Ultralow Temperature Regime Research Articles

Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy.

We employ the kth nearest-neighbor estimator of configurational entropy in order to decode within a parameter-free numerical approach the complex high-order structural correlations in fluxional molecules going much beyond the usual linear, bivariate correlations. This generic entropy-based scheme for determining many-body correlations is applied to the complex configurational ensemble of protonated acetylene, a prototype for fluxional molecules featuring large-amplitude motion. After revealing the importance of high-order correlations beyond the simple two-coordinate picture for this molecule, we analyze in detail the evolution of the relevant correlations with temperature as well as the impact of nuclear quantum effects down to the ultralow temperature regime of 1 K. We find that quantum delocalization and zero-point vibrations significantly reduce all correlations in protonated acetylene in the deep quantum regime. Even at low temperatures up to about 100 K, most correlations are essentially absent in the quantum case and only gain importance at higher temperatures. In the high temperature regime, beyond roughly 800 K, the increasing thermal fluctuations are found to exert a destructive effect on the presence of correlations. At intermediate temperatures of approximately 100-800 K, a quantum-to-classical cross-over regime is found where classical mechanics starts to correctly describe trends in the correlations whereas it even qualitatively fails below 100 K. Finally, a classical description of the nuclei provides correlations that are in quantitative agreement with the quantum ones only at temperatures exceeding 1000 K. This data-intensive analysis has been made possible due to recent developments of machine learning techniques based on high-dimensional neural network potential energy surfaces in full dimensionality that allow us to exhaustively sample both the classical and quantum ensemble of protonated acetylene at essentially converged coupled cluster accuracy from 1 to more than 1000 K. The presented non-parametric analysis of correlations beyond usual linear two-coordinate terms is transferable to other system classes. The technique is also expected to complement and guide the analysis of experimental measurements, in particular multidimensional vibrational spectroscopy, by revealing the complex coupling between various degrees of freedom.

Probing ultracold chemistry using ion spectrometry.

Rapid progress in atomic, molecular, and optical (AMO) physics techniques enabled the creation of ultracold samples of molecular species and opened opportunities to explore chemistry in the ultralow temperature regime. In particular, both the external and internal quantum degrees of freedom of the reactant atoms and molecules are controlled, allowing studies that explored the role of the long-range potential in ultracold reactions. The kinetics of these reactions have typically been determined using the loss of reactants as proxies. To extend such studies into the short-range, we developed an experimental apparatus that combines the production of quantum-state-selected ultracold KRb molecules with ion mass and kinetic energy spectrometry, and directly observed KRb + KRb reaction intermediates and products [M.-G. Hu and Y. Liu, et al., Science, 2019, 366, 1111]. Here, we present the apparatus in detail. For future studies that aim for detecting the quantum states of the reaction products, we demonstrate a photodissociation based scheme to calibrate the ion kinetic energy spectrometer at low energies.

Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy.

For a long time, performing converged path integral simulations at ultralow but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely, the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultralow temperature regime accessible in practice. In this work, we investigate the influence of these two thermostatting schemes on the description of hydrogen-bonded systems at temperatures down to a few Kelvin as encountered, for example, in helium nanodroplet isolation or tagging photodissociation spectroscopy experiments. For this purpose, we analyze the prototypical hydrogen bond in the Zundel cation (H5O2+) as a function of both oxygen-oxygen distance and temperature in order to elucidate how the anisotropic quantum delocalization and, thus, the shape of the shared proton adapts depending on the donor-acceptor distance. The underlying electronic structure of the Zundel cation is described in terms of Behler's Neural Network Potentials of essentially converged Coupled Cluster accuracy, CCSD(T*)-F12a/AVTZ. In addition, the performances of the PIQTB and PIGLET methods for energetic, structural, and quantum delocalization properties are assessed and directly compared. Overall, our results emphasize the validity and practical usefulness of these two modern thermostatting approaches for path integral simulations of hydrogen-bonded systems even at ultralow temperatures.

Characterization of charge-exchange collisions between ultracold Li6 atoms and Ca40+ ions

We investigate the energy dependence and the internal-state dependence of the charge-exchange collision cross sections in a mixture of $^6$Li atoms and $^{40}$Ca$^+$ ions in the collision energy range from 0.2 mK to 1 K. Deliberately excited ion micromotion is used to control the collision energy of atoms and ions. The energy dependence of the charge-exchange collision cross section obeys the Langevin model in the temperature range of the current experiment, and the measured magnitude of the cross section is correlated to the internal state of the $^{40}$Ca$^+$ ions. Revealing the relationship between the charge-exchange collision cross sections and the interaction potentials is an important step toward the realization of the full quantum control of the chemical reactions at an ultralow temperature regime.

Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation

We study equilibrium time correlations for the discrete nonlinear Schrödinger equation on a one-dimensional lattice and unravel three dynamical regimes. There is a high temperature regime with density and energy as the only two conserved fields. Their correlations have zero velocity and spread diffusively. In the low temperature regime umklapp processes are rare with the consequence that phase differences appear as an additional (almost) conserved field. In an approximation where all umklapp is suppressed, while the equilibrium state remains untouched, one arrives at an anharmonic chain. Using the method of nonlinear fluctuating hydrodynamics we establish that the DNLS equilibrium time correlations have the same signature as a generic anharmonic chain, in particular KPZ broadening for the sound peaks and Lévy 5/3 broadening for the heat peak. In the, so far not sharply defined, ultra-low temperature regime the integrability of the dynamics becomes visible. As an illustration we simulate the completely integrable Ablowitz–Ladik model and confirm ballistic broadening of the time correlations.

Ultra low-energy behavior of an ionic replacement reactionHe3He+4+He4→He2+4+He3

An accurate ab initio potential energy surface has been employed for the treatment of the full quantum dynamics for isotopic exchange reaction $^{4}\mathrm{He}^{3}\mathrm{He}_{2}^{+}+^{4}\mathrm{He}$. State-to-state reactive probabilities have been obtained using a time-independent approach at ultralow collision energies. More than one total angular momentum has been calculated in order to provide a converged rate constant for the title reaction within the ultralow temperature regime. The reaction is found to become faster than the Langevin value when $T\ensuremath{\rightarrow}0$, thus providing connection with experiments with sympathetically cooled molecular ions or superfluid helium nanodroplets.

Ultracold quantum dynamics: Spin-polarizedK+K2collisions with three identical bosons or fermions

We have developed a new potential energy surface for spin-polarized K($^2$S) + K$_{2}(^3\Sigma^+_u)$ collisions and carried out quantum dynamical calculations of vibrational quenching at low and ultralow collision energies for both bosons $^{39}$K and $^{41}$K and fermions $^{40}$K. At collision energies above about 0.1 mK the quenching rates are well described by a classical Langevin model, but at lower energies a fully quantal treatment is essential. We find that for the low initial vibrational state considered here ($v=1$), the ultracold quenching rates are {\it not} substantially suppressed for fermionic atoms. For both bosons and fermions, vibrational quenching is much faster than elastic scattering in the ultralow-temperature regime. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.

Ultrasonic attenuation in clean d-wave superconductors

We calculate the low temperature longitudinal ultrasonic attenuation α S in clean d-wave superconductors. We consider the contribution of previously ignored processes involving the excitation of a pair of quasi-holes or quasi-particles. These processes, which are forbidden by energy conservation in conventional s-wave superconductors, have a finite phase space in d-wave superconductors due to the presence of nodes in the gap which give rise to soft low-energy electronic excitations. We find the contribution to α S from these processes to be proportional to T in the regime k B T≪ Qv Δ ≪ Δ 0 (ultra-low temperature regime) and to be proportional to 1/ T in the region Qv F≪ k B T≪ Δ 0 (low temperature regime), where Q is the ultrasound wave vector and Δ 0 is the maximum gap amplitude. We explicitly evaluate these terms, for parameters appropriate to the cuprates, for Q along the nodal and the antinodal directions and compare it with the contribution from processes considered earlier [Phys. Rev. B 59 (1999) 7123]. In the ultra-low temperature regime, the processes considered by us make a contribution which is smaller by about a factor of 10 for Q along the nodal direction, while along the antinodal direction it is larger by a factor of 100 or so. In the low temperature regime on the other hand the contribution made by these terms is small. However taken together with the original terms we describe a possible way to evaluate the parameter v F/ v Δ .

Preliminary Measurements of Andreev Reflection of Quasiparticles by Turbulence in Superfluid 3He

We present preliminary measurements of Andreev scattering of quasiparticles from turbulence in the B-phase of superfluid 3 He-B. The turbulence is generated by a vibrating wire resonator driven above its pair-breaking critical velocity. The vortices intercept a beam of quasiparticles generated by a nearby black-body radiator. A substantial fraction of the incident quasiparticles are retro-reflected back into the radiator by Andreev scattering processes. The resulting temperature rise within the radiator provides a direct measurement of the flux of quasiparticles Andreev reflected. The technique provides a sensitive probe of superfluid turbulence in the ultra-low temperature regime.

Andreev Reflection of Quasiparticles by a Vortex Tangle in Superfluid 3He-B?

We have made the surprising discovery that the thermal damping of a vibrating wire resonator in superfluid He-3-B at ultra low temperatures is considerably depressed when a second wire in the vicinity is driven supercritically. The damping of a vibrating wire resonator at low velocities in the B-phase arises from the scattering of quasiparticle excitations and has a temperature dependence proportional to the Boltzmann factor exp(-Delta /kT) at low temperatures. At higher velocities (v > v(L)/3), the wire breaks Cooper pairs and emits a quasiparticle beam. At first sight it seems paradoxical that heating the superfluid can reduce the quasiparticle flux: on a neighbouring wire. We can only understand this on the basis that vorticity emitted by the supercritical wire shields, via Andreev reflection, part of the background quasiparticle flux: from reaching the other wire. If this interpretation, is correct, these techniques will provide a sensitive probe of vortex dynamics in the ultra low temperature regime.

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in super-fluid He-3 at ultralow temperatures. The aerogel disk is attached to a goal post shaped vibrating wire resonator and immersed in liquid He-3 cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of He-3 in aerogel in the ultralow temperature regime.