 interaction potentials based on machine learning techniques, which retain the full flexibility of the dopant species. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly accurate AHR-averaged NNPs at coupled cluster accuracy, namely, explicitly correlated coupled cluster single, double, and scaled perturbative triples, CCSD(T*)-F12a/aVTZcp, in an automated manner. We apply this methodology to the water and protonated water molecules as representative cases for quasi-rigid and highly flexible molecules, respectively, and obtain AHR-averaged NNPs that reliably describe the corresponding H2O⋯ pH2 and H3O+⋯ pH2 interactions. Using path integral simulations, we show for the hydronium cation, H3O+, that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The automated and data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.

Zonal Estimators for Quasiperiodic Bosonic Many-Body Phases

In this work, we explore the relevant methodology for the investigation of interacting systems with contact interactions, and we introduce a class of zonal estimators for path-integral Monte Carlo methods, designed to provide physical information about limited regions of inhomogeneous systems. We demonstrate the usefulness of zonal estimators by their application to a system of trapped bosons in a quasiperiodic potential in two dimensions, focusing on finite temperature properties across a wide range of values of the potential. Finally, we comment on the generalization of such estimators to local fluctuations of the particle numbers and to magnetic ordering in multi-component systems, spin systems, and systems with nonlocal interactions.

Molecular Bonding in an Orbital-Free-Related Density Functional Theory

A density functional theory based on polymer self-consistent field theory is applied to systems of two atoms in order to show that this approach is capable of predicted molecular bonding. Periodic table elements from hydrogen up to neon are examined and homonuclear diatomic molecules are found to form for H₂, N₂, O₂, and F₂, in agreement with known results. The heteronuclear molecules CO and HF, which are known to exist under ambient conditions, are also found to be stable. Bond lengths for most of these molecules agree with experimental results to within less than 8%, with the exception of O₂ and F₂ which deviate more significantly. The bonding energy for H₂ is given and is within 16% of the known value, but fundamental vibrational frequencies do not agree well with experiment. The main approximations of the theory are very simple and include a Fermi-Amaldi correction to the electron-electron interaction to account for self-interactions and a basic expression for the Pauli potential to account for the exclusion principle. The self-consistent equations are solved in terms of basis functions that encode the cylindrical symmetry of diatomic molecules. Since orbitals are not used, the approach is related to orbital-free density functional theory.

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.

A path integral ground state approach for asymmetric top rotors with nuclear spin symmetry: Application to water chains

A path integral ground state (PIGS) approach for the simulation of asymmetric top rotors is presented. The method is based on Monte Carlo sampling of angular degrees of freedom. A symmetry-adapted rotational density matrix is used to account for nuclear spin statistics. To illustrate the method, ground-state properties of collections of para-water molecules confined to a one-dimensional lattice are computed. Those include energetic and structural observables. An advantage of the PIGS method is that expectation values can be obtained directly since the square of the wavefunction is sampled during a simulation. To benchmark the method, ground state energies and orientational distributions are computed using exact diagonalization for a single para-water molecule in an external field using a finite basis of symmetric top eigenfunctions. Benchmark results are also provided for N = 2 para-water molecules pinned to lattice sites at various distances to sample the crossover from hydrogen bonding to the dipole-dipole interaction regime. Excellent agreement between the PIGS results and the finite basis set calculations is observed. A thorough analysis of the convergence in terms of the imaginary time propagation length and systematic Trotter error is performed. The PIGS approach is then applied to a chain of N = 11 water molecules, and an equation of state is constructed in terms of the intermolecular separation. Ordering effects are also studied, and a transition between hydrogen bonding to dipole-dipole alignment is observed. The method is scalable and can also be applied in higher dimensions.

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.

