Ultracold Gases Research Articles

Finite-temperature ferromagnetic transition in coherently coupled Bose gases

A paramagnetic-ferromagnetic quantum phase transition is known to occur at zero temperature in a two-dimensional coherently coupled Bose mixture of dilute ultracold atomic gases provided the interspecies interaction strength is large enough. Here we study the fate of such a transition at finite temperature by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii formalism, which includes both thermal and beyond mean-field effects. By extracting the average magnetization, the magnetic fluctuations and characteristic relaxation frequency (or critical slowing down), we identify a finite-temperature critical line for the transition. We find that the critical point shifts linearly with temperature and, in addition, the three quantities used to probe the transition exhibit a temperature power-law scaling. The scaling of the critical slowing down is found to be consistent with thermal critical exponents and is very well approximated by the square of the spin excitation gap at zero temperature.

Thermodynamics of decoherence

We investigate the non-equilibrium thermodynamics of pure decoherence. In a pure decoherence process, the system Hamiltonian is a constant of motion and there is no direct energy exchange between the system and its surroundings. Nevertheless, the environment’s energy is not generally conserved and in this work we show that this leads to non-trivial heat dissipation as a result of decoherence alone. This heat has some very distinctive properties: it obeys an integral fluctuation relation and can be interpreted in terms of the entropy production associated with populations in the energy eigenbasis of the initial state. We show that the heat distribution for a pure decoherence process is different from the distribution of work done by the initial system–bath interaction quench. Instead, it corresponds to a mixture of work distributions of cyclical processes, each conditioned on a state of the open system. Inspired by recent experiments on impurities in ultracold gases, we demonstrate our general results by studying the heat generated by the decoherence of a qubit immersed within a degenerate Fermi gas in the lowest band of a species-selective optical lattice.

Finite temperature phases and excitations of bosons on a square lattice: a cluster mean field study

We study the finite temperature phases and collective excitations of hardcore as well as softcore bosons on a square lattice with nearest and next nearest neighbor interactions, focusing on the formation of various types of supersolid (SS) phases and their stability under thermal fluctuations. The interplay between the on-site, nearest, and next nearest neighbor interactions leads to various density ordering and structural transitions, which we have plotted out. Thermodynamic properties and phase diagrams are obtained by cluster mean field theory at finite temperatures, which includes quantum effects systematically, and they are compared with the single-site mean field (MF) results. We investigate the melting process of the SS phase to normal fluid (NF), which can occur in at least two steps due to the presence of two competing orders in the SS. A tetra-critical point exists at finite temperature and exhibits intriguing behavior, which is analyzed for different regimes of interactions. The phase diagrams reveal the different pathways of the thermal transition of SSs to the NF phase, for different interaction regimes, which can be accessible by thermal quench protocols used in recent experiments. We show how the phases and the transitions between them can be identified from the characteristic features of the excitation spectrum. We analyze the appearance of a low-energy gapped mode apart from the gapless sound mode in the SS phase, which is analogous to the gapped mode recently studied for dipolar SS phases. Finally, we discuss the relevance of the results of the present work in the context of ongoing experiments on ultracold atomic gases and newly observed SS phases.

Two-dimensional polaron spectroscopy of Fermi superfluids

Multidimensional spectroscopy is becoming an increasingly popular tool and there is an ongoing effort to access electronic transitions and many-body dynamics in correlated materials. We apply the protocol recently proposed by Wang [Phys. Rev. A 107, 013305 (2023)] to extract two-dimensional polaron spectra in a Fermi superfluid with an impurity. The bath is described by a BCS ansatz and it assumed that the impurity can scatter at most one quasiparticle pair. The spectral response contains a symmetric contribution, which carries the same information as Ramsey spectra, and an asymmetric one. While a priori it may seem promising to probe the quasiparticle gap from the asymmetric contribution, we show explicitly that this is not the case and, in the absence of incoherent processes, multidimensional spectroscopy does not bring much additional information. Our calculation is suitable for ultracold gases, but we discuss implications for exciton polarons in two-dimensional materials.

Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices

Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimension lower than the bulk have significantly opened a new perspective for understanding of topological quantum matters. Here, we propose to generate two-dimensional topological boundary states for implementing synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices, which includes Chern insulator, Dirac semimetals, and second-order topological phase (SOTP) by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of bulk, Wilson loop spectra, and the spin textures at the higher symmetric points of system. We show that the SOTP exhibits a pair of $0$D boundary states. While the phases of Dirac semimetals and Chern insulator support the conventional $1$D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the emerged boundary states for Dirac semimetals and SOTP are topologically protected by $\cal P T$-symmetry and chiral-mirror symmetry ($\mathcal{\widetilde{M}}_{\alpha}$), respectively. In particular, the location of $0$D corner states for SOTP which are associated with existing $\mathcal{\widetilde{M}}_{\alpha}$-symmetry can be highly manipulated by tuning magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.

Measuring nonlocal three-body spatial correlations with Rydberg trimers in ultracold quantum gases

We measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic ($^{84}\mathrm{Sr}$) and spin-polarized fermionic ($^{87}\mathrm{Sr}$) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of 6 (3!), in the case of bosonic $^{84}\mathrm{Sr}$ due to bunching and a marked reduction for spin-polarized fermionic $^{87}\mathrm{Sr}$ due to antibunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to in situ studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.

Itinerant ferromagnetism in dilute SU(N) Fermi gases

We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.

Ultracold Gas of Dipolar NaCs Ground State Molecules.

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22 000 dipolar NaCs molecules at a temperature of 300(50)nK and a peak density of 1.0(4)×10^{12} cm^{-3}. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. We measure the ground state ac polarizability at 1064nm along with the two-body loss rate, which we find to be universal. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6D at a dc electric field of 2.1(2) kV/cm and demonstrate strong microwave coupling between the two lowest rotational states with a Rabi frequency of 2π×45 MHz. A large electric dipole moment, accessible at relatively small electric fields, makes ultracold gases of NaCs molecules well suited for the exploration of strongly interacting phases of dipolar quantum matter.

Solving 2D and 3D Lattice Models of Correlated Fermions—Combining Matrix Product States with Mean-Field Theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.13 MoreReceived 8 July 2022Revised 7 December 2022Accepted 3 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011039Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFermionsSuperconductivityPhysical Systems3-dimensional systemsStrongly correlated systemsUnconventional superconductorsTechniquesBosonizationDensity matrix renormalization groupMean field theoryCondensed Matter, Materials & Applied Physics

Vortices number and the critical atoms number of a rotating Bose–Einstein condensates in two-dimensional optical lattice

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential [Formula: see text]. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

Ultrafast dynamics of cold Fermi gas after a local quench

The authors show that the von Neumann entropy production induced by the local quench in a Fermi gas is an ultrafast process independent of the thermal flow and defining the system's dynamics on a timescale of the Fermi time. In ultracold atomic gases where the Fermi time is a fraction of a millisecond, this provides a possibility to track quantum correlations' generation at finite temperature.

Disordered structures in ultracold spin-imbalanced Fermi gas

We investigate properties of spin-imbalanced ultracold Fermi gas in a large range of spin polarizations at low temperatures. We present results of microscopic calculations based on mean-field and density functional theory approaches, with no symmetry constraints. At low polarization values we predict the structure of the system as consisting of several spin-polarized droplets. As the polarization increases, the system self-organizes into a disordered structures similar to liquid crystals, and energetically they can compete with ordered structures such as grid-like domain walls. At higher polarizations the system starts to develop regularities that, in principle, can be called supersolid, where periodic density modulation and pairing correlations coexist. The robustness of the results has been checked with respect to temperature effects, dimensionality, and the presence of a trapping potential. Dynamical stability has also been investigated.

Lev Petrovich Pitaevskii

Lev Petrovich Pitaevskii

Mixtures of ultracold atomic gases in optical lattices with nonzero pair or counterflow hopping

We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.

Equatorial waves in rotating bubble-trapped superfluids

As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation by a Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian is topologically nontrivial. Furthermore, we solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.

Raman laser induced self-organization with topology in a dipolar condensate.

