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In this paper, we consider the generalized inverse iteration for computing ground states of the Gross–Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross–Pitaevskii operator, recovering the same rates as for linear eigenvector problems. With this we establish the first local convergence result for the basic inverse iteration for the GPE without damping. We also show how our findings directly generalize to extended inverse iterations, such as the Gradient Flow Discrete Normalized (GFDN) proposed in [W. Bao and Q. Du, Computing the ground state solution of Bose–Einstein condensates by a normalized gradient flow, SIAM J. Sci. Comput. 25 (2004) 1674–1697] or the damped inverse iteration suggested in [P. Henning and D. Peterseim, Sobolev gradient flow for the Gross–Pitaevskii eigenvalue problem: Global convergence and computational efficiency, SIAM J. Numer. Anal. 58 (2020) 1744–1772]. Our analysis also reveals why the inverse iteration for the GPE does not react favorably to spectral shifts. This empirical observation can now be explained with a blow-up of a weighting function that crucially contributes to the convergence rates. Our findings are illustrated by numerical experiments.

For an action of a finite cyclic group $F$ on an $n$-dimensional noncommutative torus $A_\theta,$ we give sufficient conditions when the fundamental projective modules over $A_\theta$, which determine the range of the canonical trace on $A_\theta,$ extend to projective modules over the crossed product C*-algebra $A_\theta \rtimes F.$ Our results allow us to understand the range of the canonical trace on $A_\theta \rtimes F$, and determine it completely for several examples including the crossed products of 2-dimensional noncommutative tori with finite cyclic groups and the flip action of $\mathbb{Z}_2$ on any $n$-dimensional noncommutative torus. As an application, for the flip action of $\mathbb{Z}_2$ on a simple $n$-dimensional torus $A_\theta$, we determine the Morita equivalence class of $A_\theta \rtimes \mathbb{Z}_2,$ in terms of the Morita equivalence class of $A_\theta.$, Comment: 19 pages, minor corrections. To appear in the Journal of Noncommutative Geometry

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell., 91 pages, 1 figure

We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the system is a convex superposition of minimizers of a 3D energy-critical nonlinear Schr\"odinger functional where the nonlinear coupling constant is proportional to the scattering energy of the interaction potential. In particular, the $N$-body ground state exhibits complete Bose--Einstein condensation if the nonlinear Schr\"odinger minimizer is unique up to a complex phase., Comment: 57 pages

Turbulent phenomena are among the most striking effects that both classical and quantum fluids can exhibit. While classical turbulence is ubiquitous in nature, the observation of quantum turbulence requires the precise manipulation of quantum fluids such as superfluid helium or atomic Bose-Einstein condensates. In this work we demonstrate the turbulent dynamics of a 2D quantum fluid of exciton-polaritons, hybrid light-matter quasiparticles, both by measuring the kinetic energy spectrum and showing the onset of vortex clustering. We demonstrate that the formation of clusters of quantum vortices is triggered by the increase of the incompressible kinetic energy per vortex, showing the tendency of the vortex-gas towards highly excited configurations despite the dissipative nature of our system. These results lay the basis for the investigations of quantum turbulence in two-dimensional fluids of light.

Excitons, Coulomb-bound electron-hole pairs, play a fundamental role in both optical excitation and correlated phenomena in solids. When an exciton interacts with other quasi-particles, few- and many-body excited states, such as trions, exciton Fermi-polarons, Mahan excitons can appear. Here, we report a new interaction between exciton and charges enabled by unusual quantum confinement in 2D moir\'e superlattices, which results in novel exciton many-body ground states composed of moir\'e excitons and correlated electron lattices. Unique to H-stacked (or 60o-twisted) WS2/WSe2 heterobilayer, we found that the interlayer atomic registry and moir\'e structural reconstruction leads to an interlayer moir\'e exciton (IME) whose hole in one layer is surrounded by its partner electron's wavefunction spread among three adjacent moir\'e traps in the other layer. This 3D excitonic structure can enable large in-plane electrical quadrupole moments in addition to the vertical dipole. Upon doping, the electric quadrupole facilitates the binding of IME to the charges in neighboring moir\'e cells, forming an intercell charged exciton complex. The exciton complex is unveiled by the IME photoluminescence energy jumps when the electron lattices form at both fractional and integer-filled moir\'e minibands, with replica-like spectral features between successive integer moir\'e fillings. Our work provides the framework in understanding and engineering emergent exciton many-body states in correlated moir\'e charge orders.

