We propose an ultracold-atom setting where a fermionic superfluidity with attractive s-wave interaction is uploaded in a non-Hermitian Lieb optical lattice. The existence of a real-energy flat band solution is revealed. We show that the interplay between the skin effect and flat-band localization leads to exotic localization properties. We develop a multiband mean-field description of this system and use both order parameters and superfluid weight to describe the phase transition. A relation between the superfluid weight and non-Hermitian quantum metric of the quantum states manifold is built. We find non-monotone criticality depending on the non-Hermiticity, and the non-reciprocity prominently enhances the phase coherence of the pairing field, suggesting ubiquitous critical behavior of the non-Hermitian fermionic superfluidity.
Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of non-diagonalizable exceptional points, lines, and s…
The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invarian…
Berezinskii-Kosterlitz-Thouless (BKT) transition, the topological phase transition to a quasi-long range order in a two-dimensional (2D) system, is a hallmark of low-dimensional topological physics. The recent emergence of non-Hermitian physics, particularly parity-time ($\mathcal{PT}$) symmetry, raises a natural question about the fate of low-dimensional orders (e.g., BKT transition) in the presence of complex energy spectrum. Here we investigate the BKT phase transition in a 2D degenerate Fermi gas with an imaginary Zeeman field obeying $\mathcal{PT}$-symmetry. Despite complex energy spectru…
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here, we provide a general result for the superfluid weight $D_{\rm s}$ of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number $C$. We find that the integral over the Brillouin zone of the quantum metric, an invariant calculated from the Bloch functions, …
The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure invariant obtained from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BC…
Recently spin-orbit (SO) coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in suitable parameter region the lowest Bloch state forms an isolated flat band in a one dimensional (1D) SO coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flat band physics in lattice s…
Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to such flat bands. In parallel, theory work has discovered that superconductivity and superfluidity is determined by the quantum geometry and topology of the band structure. These recent key developments are merging to a flourishing research topic: understanding the possible connection and ramifications of quantum geometry on the induced superconductivity and su…
At low temperatures bosons typically condense to minimize their single-particle kinetic energy while interactions stabilize superfluidity. Optical lattices with artificial spin-orbit coupling challenge this paradigm because here kinetic energy can be quenched in an extreme regime where the single-particle band flattens. To probe the fate of superfluidity in the absence of kinetics we construct and numerically solve interaction-only tight-binding models in flat bands. We find that novel superfluid states arise entirely from interactions operating in quenched kinetic energy bands, thus revealing…
Quantum Geometry, Anomalous Scaling, and Strong Pseudogap Superfluidity in a Flat-Band Lieb Lattice
Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）；Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（上海量子科学研究中心和中国科学院量子信息科学与技术重点实验室，中国科学技术大学）；Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（合肥微尺度物质科学国家研究中心和物理学院，中国科学技术大学）；Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University（人工结构力学与量子控制重点实验室，物理与天文学院，上海交通大学）
Hydrodynamic phenomena can be observed with light thanks to the analogy between quantum gases and nonlinear optics. In this Letter, we report an experimental study of the superfluid-like properties of light in a (1+1)-dimensional nonlinear optical mesh lattice, where the arrival time of optical pulses plays the role of a synthetic spatial dimension. A spatially narrow defect at rest is used to excite sound waves in the fluid of light and measure the sound speed. The critical velocity for superfluidity is probed by looking at the threshold in the deposited energy by a moving defect, above which…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
Competition between pair and single-particle superfluidity in bosonic quasi-flat bands: A Gaussian state approach
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；International Solvay Institutes（国际索尔维研究所）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（巴黎文理研究大学卡斯勒布罗塞尔实验室）
In this letter we consider spinless bosons in a Kagome lattice with nearest-neighbor hopping and on-site interaction, and the sign of hopping is inverted by insetting a π flux in each triangle of Kagome lattice so that the lowest single particle band is perfectly flat. We show that in the high density limit, despite of the infinite degeneracy of the single particle ground states, interaction will select out the Bloch state at the K point of Brillouin zone for boson condensation at the lowest temperature. As temperature increases, the single boson superfluid order can be easily destroyed, while…
We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory (DMFT). The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial su…
The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-$1$ non-Hermitian Hamiltonian) with the complex hopping and flat band in the context of a polariton condensate, with the emphasis on the higher spin degree of freedom on topological properties of non-Hermitian Hamiltonian. The topological inva…
Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas these intriguing phenomena have been considered peculiar to non-Hermitian systems, we show that they can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces. For instance, prototypical one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to th…
There is a growing interest in using cold-atom systems to explore the effects of strong interactions in topological band structures. Here we investigate interacting bosons in a Cruetz ladder, which is characterised by topological flat energy bands where it has been proposed that interactions can lead to the formation of bound atomic pairs giving rise to pair superfluidity. By investigating realistic experimental implementations, we understand how the lattice topology enhances the properties of bound pairs giving rise to relatively large effective pair-tunnelling in these systems which can lead…
Tunable exciton condensates in two dimensional electron gas systems under strong magnetic field exhibits anomalous Hall transport owing to mutual Coulomb coupling, and have attracted a lot of research activity. Here, we explore another framework using topological flat band models in the absence of Landau levels, for realizing the many-body exciton phases of two-component fermions under strong intercomponent interactions. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we show the theoretical discovery of the emergence of…
