Ultracold Quantum Gases Research Articles

Stripe-on-plane-wave phase of a binary dipolar Bose gases with soft-core long-range interactions

Long-range interactions are ubiquitous in nature and are studied in a variety of physical fields. The recent realization of soft-core long-range interaction in ultracold quantum gases broadens the research field of long-range interactions. We consider a binary Bose–Einstein condensate with both long-range dipolar and long-range soft-core interactions. The ground-state phase diagrams of the system have been mapped out in full parameter space accounting for the dipolar and soft-core long-range interactions, as well as the orientation of the dipoles. The results show that the interplay between long-range isotropic and anisotropic interactions results in a variety of ground state phases, such as supersolid, standing wave, and stripe-on-plane-wave phases. In particular, the effects of dipolar and soft-core long-range interaction, together with the orientation of the dipoles, have also been discussed in each ground state phase. The experimental feasibility of the parameters are within the current experimental capacity.

Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

Probing Quantum Speed Limits with Ultracold Gases.

Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.

Finite-temperature transport in one-dimensional quantum lattice models

The last decade has witnessed an impressive progress in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable, including the anisotropic spin-1/2 Heisenberg (also called spin-1/2 XXZ chain) and the Fermi-Hubbard model. Nevertheless, practical computations of, for instance, correlation functions and transport coefficients pose hard problems from both the conceptual and technical point of view. Only due to recent progress in the theory of integrable systems on the one hand and due to the development of numerical methods on the other hand has it become possible to compute their finite temperature and nonequilibrium transport properties quantitatively. Most importantly, due to the discovery of a novel class of quasilocal conserved quantities, there is now a qualitative understanding of the origin of ballistic finite-temperature transport, and even diffusive or super-diffusive subleading corrections, in integrable lattice models. We shall review the current understanding of transport in one-dimensional lattice models, in particular, in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, and we elaborate on state-of-the-art theoretical methods, including both analytical and computational approaches. Among other novel techniques, we discuss matrix-product-states based simulation methods, dynamical typicality, and, in particular, generalized hydrodynamics. We will discuss the close and fruitful connection between theoretical models and recent experiments, with examples from both the realm of quantum magnets and ultracold quantum gases in optical lattices.

Effect of disorder on topological charge pumping in the Rice-Mele model

Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.

Bose-Hubbard model on polyhedral graphs

Ever since the first observation of Bose-Einstein condensation in the nineties, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum mechanics. Ultracold bosonic atoms loaded in an optical lattice are usually described by the Bose-Hubbard model or a variant of it. In addition to the common insulating and superfluid phases, other phases (like density waves and supersolids) may show up in the presence of a short-range interparticle repulsion and also depending on the geometry of the lattice. We herein explore this possibility, using the graph of a convex polyhedron as "lattice" and playing with the coordination of nodes to promote the wanted finite-size ordering. To accomplish the job we employ the method of decoupling approximation, whose efficacy is tested in one case against exact diagonalization. We report zero-temperature results for two Catalan solids, the tetrakis hexahedron and the pentakis dodecahedron, for which a thorough ground-state analysis reveals the existence of insulating "phases" with polyhedral order and a widely extended supersolid region. The key to this outcome is the unbalance in coordination between inequivalent nodes of the graph. The predicted phases can be probed in systems of ultracold atoms using programmable holographic optical tweezers.

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

Pythonic Black-box Electronic Structure Tool (PyBEST). An open-source Python platform for electronic structure calculations at the interface between chemistry and physics