The low dimensional inorganic–organic (IO) hybrid semiconductors become a fascinating subject of interest due to their unique crystal structural packing and tunable optical exciton emission features. These naturally self-assembled 2D IO hybrid semiconductors form multiple quantum wells (MQWs) like structure due to the quantum widths of both organic moiety and inorganic network , enabling them to show stable room temperature Mott-type excitons with large exciton binding energy. A systematic co-existence of two kinds of excitons observable from one-(ħω ≥ Eg) and two-photon (2ħω ≥ Eg) excitations is studied to probe into deeper details of sensitive structural changes in the IO-hybrids thin film and single crystals.

In this note we adapt the work of Hall to find quasi-Einstein metrics on sphere bundles over products of Fano Kaehler-Einstein manifolds, as well as bundles where only one end is blown down., 8 pages, to appear in Involve

Perfect state transfer and fractional revival can be used to move information between pairs of vertices in a quantum network. While perfect state transfer has received a lot of attention, fractional revival is newer and less studied. One problem is to determine the differences between perfect state transfer and fractional revival. If perfect state transfer occurs between two vertices in a graph, the vertices must be cospectral. Further if there is perfect state transfer between vertices $a$ and $b$ in a graph, there cannot be perfect state transfer from $a$ to any other vertex. No examples of unweighted graphs with fractional revival between non-cospectral vertices were known; here we give an infinite family of such graphs. No examples of unweighted graphs where the pairs involved in fractional revival overlapped were known; we give examples of such graphs as well.

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems., Comment: 7 pages for main text. Science Bulletin (2022)

Journal of magnesium and alloys 10(11), 3281-3287 (2022). doi:10.1016/j.jma.2021.08.008, Published by Elsevier, Amsterdam [u.a.]

We study Bose gases in $d \ge 2$ dimensions with short-range repulsive pair interactions at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus on the non-percolation regime. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose–Einstein condensation into a sufficiently localized, normalized one-particle state. The results apply to the canonical eigenstates of the underlying one-particle Hamiltonian.

In this paper we study the field of definition of abelian subvarieties $B\subset A_{\overline{K}}$ for an abelian variety $A$ over a field $K$ of characteristic $0$. We show that, provided that no isotypic component of $A_{\overline{K}}$ is simple, there are infinitely many abelian subvarieties of $A_{\overline{K}}$ with field of definition $K_A$, the field of definition of the endomorphisms of $A_{\overline{K}}$. This result combined with earlier work of R\'emond gives an explicit maximum for the minimal degree of a field extension over which an abelian subvariety of $A_{\overline{K}}$ is defined with varying $A$ of fixed dimension and $K$ of characteristic $0$., Comment: Comments welcome

A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second-order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well-known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.

For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the time evolution observables of disjoint sets of particles of each species have correlation functions that remain asymptotically small in the total number of particles and display a controlled growth in time. This is obtained by means of ad hoc estimates of Lieb–Robinson type on the propagation of the interaction, established here for the multi-component Bose mixture.

The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials. For bosons, the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site interactions. However, accessing longer-range couplings has remained elusive experimentally. This marks the frontier towards the extended Bose-Hubbard Hamiltonian that allows insulating ordered phases at fractional lattice fillings. Here we implement this Hamiltonian by confining semiconductor dipolar excitons in an artificial two-dimensional square lattice. Strong dipolar repulsions between nearest neighbouring lattice sites then stabilise an insulating state at half filling. This characteristic feature of the extended Bose-Hubbard model exhibits signatures theoretically expected for a checkerboard spatial order. Our work thus highlights that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and over 100 sites., 14 pages, 7 figures

Long-lived indirect excitons (IXs) exhibit a rich phase diagram, including a Bose-Einstein condensate (BEC), a Wigner crystal, and other exotic phases. Recent experiments have hinted at a new, "classical" liquid of IXs above the BEC transition. To uncover the nature of this phase, we use a broad range of theoretical tools and find no evidence of a driving force towards classical condensation. Instead, we attribute the condensed phase to a quantum electron-hole liquid (EHL), first proposed by Keldysh for direct excitons. Taking into account the association of free carriers into bound excitons, we study the phase equilibrium between a gas of excitons, a gas of free carriers, and an EHL for a wide range of electron-hole separations, temperatures, densities, and mass ratios. Our results agree reasonably well with recent measurements of GaAs/AlGaAs coupled quantum wells., 11 pages, 5 figures (main text); 30 pages, 5 figures (supplemental material)

