Ultracold Physics Research Articles

Full spectroscopic model and trihybrid experimental-perturbative-variational line list for NH

ABSTRACT Imidogen (NH) is a reactive molecule whose presence in astrochemical environments is of interest due to its role in the formation of nitrogen-containing molecules and as a potential probe of nitrogen abundance. Spectroscopic NH monitoring is useful for Earth-based combustion and photolysis processes of ammonia and other nitrogen-containing species. NH is also relevant to ultracold molecular physics and plasma studies. To enable these diverse applications, high-quality molecular spectroscopic data are required. Here, a new line list with significant advantages over existing data is presented. Most notably, this line list models isotopologue spectroscopy and forbidden transitions (important for NH visible absorption), alongside some overall improvements to accuracy and completeness. This approach takes advantage of existing experimental data (from a previous MARVEL compilation) and perturbative line lists together with new MRCI ab initio electronic data. These are used to produce a novel variational spectroscopic model and trihybrid line list for the main 14N1H isotopologue, as well as isotopologue-extrapolated hybrid line lists for the 14N2H, 15N1H, and 15N2H isotopologues. The new 14N1H ExoMol-style trihybrid line list, kNigHt, comprises 4076 energy levels (1078 experimental) and 327 014 transitions up to 47 500 cm−1 (211 nm) between five low-lying electronic states (X 3Σ−, a 1Δ, b 1Σ+, A 3Π, and c 1Π). For most anticipated applications aside from far-infrared studies, this line list will be of sufficient quality; any improvements should focus on the b 1Σ+ energies, and the a 1Δ – A 3Π and b 1Σ+ – A 3Π spin–orbit couplings.

Exploring disordered quantum spin models with a multilayer multiconfigurational approach

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area-laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this work, we employ a numerical technique referred to as multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems for the first time. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multi-layering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

Quantum control of field-free molecular orientation.

Generating field-free (non-stationary) orientation of molecules in space has been a longstanding goal in the field of quantum control of molecular rotation, which has significant applications in physical chemistry, chemical physics, strong-field physics, and quantum information science. In this Perspective, we review and examine several representative control schemes developed in recent years and implemented in theoretical and experimental areas for generating field-free orientation of molecules. By conducting numerical simulations of different control schemes on the same molecular system, we demonstrate that quantum coherent control, specifically targeting a limited number of the lowest-lying rotational levels to achieve an optimal superposition, can result in a high degree of orientation. To this end, we provide an overview of our latest developed analytical method, which enables the precise design of terahertz field parameters through resonant excitation. This design approach facilitates the attainment of desired field-free orientations by optimizing the amplitudes and phases of rotational wave functions for the selected rotational levels. Finally, we outlook the significance of such progress in multiple frontier research fields, highlighting its potential applications in ultracold physics, quantum computation, quantum simulation, and quantum metrology.

Ground state of Rydberg-dressed Bose gas confined in periodic moiré lattices

The experimental realization of Rydberg dressing and spin-orbit coupling greatly broadens the research field of ultracold atoms as a quantum simulation platform. Very recently, moiré lattices have attracted intensive study, ranging from condensed matter to ultracold physics. In this paper, the ground-state structure of Rydberg-dressed Bose gas with spin-orbit coupling and confined in moiré lattices is studied, and the effects of nonlocal Rydberg interaction and spin-orbit coupling on the ground state of the system are explored. Our results show that the system has no translational symmetry due to the presence of nonlocal Rydberg interaction, and more and more regular periodic structures present with the increases of the strength of nonlocal Rydberg interaction. In the presence of spin-orbit coupling, the Hamiltonian of the system has an imaginary part, and the phase of the system is not uniformly distributed. It is found that the ground state of the system with spin-orbit coupling present more abundant internal structure base on these periodic structures. The results pave the way for future study of moiré physics in ultracold atom system.

Perspectives and opportunities: a molecular toolkit for fundamental physics and matter-wave interferometry in microgravity * *A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

The study of molecular physics using ultracold gases has provided a unique probe into the fundamental properties of nature and offers new tools for quantum technologies. In this article we outline how ultracold molecular physics in a space environment opens opportunities for (a) exploring ultra-low energy regimes of molecular physics with high efficiency, (b) providing a toolbox of capabilities for fundamental physics, and (c) enabling new classes of matter-wave interferometers with applications in precision measurement for fundamental and many-body physics.