Pythonic Black-box Electronic Structure Tool (PyBEST) represents a fully-fledged modern electronic structure software package developed at Nicolaus Copernicus University in Toruń. The package provides an efficient and reliable platform for electronic structure calculations at the interface between chemistry and physics using unique electronic structure methods, analysis tools, and visualization. Examples are the (orbital-optimized) pCCD-based models for ground- and excited-states electronic structure calculations as well as the quantum entanglement analysis framework based on the single-orbital entropy and orbital-pair mutual information. PyBEST is written primarily in the Python programming language with additional parts written in C＋＋, which are interfaced using Pybind11, a lightweight header-only library. By construction, PyBEST is easy to use, to code, and to interface with other software packages. Moreover, its modularity allows us to conveniently host additional Python packages and software libraries in future releases to enhance its performance. The electronic structure methods available in PyBEST are tested for the half-filled 1-D model Hamiltonian. The capability of PyBEST to perform large-scale electronic structure calculations is demonstrated for the model vitamin B12 compound. The investigated molecule is composed of 190 electrons and 777 orbitals for which an orbital optimization within pCCD and an orbital entanglement and correlation analysis are performed for the first time. Program summaryProgram title: PyBESTCPC Library link to program files:https://doi.org/10.17632/xf9kb7yfwr.1Developer’s repository link:https://zenodo.org/record/3925278#.X5KAZS8Rq6sLicensing provisions: GNU General Public License 3Programming language:Python, C＋＋Nature of problem: Efficient and reliable modeling of electronic structures featuring both weakly- and strongly-correlated electrons. Small- and large-scale quantum-mechanical problems at the interface between chemistry and physics comprising both quantum chemical and model Hamiltonians. Specifically, modeling potential energy surfaces of complex electronic structures including bond breaking/formation, elucidating complex electronic structures through the picture of interacting orbitals, describing noncovalent interactions, ultra-cold trapped quantum gases, and a variety of applications in interdisciplinary quantum mechanical-based problems.Solution method: Modular implementation of a series of unconventional (and conventional) electronic structure models based on the pCCD ansatz to solve the electronic Schrödinger equation. These include the description of both ground- and excited-states, the determination of interaction energies, and the analysis and interpretation of electronic wavefunctions. All modules are implemented in the modern Python programming language, where bottleneck operations are handled by C＋＋ code interfaced by the Pybind11 header-only library. The implemented (wavefunction) modules and modular code structure make PyBEST a very efficient alternative to existing electronic structure packages.Additional comments including restrictions and unusual features:PyBEST features unconventional electronic structure methods (pCCD and post-pCCD methods) that are not available in any other quantum chemistry/physics software package. It also includes a general orbital entanglement and correlation module that supports both pCCD and selected post-pCCD methods. PyBEST is designed to be easy to use and code in. Due to its modularity (for instance of the tensor contraction engine), new Python modules and features can be straightforwardly imported and exploited without changing any wavefunction modules directly.

Direct control of high magnetic fields for cold atom experiments based on NV centers

In ultracold quantum gases, the interactions between the individual atoms can be controlled by applying magnetic bias fields. As magnetic field fluctuations limit the precision here, typically a feedback loop needs to be employed to regulate the current through a pair of Helmholtz coils. No commercially available magnetic field sensor allows to measure large fields directly with high enough precision, leading to many unsatisfactory solutions being used in experiments. Here, we demonstrate a direct magnetic field stabilization in a regime previously not accessible, using NV centers as the magnetic field sensor. This allows us to measure and stabilize fields of 4.66 mT down to 12 nT RMS noise over the course of 24 h, measured on a 1 Hz bandwidth. We achieve a control of better than 1 ppm after 20 min of integration time, ensuring high long-term stability for experiments. This approach extends direct magnetic field control to strong magnetic fields, which could enable new precise quantum simulations in this regime.

Dynamical phase diagram of ultracold Josephson junctions

We provide a complete study of the phase diagram characterising the distinct dynamical regimes emerging in a three-dimensional Josephson junction in an ultracold quantum gas. Considering trapped ultracold superfluids separated into two reservoirs by a barrier of variable height and width, we analyse the population imbalance dynamics following a variable initial population mismatch. We demonstrate that as the chemical potential difference is increased, the system transitions from Josephson plasma oscillations to either a dissipative (in the limit of low and narrow barriers) or a self-trapped regime (for large and wider barriers), with a crossover between the dissipative and the self-trapping regimes which we explore and characterize for the first time. This work, which extends beyond the validity of the standard two-mode model, connects the role of the barrier width, vortex rings and associated acoustic emission with different regimes of the superfluid dynamics across the junction, establishing a framework for its experimental observation, which is found to be within current experimental reach.

Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate

We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resolved field-dissociation technique to trace the relaxation dynamics of the recombination products. Our observations are in good agreement with numerical simulations based on Langevin capture dynamics and provide complementary means to study stability and reaction dynamics of ionic impurities in ultracold quantum gases.

Self-bound supersolid stripe phase in binary Bose-Einstein condensates

Supersolidity - a coexistence of superfluidity and crystalline or amorphous density variations - has been vividly debated ever since its conjecture. While the initial focus was on helium-4, recent experiments uncovered supersolidity in ultra-cold dipolar quantum gases. Here, we propose a new self-bound supersolid phase in a binary mixture of Bose gases with short-range interactions, making use of the non-trivial properties of spin-orbit coupling. We find that a first-order phase transition from a self-bound supersolid stripe phase to a zero-minimum droplet state of the Bose gas occurs as a function of the Rabi coupling strength. These phases are characterized using the momentum distribution, the transverse spin polarization and the superfluid fraction. The critical point of the transition is estimated in an analytical framework. The predicted density-modulated supersolid stripe and zero-minimum droplet phase should be experimentally observable in a binary mixture of $^{39}$K with spin-orbit coupling.