We investigate the many-body state and the static and the dynamic behaviour of the pair-correlation function of a Bose-Einstein condensate with a finite atom number, which is confined in a quasi-one-dimensional toroidal/annular potential, both for repulsive, and for attractive interactions. We link the dynamic pair-correlation function that we evaluate with the problem of quantum time crystals. For weak repulsive interatomic interactions and a finite number of atoms the pair-correlation function shows a periodic temporal behaviour, which disappears in the limit of a large atom number, in agreement with general arguments. Finally we provide some insight into older results of attractive interactions, where the time-crystalline behaviour exists only in the limit of a large atom number., Revised version, accepted for publication

We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: $\rho(\textbf{r})=const$. Moreover, under the perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density., Comment: 21 pages, no figures; v2: sections are rearranged; a discussion of fractional statistics is added in section 2

The p-wave superfluid is characterized by nontrivial topological characteristics essential for fault-tolerant quantum state manipulation. However, the practical realization of the p-wave state remains a challenging problem. We study the s- and p-wave superfluidity in mixtures of fermionic and spinor bosonic gases and derive a general set of the gap equations for these superfluid states. Numerically solving the gap equations for the s-wave state, we quantify the physical conditions for the realization of the pure p-wave state in a well-controlled environment of atomic physics in the absence of an admixture of the s-wave state., 9 pages, 2 figures

We introduce the concept of TRAP (Traces and Permutations), which can roughly be viewed as a wheeled PROP (Products and Permutations) without unit. TRAPs are equipped with a horizontal concatenation and partial trace maps. Continuous morphisms on an infinite dimensional topological space and smooth kernels (resp. smoothing operators) on a closed manifold form a TRAP but not a wheeled PROP. We build the free objects in the category of TRAPs as TRAPs of graphs and show that a TRAP can be completed to a unitary TRAP (or wheeled PROP). We further show that it can be equipped with a vertical concatenation, which on the TRAP of linear homomorphisms of a vector space, amounts to the usual composition. The vertical concatenation in the TRAP of smooth kernels gives rise to generalised convolutions. Graphs whose vertices are decorated by smooth kernels (resp. smoothing operators) on a closed manifold form a TRAP. From their universal properties we build smooth amplitudes associated with the graph., 52 pages, many figures. arXiv admin note: substantial text overlap with arXiv:2005.02115

Moir\'e superlattices in atomically thin van-der-Waals heterostructures hold great promise for an extended control of electronic and valleytronic lifetimes, the confinement of excitons in artificial moir\'e lattices, and the formation of novel exotic quantum phases. Such moir\'e-induced emergent phenomena are particularly strong for interlayer excitons, where the hole and the electron are localized in different layers of the heterostructure. In order to exploit the full potential of correlated moir\'e and exciton physics, a thorough understanding of the ultrafast interlayer exciton formation process and the real-space wavefunction confinement in the moir\'e potential is indispensable. However, direct experimental access to these parameters is limited since most excitonic quasiparticles are optically dark. Here we show that femtosecond photoemission momentum microscopy provides quantitative access to these key properties of the moir\'e interlayer excitons. We find that interlayer excitons are dominantly formed on the sub-50~fs timescale via interlayer tunneling at the K valleys of the Brillouin zones. In addition, we directly measure energy-momentum fingerprints of the moir\'e interlayer excitons by mapping their spectral signatures within the mini Brillouin zone that is built up by the twisted heterostructure. From these momentum-fingerprints, we gain quantitative access to the modulation of the exciton wavefunction within the moir\'e potential in real-space. Our work provides the first direct access to the interlayer moir\'e exciton formation dynamics in space and time and reveals new opportunities to study correlated moir\'e and exciton physics for the future realization of exotic quantum phases of matter., Comment: 7 pages main text, 11 pages SI