We investigate the ground states of a dipolar Bose-Einstein condensate (BEC) subject to Raman laser induced spin-orbit coupling with mean-field theory. Owing to the interplay between spin-orbit coupling and atom-atom interactions, the BEC presents remarkable self-organization behavior and thus hosts various exotic phases including vortex with discrete rotational symmetry, stripe with spin helix, and chiral lattices with C4 symmetry. The peculiar chiral self-organized array of square lattice, which spontaneously breaks both U(1) and rotational symmetries, is observed when the contact interaction is considerable in comparison with the spin-orbit coupling. Moreover, we show that the Raman-induced spin-orbit coupling plays a crucial role in forming rich topological spin textures of the chiral self-organized phases by introducing a channel for atoms to turn on spin flipping between two components. The self-organization phenomena predicted here feature topology owing to spin-orbit coupling. In addition, we find long-lived metastable self-organized arrays with C6 symmetry in the case of strong spin-orbit coupling. We also present a proposal to observe these predicted phases in ultracold atomic dipolar gases with laser-induced spin-orbit coupling, which may stimulate broad theoretical as well as experimental interest.

Quantum-fluctuation-driven dynamics of droplet splashing, recoiling, and deposition in ultracold binary Bose gases

Droplet impact on a surface is practically relevant to a variety of fields in nature and industry, while a complete control of its outcomes remains challenging due to various unmanageable factors. In this work, we propose the quantum simulation of droplet impact outcomes in the platform of ultracold atoms. Specifically, we study the quantum-fluctuation-driven dynamics (QFDD) of two-dimensional Bose-Bose mixtures from an initial Townes soliton towards the formation of a quantum droplet. By tuning the fluctuation energy of the initial Townes state through its size and number, the subsequent QFDD can produce various outcomes including splashing, recoiling, and deposition, similar to those in droplet impact dynamics. We have utilized the Weber number to identify the thresholds of splashing and recoiling, and further established a universal scaling law between the maximum spreading factor and the Weber number in the recoiling regime. In addition, we show that the residual QFDD in the deposition regime can be used to probe the collective breathing modes of a quantum droplet. Our results reveal a mechanism for the droplet impact outcomes, which can be directly tested in cold-atom experiments and can pave the way for exploring intriguing droplet dynamics in a clean and fully controlled quantum setting.

Universal intrinsic higher-rank spin tensor Hall effect

The spin Hall effect with nonzero transverse spin current but vanishing charge current has important applications in spintronics. Owing to the half-spin nature of electrons, the spin transport has hitherto been restricted to the rank-1 spin vector, whereas higher-rank spin tensors exist and play important roles in larger-spin ($\ensuremath{\ge}1$) systems. For instance, there are five linearly independent rank-2 spin quadrupole tensors, characterizing the spin nematics, in a spin-1 system. While these internal spin-tensor degrees of freedom substantially enrich the quantum phases and dynamics of large-spin ultracold gases, the quantum transport of spin tensors remains largely unexplored yet. Here we investigate the higher-rank spin tensor current and introduce the concept of the spin tensor Hall effect (STHE) in a large-spin system. We find that a net transverse spin tensor current can be driven by an external field in the longitudinal direction, while no lower-rank spin or charge current exists. Significantly, we identify a universal rank-2 spin tensor Hall conductivity $q/8\ensuremath{\pi}$ (with the carrier charge $q$) in a spin-1 model with intrinsic spin-orbit coupling, which is independent of the detailed model parameters. The STHE requires the violation of time-reversal symmetry (TRS) but can be protected by a unique pseudo-TRS associated with the rank-2 spin tensor. An experimental scheme is proposed to realize and detect the STHE with pseudospin-1 ultracold fermionic atoms and through the spin tensor accumulation. A general route towards the generalization of the STHE for larger spins is provided, using the SU(2) subalgebra and generalized Gell-Mann matrix representation of the $\mathrm{SU}(N$) group. Our work reveals an intrinsic spin tensor transport phenomenon and introduce a new member to the Hall effect families, which may pave the way to spin-tensor-tronics.

Carnot Cycles in a Harmonically Confined Ultracold Gas across Bose–Einstein Condensation

Carnot cycles of samples of harmonically confined ultracold 87Rb fluids, near and across Bose-Einstein condensation (BEC), are analyzed. This is achieved through the experimental determination of the corresponding equation of state in terms of the appropriate global thermodynamics for non-uniform confined fluids. We focus our attention on the efficiency of the Carnot engine when the cycle occurs for temperatures either above or below the critical temperature and when BEC is crossed during the cycle. The measurement of the cycle efficiency reveals a perfect agreement with the theoretical prediction (1-TL/TH), with TH and TL serving as the temperatures of the hot and cold heat exchange reservoirs. Other cycles are also considered for comparison.