Ideal Weyl semimetal with 3D spin-orbit coupled ultracold quantum gas

There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional (3D) spin-orbit (SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics.

Quantum density anomaly in optically trapped ultracold gases

We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-like anomalies in the area of ultracold quantum gases.

Exploring event horizons and Hawking radiation through deformed graphene membranes

Analogue gravitational systems are becoming an increasing popular way of studying the behaviour of quantum systems in curved spacetime. Setups based on ultracold quantum gases in particular, have been recently harnessed to explore the thermal nature of Hawking’s and Unruh’s radiation that was theoretically predicted almost 50 years ago. For solid state implementations, a promising system is graphene, in which a link between the Dirac-like low-energy electronic excitations and relativistic quantum field theories has been unveiled soon after its discovery. This link could be extended to the case of curved quantum field theory when the graphene sheet is shaped in a surface of constant negative curvature, known as Beltrami’s pseudosphere. Here we provide numerical evidence that energetically stable negative curvature graphene surfaces can be realized. Owing to large-scale simulations, our geometrical realizations are characterized by a ratio between the carbon–carbon bond length and the pseudosphere radius small enough to allow the formation of an analog of a black hole event horizon. Additionally, from the energy dependence of the spatially resolved density of states, we infer some thermal properties of the corresponding gravitational system, which could be investigated using low temperature scanning tunnelling microscopy or optical near field spectroscopy. These findings pave the way to the realization of a solid-state system in which the curved spacetime dynamics of quantum many body systems can be investigated.

Synthetic magnetic fields for cold erbium atoms

The implementation of the fractional quantum Hall effect in ultracold atomic quantum gases remains, despite substantial advances in the field, a major challenge. Since atoms are electrically neutral, a key ingredient is the generation of sufficiently strong artificial gauge fields. Here we theoretically investigate the synthetization of such fields for bosonic erbium atoms by phase imprinting with two counterpropagating optical Raman beams. Given the nonvanishing orbital angular momentum of the rare-earth atomic species erbium in the electronic ground state and the availability of narrow-line transitions, heating from photon scattering is expected to be lower than in atomic alkali-metal species. We give a parameter regime for which strong synthetic magnetic fields with good spatial homogeneity are predicted. We also estimate the size of the Laughlin gap expected from the s-wave contribution of the interactions for typical experimental parameters of a two-dimensional atomic erbium microcloud. Our analysis shows that cold rare-earth atomic ensembles are highly attractive candidate systems for experimental explorations of the fractional quantum Hall regime.

Effect of Inter-Well Interactions on Non-Linear Beam Splitters for Matter-Wave Interferometers

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of either coherent, or Twin-Fock, or NOON states. We first review the non-interacting limit and the case in which only the local interaction is present, including the study of sensitivity near the self-trapping threshold. Then, we consider the two-mode model in the presence of inter-well interactions and consider the scaling of the sensitivity as a function of the non-local coupling strength. Our analysis clearly shows that non-local interactions can compensate the degradation of the sensitivity induced by local interactions, so that they may be used to restore optimal sensitivity.

A digital feedback controller for stabilizing large electric currents to the ppm level for Feshbach resonance studies.

Magnetic Feshbach resonances are a key tool in the field of ultracold quantum gases, but their full exploitation requires the generation of large, stable magnetic fields up to 1000 G with fractional stabilities of better than 10-4. Design considerations for electromagnets producing these fields, such as optical access and fast dynamical response, mean that electric currents in excess of 100 A are often needed to obtain the requisite field strengths. We describe a simple digital proportional-integral-derivative current controller constructed using a field-programmable gate array and off-the-shelf evaluation boards that allows for gain scheduling, enabling optimal control of current sources with non-linear actuators. Our controller can stabilize an electric current of 337.5 A to the level of 7.5 × 10-7 in an averaging time of 10 min and with a control bandwidth of 2 kHz.

Some recent progresses on the study of ultracold quantum gases with spin-orbit coupling

Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.

Laser-Assisted Self Induced Feshbach Resonance : a new tool for controlling ultracold atomic collisions

SynopsisWe propose a new kind of Feshbach Resonance (FR) : the Laser-Assisted Self-Induced Feshbach Resonance (LASIFR), applicable for all mixtures of ultracold atoms. The interspecies scattering length characterizing elastic collisions, a key property for many applications of ultracold quantum gases, can be controlled by a LASIFR through the laser intensity and the frequency. It can be also used for the formation of ultracold polar molecules.