High resolution infrared spectroscopy of (HCl)2 and (DCl)2 isolated in solid parahydrogen: Interchange-tunneling in a quantum solid

Infrared spectroscopic studies of weakly bound clusters isolated in solid parahydrogen (pH₂) that exhibit large-amplitude tunneling motions are needed to probe how quantum solvation perturbs these types of coherent dynamics. We report high resolution Fourier transform infrared absorption spectra of (HCl)₂, HCl-DCl, and (DCl)₂ isolated in solid pH₂ in the 2.4-4.8 K temperature range. The (HCl)₂ spectra show a remarkable amount of fine structures that can be rigorously assigned to vibration-rotation-tunneling transitions of (HCl)₂ trapped in double substitution sites in the pH₂ matrix where end-over-end rotation of the cluster is quenched. The spectra are assigned using a combination of isotopically (H/D and ³⁵Cl/³⁷Cl) enriched samples, polarized IR absorption measurements, and four-line combination differences. The interchange-tunneling (IT) splitting in the ground vibrational state for in-plane and out-of-plane H³⁵Cl-H³⁷Cl dimers is 6.026(1) and 6.950(1) cm^-1, respectively, which are factors of 2.565 and 2.224 smaller than in the gas phase dimer. In contrast, the (DCl)₂ results show larger perturbations where the ground vibrational state IT splitting in D³⁵Cl-D³⁷Cl is 1.141(1) cm^-1, which is a factor of 5.223 smaller than in the gas phase, and the tunneling motion is quenched in excited intramolecular vibrational states. The results are compared to similar measurements on (HCl)₂ made in liquid helium nanodroplets to illustrate the similarities and differences in how both these quantum solvents interact with large amplitude tunneling motions of an embedded chromophore.

Quantum Bubbles in Microgravity

The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.

Equation of state and first principles prediction of the vibrational matrix shift of solid parahydrogen

We generate the equation of state (EOS) of solid parahydrogen (para-H₂) using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor potential energy curve for the para-H₂ dimer. The EOS curves for the fcc and hcp structures of solid para-H₂ near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid para-H₂, we eliminated by extrapolation the systematic errors associated with the choice of simulation parameters used in the PIMC calculation. We also investigate the temperature dependence of the EOS curves, and the invariance of the equilibrium density with temperature is satisfyingly reproduced. The pressure as a function of density and the compressibility as a function of pressure are both calculated using the obtained EOS and are compared with previous simulation results and experiments. We also report the first ever a priori prediction of a vibrational matrix shift from first-principles two-body potential functions, and its result for the equilibrium state agrees well with experiment.

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.

Suppression of Parahydrogen Superfluidity in a Doped Nanoscale Bose Fluid Mixture

Helium (^{4}He) nanodroplets provide a unique environment to observe the microscopic origins of superfluidity. The search for another superfluid substance has been an ongoing quest in the field of quantum fluids. Nearly two decades ago, experiments on doped parahydrogen (p-H_{2}) clusters embedded in ^{4}He droplets displayed anomalous spectroscopic signatures that were interpreted as a sign of the superfluidity of p-H_{2} [S. Grebenev et al., Science 289, 1532 (2000)SCIEAS0036-807510.1126/science.289.5484.1532]. Here, we observe, using first-principles quantum Monte Carlo simulations, a phase separation between a symmetric and localized p-H_{2} core and ^{4}He shells. The p-H_{2} core has minimal superfluid response. These findings are consistent with the recorded spectra but not with their original interpretation, and lead us to conclude that doped p-H_{2} clusters form a nonsuperfluid core in ^{4}He droplets.

