Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these first results in several ways. First, we numerically benchmark the working conditions of the analog simulator, and find less demanding experimental setups where chemistry-like behaviour in three-dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behaviour of two-electron atoms (He) and molecules (HeH$^+$) beyond the example considered in the original work.
Computing the electronic structure of molecules with high precision is a central challenge in the field of quantum chemistry. Despite the enormous success of approximate methods, tackling this problem exactly with conventional computers is still a formidable task. This has triggered several theoretical and experimental efforts to use quantum computers to solve chemistry problems, with first proof-of-principle realizations done in a digital manner. An appealing alternative to the digital approach is analog quantum simulation, which does not require a scalable quantum computer, and has already b…
In the last 5 years, a novel field of physics and chemistry has developed in which cold trapped ions and ultracold atomic gases are brought into contact with each other. Combining ion traps with traps for neutral atoms yields a variety of new possibilities for research and experiments. These range from studies of cold atom-ion collisions and atom-ion chemistry to applications in quantum information science and condensed matter related research. In this article we give a brief introduction into this new field and describe some of the perspectives for its future development.
Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$_2^+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions. We extend this approach to larger systems by introducing as many media…
This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. …
Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with…
An oscillatory term is found in both the energy expectation and dynamics of a wave-packet in a time-varying harmonic trap and infinite potential well. They are proved to oscillate in coherence with the time lapse within each period depending on both the cutoff in transition energies and the specific route via which the potential is being varied. This oscillatory term is general to arbitrary potential forms since it derives from the interference between crossed transition trajectories. Close analogy is made to the Ruderman-Kittel-Kasuya-Yosida interaction for giant-magnetoresistance trilayers, …
We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated …
There has been a long-standing quest to observe chemical reactions at low temperatures where reaction rates and pathways are governed by quantum mechanical effects. So far this field of Quantum Chemistry has been dominated by theory. The difficulty has been to realize in the laboratory low enough collisional velocities between neutral reactants, so that the quantum wave nature could be observed. We report here the first realization of merged neutral supersonic beams, and the observation of clear quantum effects in the resulting reactions. We observe orbiting resonances in the Penning ionizatio…
The potential energy curves, permanent and transition dipole moments, and the static dipolar polarizability, of molecular ions composed of one alkali-metal atom and a Strontium ion are determined with a quantum chemistry approach. The molecular ions are treated as effective two-electron systems and are treated using effective core potentials including core polarization, large gaussian basis sets, and full configuration interaction. In the perspective of upcoming experiments aiming at merging cold atom and cold ion traps, possible paths for radiative charge exchange, photoassociation of a cold …
Cold atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly-periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap which should be observable in optical lattices.
Experimental setups that study laser-cooled ions immersed in baths of ultracold atoms merge the two exciting and well-established fields of quantum gases and trapped ions. These experiments benefit both from the exquisite read-out and control of the few-body ion systems as well as the many-body aspects, tunable interactions, and ultracold temperatures of the atoms. However, combining the two leads to challenges both in the experimental design and the physics that can be studied. Nevertheless, these systems have provided insights into ion-atom collisions, buffer gas cooling of ions and quantum …
Hybrid ion-atom systems provide an excellent platform for studies of state-resolved quantum chemistry at low temperatures, where quantum effects may be prevalent. Here we study theoretically the process of vibrational relaxation of an initially weakly bound molecular ion due to collisions with the background gas atoms. We show that this inelastic process is governed by the universal long-range part of the interaction potential, which allows for using simplified model potentials applicable to multiple atomic species. The product distribution after the collision can be estimated by making use of…
The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the harmonic oscillator and the angular momentum. We also introduce q-analogues of the hydrogen atom by means of a q-deformation of the Pauli equations and of the so-called Kustaanheimo-Stiefel transformation.
There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possi…
Ultra-cold atom-ion mixtures are gaining increasing interest due to their potential applications in quantum chemistry, quantum computing and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultra-cold atoms. We measured the ion's energy distribution and observed a clear deviation from Maxwell-Boltzmann to a Tsallis characterized by a power-law tail of high energies. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the io…
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca$^+$, Sr$^+$, Ba$^+$) and Yb$^+$, and between Li and Yb$^+$, are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to availabl…
Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present the first detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate signif…
A mixed system of cooled and trapped, ions and atoms, paves the way for ion assisted cold chemistry and novel many body studies. Due to the different individual trapping mechanisms, trapped atoms are significantly colder than trapped ions, therefore in the combined system, the strong binary ion$-$atom interaction results in heat flow from ions to atoms. Conversely, trapped ions can also get collisionally heated by the cold atoms, making the resulting equilibrium between ions and atoms intriguing. Here we experimentally demonstrate, Rubidium ions (Rb$^+$) cool in contact with magneto-optically …
In this work we investigate the possibility to create cold Fr$\_2$, RbFr, and CsFr molecules through photoassociation of cold atoms. Potential curves, permanent and transition dipole moments for the Francium dimer and for the RbFr and RbCs molecules are determined for the first time. The Francium atom is modelled as a one valence electron moving in the field of the Fr$^+$ core, which is described by a new pseudopotential with averaged relativistic effects, and including effective core polarization potential. The molecular calculations are performed for both the ionic species Fr$\_2^+$, RbFr$^+…
We present a theoretical analysis of optical pathways for formation of cold Ca($^1$S)Na$^+$($^1$S) molecular ions via an intermediate state. The formation schemes are based on ab initio potential energy curves and transition dipole moments calculated using effective-core-potential methods of quantum chemistry. In the proposed approach, starting from a mixture of cold trapped Ca$^+$ ions immersed into an ultracold gas of Na atoms, (NaCa)$^+$ molecular ions are photoassociated in the excited E$^{1}Σ^+$ electronic state and allowed to spontaneously decay either to the ground electronic state or a…
Radiative decay processes at cold and ultra cold temperatures for Sulfur atoms colliding with protons are investigated. The MOLPRO quantum chemistry suite of codes was used to obtain accurate potential energies and transition dipole moments, as a function of internuclear distance, between low-lying states of the SH$^{+}$ molecular cation. A multi-reference configuration-interaction (MRCI) approximation together with the Davidson correction is used to determine the potential energy curves and transition dipole moments, between the states of interest, where the molecular orbitals (MO's) are obta…
