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We present an explicit Bethe-ansatz wavefunction to a 1D spin-$\frac{1}{2}$ interacting fermion system, manifesting a many-body resonance resulting from the interplay between interaction and non-Hermitian spin-orbit coupling. In the dilute limit, the wavefunction is greatly simplified and then factorized into Slater determinants and a Jastrow factor. An effective thermodynamic distribution is constructed with an effective Hamiltonian including a repulsion resulting from Pauli's exclusion principle and a distinctive zigzag potential arising from the resonance. The competition between these effects leads to a transition from a uniformly distributed configuration to a phase separation. The connection to the recent cold atom experimental efforts of realizing on-site atom-loss is discussed., Comment: 6+4 pages, 2+2 figures

Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose-Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC., Comment: 6 pages, 4 figures

A gas of ultracold atoms probed with laser light is a nearly-ideal experimental realization of a medium of resonant point-like scatterers, a key problem from condensed matter to biology or photonics. Yet, several recent experiments have reported large discrepancies with theory. In this work, we measure the complex transmission through a slab of ultracold two-level atoms with an interferometric technique. We find good agreement with first-principles simulations of mutually-coupled, laser-driven dipoles, and provide an explanation for the discrepancies in earlier measurements., Comment: Supplementary informations available as ancillary file

We benchmark simulations of many-body quantum systems on heterogeneous hardware platforms using CPUs, GPUs, and TPUs. We compare different linear algebra backends, e.g., numpy versus the torch, jax, or tensorflow library, as well as a mixed-precision-inspired approach and optimizations for the target hardware. Quantum red TEA out of the Quantum TEA library specifically addresses handling tensors with different libraries or hardware, where the tensors are the building block of tensor network algorithms. The benchmark problem is a variational search of a ground state in an interacting model. This is a ubiquitous problem in quantum many-body physics, which we solve using tensor network methods. This approximate state-of-the-art method compresses quantum correlations which is key to overcoming the exponential growth of the Hilbert space as a function of the number of particles. We present a way to obtain speedups of a factor of 34 when tuning parameters on the CPU, and an additional factor of 2.76 on top of the best CPU setup when migrating to GPUs., Comment: 15 pages, 6 figures/tables, submitted to the 10th bwHPC Symposium

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics., Comment: 48+8 pages, 24+3 figures

We study the dynamics of phonon-mediated qubit-qubit interactions between trapped ions in the presence of an ultracold atomic gas. By deriving and solving a master equation to describe the combined system, we show that the presence of the atoms causes the quantum gate quality to reduce because of motional decoherence. On the other hand, we calculate that the gas may be used to keep the ion crystal cold in the presence of external heating due to electric field noise. We show that tuning the atom-ion scattering length allows to tune the cooling rate of the ions and would make it possible to temporarily reduce the effects of the gas during a quantum gate while keeping the ions cold over long timescales. In this way, the trapped ion quantum computer may be buffer gas cooled. The system may also be used for quantum-enhanced measurements of the atom-ion interactions or properties of the atomic bath., Comment: 10 pages, 4 figures

The interplay between topology and soliton is a central topic in nonlinear topological physics. So far, most studies have been confined to conservative settings. Here, we explore Thouless pumping of dissipative temporal solitons in a nonconservative one-dimensional optical system with gain and spectral filtering, described by the paradigmatic complex Ginzburg-Landau equation. Two dissipatively induced nonlinear topological phase transitions are identified. First, when varying dissipative parameters across a threshold, the soliton transitions from being trapped in time to quantized drifting. This quantized temporal drift remains robust, even as the system evolves from a single-soliton state into multi-soliton state. Second, a dynamically emergent phase transition is found: the soliton is arrested until a critical point of its evolution, where a transition to topological drift occurs. Both phenomena uniquely arise from the dynamical interplay of dissipation, nonlinearity and topology., Comment: 6 pages, 3 figures

