We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting effective two-particle potential with an oscillating behaviour. For this system we calculate the spectrum and the wave functions of the bound states. The full quantum solutions show clear imprints of the tendency for the system to form chains of dipoles along the helix, i.e. a configuration in which the dipoles are sitting approximately one winding of the helix apart so that they can take maximal advantage of the strong head-to-tail attraction that is a generic feature of the dipole-dipole interaction.
We consider crystal formation of particles with dipole-dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis of the confining helix. The stable classical lowest energy configurations are found to be chain structures for a large range of pitch-to-radius ratios for relatively low density of dipoles and a moderate total number of particles. The classical normal mode spectra support the chain interpretation both through structure and the distinct degeneracies depending discretely on the number of dipoles per r…
We consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intratube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to the case of many tubes and layers, and outline the implications of our results on many-body physics.
We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical non-destructive detection scheme that enables in-situ observation of the creation and dissociation of the few-body complexes…
We analyze the microscopic few-body properties of dipolar particles confined in two parallel quasi-one-dimensional harmonic traps. In particular, we show that an adiabatic rotation of the dipole orientation about the trap axes can drive an initially non-localized few-fermion state into a localized state with strong inter-trap pairing. For an instant, non-adiabatic rotation, however, localization is inhibited and a highly excited state is reached. This state may be interpreted as the few-body analog of a super-Tonks-Girardeau state, known from one-dimensional systems with contact interactions.
Helical spin textures in a $^{87}$Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. This evolution is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. This is confirmed by eliminating the dipolar interactions by a sequence of rf pulses and observing a suppression of the formation of the short-range domains. This study confirms the significance of magnetic dipole interactions in degenerate $^{87}$Rb F=1 spinor gases.
Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum coherent dynamics of a 3D many-spin system with dipolar interactions, and determine its critical exponents. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. The resulting dynamics of the system coherence can be localized or extended, depending o…
We consider two-dimensional bosonic dipoles oriented perpendicularly to the plane. On top of the usual two-body contact and long-range dipolar interactions we add a contact three-body repulsion as expected, in particular, for dipoles in the bilayer geometry with tunneling. The three-body repulsion is crucial for stabilizing the system, and we show that our model allows for stable continuous space supersolid states in the dilute regime and calculate the zero-temperature phase diagram.
Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the d…
Quantum many-body scars, long-lived excited states of correlated quantum chaotic systems that evade thermalization, are of great fundamental and technological interest. We create novel scar states in a bosonic 1D quantum gas of dysprosium by stabilizing a super-Tonks-Girardeau gas against collapse and thermalization with repulsive long-range dipolar interactions. Stiffness and energy density measurements show that the system is dynamically stable regardless of contact interaction strength. This enables us to cycle contact interactions from weakly to strongly repulsive, then strongly attractive…
The most direct approach for characterizing the quantum dynamics of a strongly-interacting system is to measure the time-evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate framework is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Our work centers on the following question: What can the decoherence dynamics of such a probe tell us about the many-body system? In particular, we utilize optically addressable probe spins …
Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules/layers and other geometries. Our analytical findings are supported by numerical c…
We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulation…
Strongly dipolar molecular Bose-Einstein condensates: From few- to many-body physics
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子研究所，维也纳工业大学）；MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology（麻省理工学院-哈佛大学超冷原子中心，电子研究实验室，物理学系，麻省理工学院）；Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart（第五物理研究所，集成量子科学与技术中心，斯图加特大学）；Department of Physics, Columbia University（物理学系，哥伦比亚大学）；Institute for Theoretical Physics, TU Wien（理论物理研究所，维也纳工业大学）；Department of Physics, The Chinese University of Hong Kong（物理学系，香港中文大学）；Institute for Molecules and Materials, Radboud University（分子与材料研究所，拉德堡德大学）；Université Paris-Saclay, CNRS, Laboratoire Aimé Cotton（巴黎萨克雷大学，法国国家科学研究中心，阿梅·科唐实验室）
Many-body gravitating quantum systems with Bose-Einstein condensates and dipolar analogue
Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (INO-CNR)（意大利国家光学研究所，意大利国家研究委员会）；Physics Department, University of Naples Federico II（那不勒斯费德里科二世大学物理系）；European Laboratory for Nonlinear Spectroscopy (LENS)（欧洲非线性光谱学实验室）；Physics Department, University of Florence（佛罗伦萨大学物理系）
Motivated by recent experimental advances in creating polar molecular gases in the laboratory, we theoretically investigate the many body effects of two-dimensional dipolar systems with the anisotropic and $1/r^3$ dipole-dipole interactions. We calculate collective modes of 2D dipolar systems, and also consider spatially separated bilayer and multilayer superlattice dipolar systems. We obtain the characteristic features of collective modes in quantum dipolar gases. We quantitatively compare the modes of these dipolar systems with the modes of the extensively studied usual two-dimensional elect…
We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing wave optical light fields exploit…
We observe the suppression of inelastic dipolar scattering in ultracold Fermi gases of the highly magnetic atom dysprosium: the more energy that is released, the less frequently these exothermic reactions take place, and only quantum spin statistics can explain this counterintuitive effect. Inelastic dipolar scattering in non-zero magnetic fields leads to heating or to loss of the trapped population, both detrimental to experiments intended to study quantum many-body physics with strongly dipolar gases. Fermi statistics, however, is predicted to lead to a kinematic suppression of these harmful…
Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here we report on the observation of stable quantum droplets containing $\sim$ 800 atoms which are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations stabilize them against the mean-field collapse. We observe in addition interference of several droplets indicating that this stable many-body state is phase coherent.