Rigid tree honeycombs were introduced by Knutson, Tao, and Woodward and they were shown by Dykema, Collins, Timotin, and the authors to be sums of extreme rigid honeycombs, with uniquely determined summands up to permutations. Two extreme rigid honeycombs are essentially the same if they have proportional exit multiplicities and, up to this identification, there are countably many equivalence classes of such honeycombs. We describe two ways to approach the enumeration of these equivalence classes. The first method produces a (finite) list of all rigid tree honeycombs of fixed weight by looking at the locking patterns that can be obtained from a certain quadratic Diophantine equation. The second method constructs arbitrary rigid tree honeycombs from rigid overlays of two rigid tree honeycombs with strictly smaller weights. This allows, in principle, for an inductive construction of all rigid tree honeycombs starting with those of unit weight. We also show that some rigid overlays of two rigid tree honeycombs give rise to an infinite sequence of rigid tree honeycombs of increasing complexity but with a fixed number of nonzero exit multiplicities. This last result involves a new inflation/deflation construction that also produces other infinite sequences of rigid tree honeycombs., Comment: 45 pages, many figures

Sympathetic cooling of a Fermi gas with a buffer gas of bosonic atoms is an efficient way to achieve quantum degeneracy in Fermi systems. However, all attempts to use this method for cooling ions until recently were ineffective because of the unremovable ion `"micromotion" in electromagnetic Paul traps, which prevents the realization of a number of hot projects with cold atom-ion systems. In this regard, we propose a new efficient method for sympathetic cooling of ions: the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonances (CIRs) [V.S. Melezhik, Phys. Rev. A103, 53109 (2021)]. We show that the destructive effect of "micromotion" on its sympathetic cooling can, however, be suppressed in the vicinity of the atom-ion CIR. Here, the resonant blocking of a close collision of an atom with an ion also resists its heating due to "micromotion". We investigate the effect of sympathetic cooling around CIRs in atom-ion, and atom-atom confined collisions within the quantum-quasiclassical approach using the Li-Yb$^+$ and Li-Yb confined systems as an example. In this approach, the Schr\"odinger equation for a cold light atom is integrated simultaneously with the classical Hamilton equations for a hotter heavy-ion or atom during a collision. We have found the region near the atom-ion CIR where the sympathetic cooling of the ion by cold atoms is possible in a hybrid atom-ion trap. We also show that it is possible to improve the efficiency of sympathetic cooling in atomic traps by using atomic CIRs., Comment: 8 pages, 4 figures, report on Int. Conf. on Pecision Physics and Fundamental Physical Constants (FFK2021) 4-8 October 2021, Stara Lesna, Slovakia. arXiv admin note: substantial text overlap with arXiv:2101.03565

Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter, implement novel quantum information schemes, or test fundamental symmetries of nature. Realizing their full potential requires cooling interacting molecular gases deeply into the quantum degenerate regime. However, the complexity of molecules which makes their collisions intrinsically unstable at the short range, even for nonreactive molecules, has so far prevented the cooling to quantum degeneracy in three dimensions. Here, we demonstrate evaporative cooling of a three-dimensional gas of fermionic sodium-potassium molecules to well below the Fermi temperature using microwave shielding. The molecules are protected from reaching short range with a repulsive barrier engineered by coupling rotational states with a blue-detuned circularly polarized microwave. The microwave dressing induces strong tunable dipolar interactions between the molecules, leading to high elastic collision rates that can exceed the inelastic ones by at least a factor of 460. This large elastic-to-inelastic collision ratio allows us to cool the molecular gas down to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such unprecedentedly cold and dense samples of polar molecules open the path to the exploration of novel many-body phenomena, such as the long-sought topological p-wave superfluid states of ultracold matter., 11 pages, 7 figures

The long-range and anisotropic nature of the dipolar interaction provides the so-called supersolid phases in Bose-Einstein condensates (BECs) in an optical lattice. However, in a certain area of dipole interaction parameters, BECs can form into a droplet. In this paper, in order to qualitatively understand the droplet formations, we propose a toy model that allows us to estimate the size and shape of droplets in dipolar Bose-Hubbard system in the optical lattice. We compare results of the toy model with numerical solutions of the mean-field calculation., 7 pages, 3 figures