We report the observation of Shapiro steps in a periodically driven Josephson junction between strongly-interacting Fermi superfluids of ultracold atoms. We observe quantized plateaus in the current-potential characteristics, the height and width of which mirror the external drive frequency and the junction nonlinear response. Direct measurements of the current-phase relationship showcase how Shapiro steps arise from the synchronization between the relative phase of the two reservoirs and the external drive. Such mechanism is further supported by the detection of periodic phase-slippage processes, in the form of vortex-antivortex pairs. Our results are corroborated by a circuital model and numerical simulations, overall providing a clear understanding of Shapiro dynamics in atomic Fermi superfluids. Our work demonstrates phase-coherent and synchronization effects in driven strongly-interacting superfluids, opening prospects for studying emergent non-equilibrium dynamics in quantum many-body systems under external drives.

We investigate the fundamental problem of a small density of bosonic impurities immersed in a dilute Bose gas at zero temperature. Within the perturbative regime of weak interactions, we show that the presence of the surrounding medium can lead to an enhanced repulsion between dressed bosonic impurities (polarons) rather than an induced attraction, in contrast to prevailing theories. Moreover, we find that the induced polaron-polaron interactions only become attractive when the impurity-boson interactions are sufficiently strong that the system is unstable towards either phase separation or collapse/droplet formation. Our work highlights the role of polaron condensation in polaron-polaron interactions, and it has important implications for theories of induced interactions in general., Comment: 6 pages, 2 figures + supplemental material

The current-voltage characteristic of a driven superconducting Josephson junction displays discrete steps. This phenomenon, discovered by Sydney Shapiro, forms today's voltage standard. Here, we report the observation of Shapiro steps in a driven Josephson junction in a gas of ultracold atoms. We demonstrate that the steps exhibit universal features, and provide key insight into the microscopic dissipative dynamics that we directly observe in the experiment. Most importantly, the steps are directly connected to phonon emission and soliton nucleation. The experimental results are underpinned by extensive numerical simulations based on classical-field dynamics and represent the transfer of the voltage standard to the realm of ultracold quantum gases., Comment: Update reference

In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. We first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model., Comment: 11 pages, 6 figures

Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore non-unitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states., Comment: 34 pages, 5 figures, Review article for Annual Reviews of Condensed Matter Physics

Gate operations composed in quantum circuits form the basis of digital quantum simulation and quantum processing. While two-qubit gates generally operate between nearest neighbours, many circuits require non-local connectivity, necessitating some form of quantum information transport, such as the repeated application of SWAP gates or qubit shuttling. Preserving motional coherence during such transport remains a key challenge to improve gate fidelity and qubit connectivity, as well as to connect local fermionic modes. Here we combine tuneable gate operations between fermionic potassium-40 atoms - based on superexchange interaction - with their bidirectional transport via topological Thouless pumping in an optical lattice. We demonstrate shuttling of atomic singlet pairs with a single-shift fidelity of 99.57(4)% over 50 lattice sites. We spatially and coherently split a large number of randomly distributed fermionic spin singlet pairs and show $($SWAP$)^\alpha$-gate operations between atoms encountering each other during transport. As a signature of entanglement between fermions separated over large distances and interwoven with each other, we observe multi-frequency singlet-triplet oscillations. Topological pumping is generally applicable to long-lived atomic and molecular states, and specifically overcomes lifetime limitations inherent to transport using state-dependent optical lattices. Our work opens up new avenues for transport of quantum information and offers unprecedented possibilities for engineering connectivity in quantum circuits, including approaches based on fermionic modes, as well as for atom interferometry.