We investigate the quantum phases of hard-core dipolar bosons confined to a square lattice in a bilayer geometry. Using exact theoretical techniques, we discuss the many-body effects resulting from pairing of particles across layers at finite density, including a novel pair supersolid phase, superfluid and solid phases. These results are of direct relevance to experiments with polar molecules and atoms with large magnetic dipole moments trapped in optical lattices.
We investigate the self-bound states of dipolar Dy condensates with the Gaussian-state ansatz which improves the conventional coherent-state ansatz with multimode squeezed coherent states. We show that the self-bound states consist of the experimentally observed self-bound liquid phase and the unobserved self-bound gas phase. The numerically obtained gas-liquid boundary is in good agreement with experimental data. Our theory also allows one to extract the real part of the three-body coupling constant of the Dy atoms from the particle number distribution of the condensates. In particular, we re…
We investigate the ground state properties and tunneling dynamics of ultracold dipolar bosons in a one dimensional triple well trap from a few-body ab-initio perspective. Our focus is primarily on the distinctive features of dipolar bosons compared to the contact interacting bosons. Formation of intra-well localization is observed for very strong dipolar interaction. General population rearangement as well as fragmentation and localization effects have been found, depending strongly on the particle number. The energy spectrum for two particles exhibits avoided crossings that lead to several di…
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to resul…
We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1Σ^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous …
A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance (NMR) observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsi…
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multi-atom Schrödinger equation, we discover that such systems can exhibit not only the well known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly…
We investigate the quench dynamics of quasi-one and two dimensional dipolar Bose-Einstein condensates (dBEC) of $^{164}$Dy atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang (LHY) correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The cr…
We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three, four, and five-body problems in two or more tubes. Our results indicate t…
Ultracold polar molecules possess long-range, anisotropic, and tunable dipolar interactions, providing the opportunities to probe quantum phenomena inaccessible with existing cold gas platforms. However, experimental progress has been hindered by the dominance of two-body loss over elastic interactions, which prevents efficient evaporative cooling. Though recent work has demonstrated controlled interactions by confining molecules to a two-dimensional geometry, a general approach for tuning molecular interactions in a three-dimensional (3D), stable system has been lacking. Here, we demonstrate …
Observing weakly broken conservation laws in a dipolar Rydberg quantum spin chain
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry（巴黎萨克雷大学、光学研究生院、法国国家科学研究中心、夏尔·法布里实验室）；Université Paris-Saclay, CNRS, Laboratoire de Physique Théorique et Modèles Statistiques（巴黎萨克雷大学、法国国家科学研究中心、理论与统计物理实验室）
We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and th…
We propose a novel platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D Transmon qubits where we use the naturally occurring dipolar interactions to realize interacting spin systems. This opens the way toward the realization of a broad class of tunable spin models in both two- and one-dimensional geometries. We illustrate the potential offered by these systems in the context of dimerized Majumdar-Ghosh-type phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder a…
Dipolar Bose-Einstein condensates have recently attracted much attention in the world of quantum many body experiments. While the theoretical principles behind these experiments are typically supported by numerical simulations, the application of optimal control algorithms could potentially open up entirely new possibilities. As a proof of concept, we demonstrate that the formation process of a single dipolar droplet state could be dramatically accelerated using advanced concepts of optimal control. More specifically, our optimization is based on a multilevel B-spline method reducing the numbe…