A triatomic molecule is laser cooled and trapped

Molecules that stretch, bend, and rotate offer many new avenues for ultracold physics experiments. But they’re also harder to control.

Laser Cooling with an Intermediate State and Electronic Structure Studies of the Molecules CaCs and CaNa.

The ground and excited electronic states of the diatomic molecules CaCs and CaNa have been investigated by implementing the ab initio CASSCF/(MRCI + Q) calculation. The potential energy curves of the doublet and quartet electronic low energy states in the representation 2s+1Λ(±) have been determined for the two considered molecules, in addition to the spectroscopic constants Te, ωe, Be, Re, and the values of the dipole moment μe and the dissociation energy De. The determination of vibrational constants Ev, Bv, Dv, and the turning points Rmin and Rmax up to the vibrational level v = 100 was possible with the use of the canonical functions schemes. Additionally, the transition and the static dipole moments curves, Einstein coefficients, the spontaneous radiative lifetime, the emission oscillator strength, and the Franck–Condon factors are computed. These calculations showed that the molecule CaCs is a good candidate for Doppler laser cooling with an intermediate state. A “four laser” cooling scheme is presented, along with the values of Doppler limit temperature TD = 55.9 μK and the recoil temperature Tr = 132 nK. These results should provide a good reference for experimental spectroscopic and ultra-cold molecular physics studies.

Evidence for the association of triatomic molecules in ultracold 23Na40K + 40K mixtures.

Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics and quantum simulation with molecules1-3. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in a mixture of ultracold atoms and diatomic molecules by using a Feshbach resonance between them4,5. Although ultracold atom-diatomic-molecule Feshbach resonances have been observed recently6,7, using these resonances to form triatomic molecules remains challenging. Here we report on evidence of the association of triatomic molecules near the Feshbach resonance between 23Na40K molecules in the rovibrational ground state and 40K atoms. We apply a radio-frequency pulse to drive the free-bound transition in ultracold mixtures of 23Na40K and 40K and monitor the loss of 23Na40K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature. The observation that the distance between the association feature and the atomic transition changes with the magnetic field provides strong evidence for the formation of triatomic molecules. The binding energy of the triatomic molecules is estimated from the measurements. Our work contributes to the understanding of the complex ultracold atom-molecule Feshbach resonances and may open up an avenue towards the preparation and control of ultracold triatomic molecules.

Van der Waals molecules consisting of a zinc or cadmium atom interacting with an alkali-metal or alkaline-earth-metal atom

Alkaline-earth-like transition-metal atoms such as Zn and Cd are promising candidates for precision measurements and quantum many-body physics experiments. Here, we theoretically investigate the properties of diatomic molecules containing these closed-shell atoms. We calculate potential energy curves, permanent electric dipole moments, and spectroscopic constants for molecules consisting of either a Zn or Cd atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use the ab initio electronic structure coupled cluster method with single, double, and triple excitations combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier atoms. We predict that the studied molecules in the ground electronic state are chemically reactive weakly bound van der Waals complexes with small permanent electric dipole moments. The present results may be useful for spectroscopy and application of the studied molecules in modern ultracold physics and chemistry experiments.

Ultracold atom-molecule conversion dynamics in a closed-loop three-level system

The production of ultracold molecules is one of the most exciting topics in the field of ultracold physics, which has important theoretical values and broad application prospects. We propose an ultracold atom-molecule conversion model in a closed-loop three-level system based on three available transitions, in which the population dynamics depends on three coupling fields and global phase. We investigate the atom-molecule conversion dynamics in the closed-loop three-level system. We show the distribution of population on excited molecular state and ground molecular state with arbitrary proportion can be achieved by adjusting pulse amplitudes of the external fields properly. We also explore the effects of time delay, pulse width and global phase on the conversion process. The results show that, by tuning these parameters, the stable atom-molecule conversion with arbitrary proportion can be realized.

Reducing anomalous reflection from complex absorbing potentials: A semiclassical approach

Numerical simulations are frequently required for quantum scattering problems and often face difficulties with finite grids and unwanted, unphysical reflections. For decades, improved complex absorbing potentials (CAPs) have been sought. Today, the rise of ultracold physics makes a solution essential as CAP errors increase at lower energies. We present a method that provides a physical, semiclassical picture of how to improve CAPs based on the behavior of classical trajectories. The method does not rely on the mathematical formalism often required by existing methods and reduces the error associated with CAP-based calculation of the low-energy scattering wavefunctions by up to several orders of magnitude relative to the standard Woods-Saxon approach, as demonstrated via the distorted-wave Born approximation. This indicates the method may be applied to the numerical simulation of collisions in the ultracold regime.