Bell non-locality stems from quantum correlations effectively identified using inequalities. Spin chains, simulated with ultra-cold atoms in optical lattices, Rydberg atoms in tweezer arrays, trapped ions, or molecules, allow single-spin control and measurement. Therefore, they are suitable for studying fundamental aspects of these correlations and non-locality. Occupation defects, such as vacancies or multiple atoms occupying a single site due to imperfect system preparation, limit the detection of Bell correlations. We investigate their impact using a simplified toy model parameterized by the probability of a site being singly occupied. We derive the corresponding Bell inequality and identify the smallest probability that establishes a lower bound for detecting Bell correlations. We relate the bound to two physical parameters leading to defects in occupations: non-zero temperature and filling factor, focusing on entangled ultra-cold atoms in optical lattices. Finally, we numerically validate the predictions of the toy model by full many-body simulations., Comment: 14 pages, 7 figures

We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to $\beta={\rm poly}(\ln(n))$. At the core of our approach is the Density Matrix Renormalization Group algorithm, which typically does not guarantee efficiency. We have created a new truncation scheme for the matrix product operator of the quantum Gibbs states, which allows us to control the error analytically. Additionally, our method is applied to simulate the time evolution of systems with long-range interactions, achieving significantly better precision than that offered by the Lieb-Robinson bound., Comment: 7 pages + 9 pages Supplementary materials, 1 figure

We propose a simple model of an interacting, fully spin--polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first--order phase transitions between the low and high density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for $d=2$ and $3$, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embeded in the fermionic nature of the system under study., Comment: 10 pages, 11 figures

Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density functional theory based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system.

We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from anisotropic forcing for a broad range of forcing amplitudes, and characterise the states through their Fourier spectra, vortex distributions, and spatial correlations. For weak forcing the steady-state wave-action spectrum exhibits a $k^{-3.5}$ scaling over wavenumber $k$; further decomposition uncovers the same power law in both compressible kinetic energy and quantum pressure, while the bulk superfluid remains phase coherent and free from extended vortices. As the forcing energy exceeds the chemical potential, extended vortices develop in the bulk, disrupting the $k^{-3.5}$ scaling. The spectrum then transitions to a $k^{-7/3}$ regime for compressible kinetic energy only, associated with dense vortex turbulence, and phase coherence limited to the healing length. The strong forcing regime is consistent with an inverse cascade of compressible energy driven by small-scale vortex annihilation., Comment: 9 pages + appendices; 11 figures

We explore the ground states and quench dynamics of one-dimensional quantum droplets with spin-orbit coupling (SOC) and an imbalance in intracomponent interactions. A plethora of miscible ground state stripe and standard (i.e., non-modulated) droplets is found depending on the SOC wavenumber and building upon Gaussian to flat-top background for increasing (decreasing) atom number (interactions). Deformations among the states were accompanied by spin population transfer caused by the Rabi coupling and could be controlled by adjusting the interactions or the SOC parameters. When considering a trap, we identified a transition from a bound to a trapped gas many-body state, characterized by a sign change of the chemical potential, which occurred at lower (larger) atom numbers for tighter traps (stronger interactions). The droplet's breathing motion was accompanied by minor population transfer, and its frequency increases for a larger intracomponent interaction ratio or reaching a maximum at SOC wavenumbers, where the transition from non-modulated flat-top to stripe droplets occurred. We witness droplet fragmentation for abrupt changes in the Rabi coupling while large amplitude quenches of the SOC wavenumber trigger spin-demixing, resulting in constant amplitude but opposite direction motion of untrapped droplets or in-trap out-of-phase oscillating droplets. Our findings have implications for controlled spin-demixing processes of droplets and the excitation of relevant magnetic bound states., Comment: 13 pages, 11 figures

We present a general framework to implement massive Nambu-Goldstone quasi-particles in driven many-body systems. The underlying mechanism leverages an explicit Lie group structure imprinted into an effective Hamiltonian that governs the dynamics of slow degrees of freedom; the resulting emergent continuous symmetry is weakly explicitly broken, giving rise to a massive Nambu-Goldstone mode, with a spectral mass gap scaling linearly with the drive period. We discuss explicit and experimentally implementable realizations, such as Heisenberg-like spin models that support gapped spin-wave excitations. We provide a protocol to certify the existence of the massive Nambu-Goldstone mode from the dynamics of specific observables, and analyse the dispersion spectrum and their lifetime in the presence of weak explicit symmetry breaking.