The phenomenon of non-reciprocal critical current in a Josephson device, termed the Josephson diode effect, has garnered much recent interest. Realization of the diode effect requires inversion symmetry breaking, typically obtained by spin-orbit interactions. Here we report observation of the Josephson diode effect in a three-terminal Josephson device based upon an InAs quantum well two-dimensional electron gas proximitized by an epitaxial aluminum superconducting layer. We demonstrate that the diode efficiency in our devices can be tuned by a small out-of-plane magnetic field or by electrostatic gating. We show that the Josephson diode effect in these devices is a consequence of the artificial realization of a current-phase relation that contains higher harmonics. We also show nonlinear DC intermodulation and simultaneous two-signal rectification, enabled by the multi-terminal nature of the devices. Furthermore, we show that the diode effect is an inherent property of multi-terminal Josephson devices, establishing an immediately scalable approach by which potential applications of the Josephson diode effect can be realized, agnostic to the underlying material platform. These Josephson devices may also serve as gate-tunable building blocks in designing topologically protected qubits.

An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) in $D$ spatial dimensions shows a violation of the area-law in real-space entanglement entropy of a subsystem (of length $L$), $S_{EE} \sim L^{D-1}\ln L$, widely believed to be a hallmark signature of the ground state of a gapless quantum critical system of interacting fermions. In this work, we apply a $T=0$ renormalisation group approach to a prototype of the FL in momentum (or, $k$)-space, unveiling thereby the RG relevant quantum fluctuations (due to forward and tangential scattering) from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids for a subsystem defined within a $k$-space window (of size $\Lambda$) proximate to the Fermi surface, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to the gapped quantum liquids emergent from the destabilisation of the Fermi surface by quantum fluctuations arising from backscattering processes. Indeed, we find that the $k$-space entanglement signatures of gapped quantum liquids appear to be governed by the nature of the Fermi surface (e.g., nested or not) from which they emerge, as well as the nature of their parent gapless metallic liquid (e.g., FL, MFL etc.). This is confirmed by our finding an enhanced entanglement entropy for the nodal MFL present at the quantum critical point recently discovered in the 2D Hubbard model at optimal hole-doping. Our work thus paves the way for an entanglement based classification of quantum liquids emergent from the criticality of interacting fermionic matter., Comment: 9 pages, 6 figures, 77 References in main manuscript. Supplementary Materials also included

In this paper, we present a new theoretical scenario in which both dynamical Dirac fermions and Einstein's gravity with a positive cosmological constant and torsion emerge via a spontaneous symmetry breaking in a topological phase. This phase does not contain any local propagating degrees of freedom and is described by a metric-independent fermionic gauge theory, which is invariant under the de Sitter group. After breaking this group to its Lorentz subgroup through a dynamical Higgs mechanism, we show that fermions become dynamical and massive while the dynamics of the locally Lorentz-invariant spacetime can be induced via the condensation of the spinor field. Within our theory, both the Dirac mass and the Newton's constant of gravitation naturally emerge through well-known physical mechanisms., Comment: 4 pages

Using the platform of a trapped-atom clock on a chip, we observe the time evolution of spin-squeezed hyperfine clock states in ultracold rubidium atoms on previously inaccessible timescales up to 1 s. The spin degree-of-freedom remains squeezed after 0.6 s, which is consistent with the limit imposed by particle loss and is compatible with typical Ramsey times in state-of-the-art microwave clocks. The results also reveal a surprising spin-exchange interaction effect that amplifies the cavity-based spin measurement via a correlation between spin and external degrees of freedom. These results open up perspectives for squeezing-enhanced atomic clocks in a metrologically relevant regime and highlight the importance of spin interactions in real-life applications of spin squeezing., 12 pages, 6 figures

Given a matrix $M = (a_{i,j})$ a square is a $2 \times 2$ submatrix with entries $a_{i,j}$, $a_{i, j+s}$, $a_{i+s, j}$, $a_{i+s, j +s}$ for some $s \geq 1$, and a zero-sum square is a square where the entries sum to $0$. Recently, Ar\'evalo, Montejano and Rold\'an-Pensado proved that all large $n \times n$ $\{-1,1\}$-matrices $M$ with discrepancy $|\sum a_{i,j}| \leq n$ contain a zero-sum square unless they are split. We improve this bound by showing that all large $n \times n$ $\{-1,1\}$-matrices $M$ with discrepancy at most $n^2/4$ are either split or contain a zero-sum square. Since zero-sum square free matrices with discrepancy at most $n^2/2$ are already known, this bound is asymptotically optimal., Comment: 19 pages, 7 figures