Dark-state sideband cooling in an atomic ensemble

We utilize the dark state in a {\Lambda}-type three-level system to cool an ensemble of 85Rb atoms in an optical lattice [Morigi et al., Phys. Rev. Lett. 85, 4458 (2000)]. The common suppression of the carrier transition of atoms with different vibrational frequencies allows them to reach a subrecoil temperature of 100 nK after being released from the optical lattice. A nearly zero vibrational quantum number is determined from the time-of-flight measurements and adiabatic expansion process. The features of sideband cooling are examined in various parameter spaces. Our results show that dark-state sideband cooling is a simple and compelling method for preparing a large ensemble of atoms into their vibrational ground state of a harmonic potential and can be generalized to different species of atoms and molecules for studying ultracold physics that demands recoil temperature and below.

Laser cooling and electronic structure studies of CaK and its ions CaK±

Aiming at a laser cooling investigation, we have used ab initio complete active space self consistent field (CASSCF)/(MRCI +Q) calculations to study the electronic structure of the diatomic molecule CaK and its molecular ions CaK+ and CaK−. The potential energy curves and the static dipole moment curves have been investigated for the considered molecules along with the spectroscopic constants T e, ω e, B e, and R e, in addition to the values of dipole moment μ e and dissociation energy D e. Overall, 19 and 14 electronic states have been studied respectively for CaK, CaK+, from which 12 for CaK and six for CaK+ have been investigated here for the first time. Our obtained results agree well with data related to states that have been previously examined. Nineteen electronic states have been explored for CaK−, which up to our knowledge have not been previously calculated. The transition dipole moments have been calculated for the lowest Σ+–Σ+ and Σ+–Π transitions along with the Franck–Condon factor, Einstein coefficient, the spontaneous radiative lifetime, and the emission oscillator strength corresponding to the investigated transitions. A ro-vibrational analysis has been done via the canonical function approach, where the vibrational parameters E v, B v, D v, and the turning points R min and R max have been determined. These calculations showed that the molecule CaK is a suitable candidate for Doppler laser cooling, and we propose a laser cooling scheme to this end. The Doppler limit temperature T D and recoil temperature T r have values as low as T D = 51 μK and T r = 156 nK. The results should provide a useful reference for experimental spectroscopic and ultra-cold molecular physics studies.

The diatomic molecular spectroscopy database

MotivationThe spectroscopy of diatomic molecules is an important research area in chemical physics due to its relevance in astrochemistry, combustion chemistry, and ultracold physics. However, there is currently no database where the user can easily retrieve, in a useful format, the spectroscopic constants of a given molecule. A similar situation appears concerning the vibrational Franck–Condon factors for diatomic molecules, a crucial parameter to infer laser cooling prospects for molecules. To address this problem, and inspired by the idea that data should be open and freely accessible, we have developed a user-friendly website (https://rios.mp.fhi.mpg.de) where the user can retrieve spectroscopic constants and Franck–Condon factors in useful formats.ImplementationIn this database, the spectroscopic constants of the ground states and first excited states of the diatomic molecules are accessible from the website and can be retrieved in readable formats. The website is implemented within the LAMP web service stacks. In particular, using Linux as the operative system, Apache as the HTTP Server, MySQL as the database management system, and PHP as the programming language for the web. Furthermore, the user can register and upload new data. This project is licensed under the Free-Libre/Open Source Software (FLOSS) license Apache License 2.0 which allows free and open access to the codes as well as efficient collaboration in the maintenance of the software.Conclusions and impactThe present data-driven website presents essential information in a user-friendly manner and may help the chemical physics community to identify molecules that should be explored through spectroscopic techniques.

Bose-Einstein Condensate Comagnetometer.

We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8)dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.

All-Optical Bose-Einstein Condensates in Microgravity

We report on the all-optical production of Bose-Einstein condensates in microgravity using a combination of grey molasses cooling, light-shift engineering and optical trapping in a painted potential. Forced evaporative cooling in a 3-m high Einstein elevator results in 4×10^{4} condensed atoms every 13.5s, with a temperature as low as 35nK. In this system, the atomic cloud can expand in weightlessness for up to 400ms, paving the way for atom interferometry experiments with extended interrogation times and studies of ultracold matter physics at low energies on ground or in Space.