Magic numbers, quantum delocalization, and orientational disordering in anionic hydrogen and deuterium clusters

The Diffusion Monte Carlo (DMC) method was applied to anionic hydrogen clusters H^-(H₂)_n (n = 1-16, 32) and their deuterated analogs using a polarizable all-atom potential energy surface (PES) developed by Calvo and Yurtsever. For the hydrogen clusters, the binding energy ΔE_n appears to be a smooth function of the cluster size n, thus contradicting the previous claim that n = 12 is a "magic number" cluster. The structures of the low energy minima of the PES for these clusters belong to the icosahedral motif with the H₂ molecules aligned toward the central H^- ion. However, their ground state wavefunctions are highly delocalized and resemble neither the structures of the global nor local minima. Moreover, the strong nuclear quantum effects result in a nearly complete orientational disordering of the H₂ molecules. For the deuterium clusters, the ground state wavefunctions are localized and the D₂ molecules are aligned toward the central D^- ion. However, their structures are still characterized as disordered and, as such, do not display size sensitivity. In addition, DMC simulations were performed on the mixed H^-(H₂)_n(D₂)_p clusters with (n, p) = (6, 6) and (16, 16). Again, in contradiction to the previous claim, we found that the "more quantum" H₂ molecules prefer to reside farther from the central H^- ion than the D₂ molecules.

Isotopic Effects on Intermolecular and Intramolecular Structure and Dynamics in Hydrogen, Deuterium, and Tritium Liquids: Normal Liquid and Weakly and Strongly Cooled Liquids

Differences in properties such as phase-transition temperature and transport coefficients among liquids of different isotopic compositions, hydrogen, deuterium, and tritium, should originate from their differently pronounced nuclear quantum effects (NQEs) rather than from any subtle difference in the electronic interaction potentials. Accurate and efficient determination of structural and dynamical isotopic effects in the quantum liquids still remains as one of the challenging problems in condensed-phase physics. With a recently developed nonempirical real-time molecular dynamics method which describes nonspherical molecules with the NQEs, we computationally realized and investigated dynamical and quantum isotopic effects of not only traditionally studied isotopes, hydrogen, and deuterium but also a lesser known radioisotope, tritium, in broad thermodynamic conditions from normal liquid to weakly and strongly cooled liquids, which have been hindered by rapid crystallization in spite of numerous experimental attempts at supercooling. Reproducing the previously reported experimental isotope dependence on the bond length and vibrational frequencies of hydrogen, deuterium, and tritium liquids, we further demonstrate that distinctive isotope effects appear in their intermolecular and intramolecular structure and dynamics not only at lower temperature but also at higher temperature, which none has so far been able to obtain quantitative results for realistic systems. Rationalization of their physical origins and the obtained physical insights will help future experimental searching and monitoring intermolecular and intramolecular dynamics and structures of these isotopes not only in normal liquid but also in supercooled liquid.

Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate

Bose Einstein condensates of spin-1 atoms are known to exist in two different phases, both having spontaneously broken spin-rotation symmetry, a ferromagnetic and a polar condensate. Here we show that in two spatial dimensions it is possible to achieve a quantum phase transition from a polar condensate into a singlet phase symmetric under rotations in spin space. This can be done by using particle density as a tuning parameter. Starting from the polar phase at high density the system can be tuned into a strong-coupling intermediate-density point where the phase transition into a symmetric phase takes place. By further reducing the particle density the symmetric phase can be continuously deformed into a Bose-Einstein condensate of singlet atomic pairs. We calculate the region of the parameter space where such a molecular phase is stable against collapse.

Distinct structural and dynamical difference between supercooled and normal liquids of hydrogen molecules

Supercooled hydrogen liquid as well as superfluid have continued to elude experimental observation due to rapid crystallization. We computationally realized and investigated supercooled hydrogen liquid by a recently developed non-empirical real-time molecular dynamics method, which describes non-spherical hydrogen molecules with the nuclear quantum effects. We demonstrated that the hydrogen supercooled liquid is not a simply cooled liquid but rather exhibits intrinsic structural and dynamical characters including a precursor of tunneling and superfluidity which neither normal hydrogen liquid nor solid possesses. All of the insights provide a milestone for planning experiments of metastable hydrogen systems like glassy and superfluid states and for identifying various unknown hydrogen phases.

Path-integral Monte Carlo method for Rényi entanglement entropies

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.