The interplay of quantum statistics and interactions in atomic Bose--Fermi mixtures leads to a phase diagram markedly different from pure fermionic or bosonic systems. However, investigating this phase diagram remains challenging when bosons condense. Here, we observe evidence for a quantum phase transition from a polaronic to a molecular phase in a density-matched degenerate Bose--Fermi mixture. The condensate fraction, representing the order parameter of the transition, is depleted by interactions and the build-up of strong correlations results in the emergence of a molecular Fermi gas. By driving through the transition, we ultimately produce a quantum-degenerate sample of sodium-potassium molecules exhibiting a large molecule-frame dipole moment of 2.7 Debye. The observed phase transition represents a new phenomenon complementary to the paradigmatic BEC-BCS crossover observed in Fermi systems., 12 pages, 9 figures

We present a systematic and complementary study of quantum correlations near a black hole by considering the measurement-induced nonlocality (MIN). The quantum measure of interest is discussed on the same footing for the fermionic, bosonic and mixed fermion-boson modes in relation to the Hawking radiation. The obtained results show that in the infinite Hawking temperature limit, the physically accessible correlations does not vanish only in the fermionic case. However, the higher frequency modes can sustain correlations for the finite Hawking temperature, with mixed system being more sensitive towards increase of the fermionic frequencies than the bosonic ones. Since the MIN for the latter modes quickly diminishes, the increased frequency may be a way to maintain nonlocal correlations for the scenarios at the finite Hawking temperature., 4 figures

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold $^1\Sigma$ and $^2\Sigma$ polar molecules using electric dipolar interactions. By encoding a spin-1/2 degree of freedom in a combined set of spin and rotational molecular levels, we theoretically demonstrate the emergence of effective spin-spin interactions of the Ising and XXZ forms, enabled by efficient magnetic control over electric dipolar interactions. We show how to use these interactions to create long-lived cluster and squeezed spin states.

Bose-Einstein condensation of electron-hole pairs, exciton condensation, has been effortfully investigated since predicted 60 years ago. Irrefutable evidence has still been lacking due to experimental difficulties in verifying the condensation of the charge neutral and non-magnetic spin-singlet excitons. Whilst, condensation of spin-triplet excitons is a promising frontier because spin supercurrent and spin-Seebeck effects will be observable. A canonical cobaltite LaCoO$_{3}$ under very high magnetic fields is a propitious candidate, yet to be verified. Here, we unveil the exotic phase diagram of LaCoO$_{3}$ up to 600 T generated using the electromagnetic flux compression method and the state-of-the-art magnetostriction gauge. We found the continuous magnetostriction curves and a bending structure, which suggest the emergence of two distinct spin-triplet exciton condensates. By constructing a phenomenological model, we showed that quantum fluctuations of excitons are crucial for the field-induced successive transitions. The spin-triplet exciton condensation in a cobaltite, which is three-dimensional and thermally equilibrated, opens up a novel venue for spintronics technologies with spin-supercurrent such as a spin Josephson junction., 6 pages, 4 figures plus supplementary material

The influence of the external classical field on a correlated two-mode of the electromagnetic field interacting with a three-level atom in the Λ structure is studied. A rotation of the atomic basis is used to remove the classical field terms. The time-dependent wave function is obtained by solving the Schrödinger equation. The influence of the classical field on the phenomenon of revival, collapse, squeezing, and marginal atomic distribution are discussed. In our analysis, the cavity field is prepared in the entangled pair coherent states and the atomic system in the upper state. The results showed that the occupation of the atomic level is significantly affected by the addition of the classical field. The presence of the classical field reduces the squeezing intervals and the extreme values of the atomic marginal distribution.

We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics., 11 pages, 6 figures, code: https://github.com/buwantaiji/FermiFlow

The Pancake graphs $P_n, n\geqslant 2$, are Cayley graphs over the symmetric group $\mathrm{Sym}_n$ generated by prefix-reversals. There are six generating sets of prefix-reversals of cardinality three which give connected Cayley graphs over the symmetric group known as cubic Pancake graphs. In this paper we study the girth of the cubic Pancake graphs. It is proved that considered cubic Pancake graphs have the girths at most twelve.