Bound and field: Programs for calculating bound states of interacting pairs of atoms and molecules

The bound program calculates the bound states of a complex formed from two interacting particles using coupled-channel methods. It is particularly suitable for the bound states of atom–molecule and molecule–molecule van der Waals complexes and for the near-threshold bound states that are important in ultracold physics. It uses a basis set for all degrees of freedom except R, the separation of the centres of mass of the two particles. The Schrödinger equation is expressed as a set of coupled equations in R. Solutions of the coupled equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, and rigid diatom + asymmetric top. Both programs provide an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in. With appropriate plug-in routines, bound can take account of the effects of external electric, magnetic and electromagnetic fields, locating bound-state energies at fixed values of the fields. The related program field uses the same plug-in routines and locates values of the fields where bound states exist at a specified energy. As a special case, it can locate values of the external field where bound states cross scattering thresholds and produce zero-energy Feshbach resonances. Plug-in routines are supplied to handle the bound states of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. Program summaryProgram Titles:bound and fieldProgram Files doi:http://dx.doi.org/10.17632/rtzgf5mwpn.1Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Solve the Schrödinger equation to locate the bound states of an interacting pair of atoms or molecules as a function of energy (for bound) or external field (for field).Solution method: The Schrödinger equation is expressed in terms of coupled equations in the interparticle distance, R. Solutions of the coupled-channel equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Bound states exist at energies where one of the eigenvalues of the log-derivative matching matrix is zero. bound calculates the number of bound states in a specified range of energy and then converges on the bound-state energies. field operates in a similar manner to bound but converges on bound states as a function of external field at fixed energy, or energy fixed with respect to a field-dependent threshold energy. The programs can also generate bound-state wavefunctions if desired.Unusual features:1. The programs include Hamiltonians for simple atom–molecule and molecule–molecule interactions, and provide an interface that allows users to specify Hamiltonians and basis sets for more complex systems. This interface allows users to include multiple external fields in the Hamiltonian.2. The programs can propagate very efficiently to long range, making them particularly suited to locating very high-lying bound states.

Development on quantum metrology with quantum Fisher information

Quantum metrology is one of the hot topics in ultra-cold atoms physics. It is now well established that with the help of entanglement, the measurement sensitivity can be greatly improved with respect to the current generation of interferometers that are using classical sources of particles. Recently, Quantum Fisher information plays an important role in this field. In this paper, a brief introduction on Quantum metrology is presented highlighting the role of the Quantum Fisher information. And then a brief review on the recent developments for i) criteria of multi-particle entanglement and its experimental generation; ii) linear and non-linear atomic interferometers; iii) the effective statistical methods for the analysis of the experimental data.

Ultracold dipolar molecules

The research field of ultracold atoms has expanded from atomic and molecular physics to a variety of fields. Ultracold polar molecules have long range and anisotropic dipole-dipole interactions, and similar to atoms, can also be conveniently manipulated by laser and other electromagnetic fields. Thus, ultracold molecules offer promising applications such as ultracold chemistry, quantum simulation, and quantum information. However, due to the difficulty in creating ultracold ground state molecules, expanding the horizon of ultracold physics from atoms to molecules is still under development. In the past decade, many research groups have successfully created bi-alkali rovibrational ground state polar molecules using magneto association and stimulated Raman adiabatic passage (STIRAP). This paper presents a review of the recent progress including creating and manipulating ultracold molecules with this method, and the collision property of molecules at ultracold temperature.

A procedure for high-accuracy numerical derivation of the thermodynamic properties of ideal Bose gases

The thermodynamic functions of ideal Bose gases are important in fundamental physics and have been widely studied via both analytical and numerical methods. Studying these functions is important for undergraduates as it is the first step for exploring ultracold physics and quantum phenomena. However, the accuracy of the calculations is usually limited owing to the discontinuity of the functions at critical points. In this study, we present an analytical procedure for deriving the chemical potential, the total energy, and the heat capacity as functions of the absolute temperature. The approximated analytical results are compared with values obtained using the numerical method to evaluate their accuracy and to determine the applicable range of the procedure. Moreover, a correction for the chemical potential calculated around the critical temperature was proposed to reduce the deviation between the approximated and numerical approaches.