We review our study of critical phenomena in superfluid $^4$He confined in nanoporous glasses. $^4$He in nanoporous media is an ideal ground to survey the quantum phase transition of bosons. In the present work, critical phenomena were examined using a newly developed hydrodynamic mechanical resonator. The critical exponent of superfluid density $\zeta$ was found to be 1.0, in contrast to 0.67 in bulk $^4$He. We also demonstrate that the superfluid density is proportional to $|P - P_{\mathrm c}|^{\zeta_p}$ with $\zeta_p = 1$ at any finite temperatures. These are the decisive evidences for the 4D XY criticality, which should have been observed only at 0 K, at finite temperatures. We propose a mechanism of the quantum criticality at finite temperatures in terms of phase alignment among the nanoscale localized Bose condensates (LBECs) in nanopores. The proposed mechanism are discussed in the consideration of the correlation length compared with the quantum effect., Comment: 8 pages, 5 figures

Significant leaps in the understanding of quantum systems have been driven by the exploration of geometry, topology, dimensionality, and interactions with ultracold atomic ensembles. A system where atoms evolve while confined on an ellipsoidal surface represents a heretofore unexplored geometry and topology. Realizing such an ultracold bubble system (potentially Bose-Einstein condensed) has areas of interest including quantized-vortex flow respecting topological constraints imposed by closed surfaces, new collective modes, and self-interference via free bubble expansion. Large ultracold bubbles, created by inflating smaller condensates, directly tie into Hubble-analog expansion physics. Here, we report observations from the NASA Cold Atom Lab facility aboard the International Space Station of bubbles of ultracold atoms created using a radiofrequency-dressing protocol. We observe a variety of bubble configurations of differing sizes and initial temperature, and explore bubble thermodynamics, demonstrating significant cooling associated with inflation. Additionally, we achieve partial coverings of bubble traps greater than 1 mm in size with ultracold films of inferred few-$\mu$m thickness, and we observe the dynamics of shell structures projected into free-evolving harmonic confinement. The observations are part of the first generation of scientific measurements made with ultracold atoms in space, exploiting the benefits of perpetual free-fall to explore gravity-free evolution of quantum systems that are prohibitively difficult to create on Earth. This work points the way to experiments focused on the nature of the Bose-Einstein condensed bubble, the character of its excitations, and the role of topology in its evolution; it also ushers in an era of orbital microgravity quantum-gas physics.

Optical bound states in the continuum (BIC) are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone, i.e., in the energy-momentum dispersion region for which radiation can propagate out of the lattice plane. These BICs possess an invariant topological charge given by the winding number of the polarization vectors, similarly to vortices in quantum fluids, such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not been fully exploited, yet. Here we show Bose-Einstein condensation of polaritons, hybrid light-matter excitations, occuring in a BIC thanks to its peculiar non-radiative nature. The combination of the ultra-long BIC lifetime and the tight confinement of the waveguide geometry allow to achieve an extremely low threshold density for condensation, which is not reached in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we unveil new ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits

Quantum vortices are the quantized version of classical vortices. Their center is a phase singularity or vortex core around which the flow of particles as a whole circulates and is typical in superfluids, condensates and optical fields. However, the exploration of the motion of the phase singularities in coherently-coupled systems is still underway. We theoretically analyze the propagation of an interference dislocation in the regime of strong coupling between light and matter, with strong mass imbalance, corresponding to the case of microcavity exciton-polaritons. To this end, we utilize combinations of vortex and tightly focused Gaussian beams, which are introduced through resonant pulsed pumping. We show that a dislocation originates from self-interference fringes, due to the non-parabolic dispersion of polaritons combined with moving Rabi-oscillating vortices. The morphology of singularities is analyzed in the Poincar\'{e} space for the pseudospin associated to the polariton states. The resulting beam carries orbital angular momentum with decaying oscillations due to the loss of overlap between the normal modes of the polariton system., Comment: 9 pages, 6 figures

Introduction The Gross-Pitaevskii equation is a class of the nonlinear Schrodinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in the intersection field of Bose-Einstein condensate with some other fields. It is an important subject to investigate their exact solutions. Objectives We give multi-soliton of a two-dimensional Gross-Pitaevskii system which contains the time-varying trapping potential with a few interactions of multi-soliton. Through analytical and graphical analysis, we obtain one-, two- and three-soliton which are affected by the strength of atomic interaction. The asymptotic expression of two-soliton embodies the properties of solitons. We can give some interactions of solitons of different structures including parabolic soliton, line-soliton and dromion-like structure. Methods By constructing an appropriate Hirota bilinear form, the multi-soliton solution of the system is obtained. The soliton elastic interaction is analyzed via asymptotic analysis. Results The results in this paper theoretically provide the analytical bright soliton solution in the two-dimensional Bose-Einstein condensation model and their interesting interaction. To our best knowledge, the discussion and results in this work are new and important in different fields. The results enrich the existing nonlinear phenomena of the Gross-Pitaevskii model in Bose-Einstein condensation, and prove that the Hirota bilinear method and asymptotic analysis method are powerful and effective techniques in physical sciences and engineering for analyzing nonlinear mathematical-physical equations and their solutions. These provide a valuable basis and reference for the controllability of bright soliton phenomenon in experiments for high-dimensional Bose-Einstein condensation.

The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur.

The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta$-Einstein and $f$ is constant. Next, we show that in a Sasakian manifold if $g$ represents an $m$-quasi-$*$-Einstein metric with a conformal vector field $V$, then $V$ is Killing and $M$ is $\eta$-Einstein. Finally, we prove that if a non-Sasakian $(\kappa,\mu)$-contact manifold admits a gradient $m$-quasi-$*$-Einstein metric, then it is $N(\kappa)$-contact metric manifold or a $*$-Einstein.

Translational symmetry breaking is antagonistic to static fluidity but can be realized in superconductors, which host a quantum-mechanical coherent fluid formed by electron pairs. A peculiar example of such a state is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, induced by a time-reversal symmetry–breaking magnetic field applied to spin-singlet superconductors. This state is intrinsically accompanied by the superconducting spin smecticity, spin density–modulated fluidity with spontaneous translational-symmetry breaking. Detection of such spin smecticity provides unambiguous evidence for the FFLO state, but its observation has been challenging. Here, we report the characteristic “double-horn” nuclear magnetic resonance spectrum in the layered superconductor Sr 2 RuO 4 near its upper critical field, indicating the spatial sinusoidal modulation of spin density that is consistent with superconducting spin smecticity. Our work reveals that Sr 2 RuO 4 provides a versatile platform for studying FFLO physics.

We have employed one of the well-known many-body techniques, density functional theory plus dynamical mean-field theory (DFT + DMFT), to investigate the electronic structure of ferromagnetic monolayer CrI3 as a function of temperature and hole-doping concentration. The computed magnetic susceptibility follows the Curie's law, indicating that the ferromagnetism of monolayer CrI3 originates from localized magnetic moments of Cr atoms rather than Stoner-type itinerant ones. The DFT + DMFT calculations show a different coherent temperature for each spin component, demonstrating apparent strong spin-dependent electronic correlation effects in monolayer CrI3. Furthermore, we have explored the doping-dependent electronic structure of monolayer CrI3 and found that its electronic and magnetic properties are easily tunable by the hole-doping., Comment: 4 figures

The notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time $\tau$ is comparable with the quantum Heisenberg time $t_H=\hbar/\Delta E$, where $\Delta E$ is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli-de Gennes-Matricon states becomes important in the super-Planckian region, i.e. when $\tau \hbar/\Delta E$., Comment: 5 pages, 2 figures, accepted for publication in JETP Letters

International audience; Finite element simulation modeling permits to predict hydrogen concentration for various initial boundary-values problems, but the results depend on the underlying transport mechanisms accounted for. Trapping process is a key factor in the apparent hydrogen diffusion, and the case of mobile traps as dislocations needs modification of the hydrogen transport equation usually considered in the literature. An extension of this model is proposed where hydrogen dragging by mobile traps is modeled by reaction-diffusion equations, involving trapping and detrapping kinetic, and is applied for evolving trap density with plastic strain. The consequences of trapped hydrogen mobility on diffusive hydrogen repartition in a reference Small Scale Yielding configuration are focused on, especially in term of acceleration of hydrogen transport. The potentiality of the model is illustrated by the modeling of the trapped hydrogen breakaway from fast moving dislocations.

The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose--Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross--Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system., 6 pages, 4 figures, to appear as [JETP Letters, 2022, Vol. 115, No. 7, pp. 415-421]