We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions., Comment: 17 pages, 6 figures, to be published in New Journal of Physics

It is well established that the optimal spin squeezing under a one-axis-twisting Hamiltonian follows a scaling law of $J^{-2/3}$ for $J$ interacting atoms after a quench dynamics. Here we prove analytically and numerically that the spin squeezing of the ground state of the one-axis-twisting Hamiltonian actually reaches the Heisenberg limit $J^{-1}$. By constructing a bilinear Bogoliubov Hamiltonian with the raising and lowering spin operators, we exactly diagonalize the spin Bogoliubov Hamiltonian, which includes the one-axis twisting Hamiltonian as a limiting case. The ground state of the spin Bogoliubov Hamiltonian exhibits wonderful spin squeezing, which approaches to the Heisenberg limit in the case of the one-axis twisting Hamiltonian. It is possible to realize experimentally the spin squeezed ground state of the one-axis-twisting Hamiltonian in dipolar spinor condensates, ultracold atoms in optical lattices, spins in a cavity, or alkali atoms in a vapor cell.

The INTENTAS project aims to develop an atomic sensor utilizing entangled Bose-Einstein condensates (BECs) in a microgravity environment. This key achievement is necessary to advance the capability for measurements that benefit from both entanglement-enhanced sensitivities and extended interrogation times. The project addresses significant challenges related to size, weight, and power management (SWaP) specific to the experimental platform at the Einstein-Elevator in Hannover. The design ensures a low-noise environment essential for the creation and detection of entanglement. Additionally, the apparatus features an innovative approach to the all-optical creation of BECs, providing a flexible system for various configurations and meeting the requirements for rapid turnaround times. Successful demonstration of this technology in the Einstein-Elevator will pave the way for a future deployment in space, where its potential applications will unlock high-precision quantum sensing.

We investigate the nature of the quantum phase transition in modulated SU(N) Heisenberg spin chains. In the odd-N case, the transition separates a trivial non-degenerate phase to a doubly-degenerate gapped chiral PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the $\mathbb{Z}_2$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated SU(N) Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the SU(N)$_1$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by changing the model parameters slightly., Comment: 13 pages, 12 figures

Adiabatic passage in systems of interacting bosons is substantially affected by interactions and inter-particle entanglement. We consider STIRAP-like schemes in Bose-Hubbard chains that exhibit low-dimensional chaos (a 3 site chain), and high-dimensional chaos (more than 3 sites). The dynamics that is generated by a transfer protocol exhibits striking classical and quantum chaos fingerprints that are manifest in the mean-field classical treatment, in the truncated-Wigner semiclassical treatment, and in the full many-body quantum simulations., Comment: 13 pages, 14 figures

The stable Bardeen-Schrieffer-Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we study the BCS state of a binary Bose gas with $s$-wave intra-species repulsions and an inter-species attraction in the mean-field-stable region. We find that above the Bose-Einstein-Condensation (BEC) transtion temperature, there is a phase transtion from the normal state to the BCS state due to inter-species pairing. When the temperature decreases, another phase transtion from the BCS state to the mixture state with both atomic BEC and inter-species pairs occurs. As the temperature is further lowered, the mixuture state is taken over by the BEC state. The phase diagram of this system is presented and experimental implications are discussed., Comment: 6 pages, 4 figures

Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations., Comment: 17 pages, 10 figures

Subwavelength atomic arrays constitute a novel light-matter platform with long-range interactions and collective dissipation that can host novel non-equilibrium many-body states. Here we investigate their steady states under coherent driving. While in the low-drive intensity regime they have often been described in terms of linear, non-interacting theories, we show that such a description is inadequate in subwavelength regimes. There, we point out that non-linearities can have large effects down to a vanishing drive intensity in the limit of large number of atoms. Then we investigate the role of fluctuations beyond Gutzwiller mean-field theory within a Dynamical Mean Field Theory (DMFT) approach in the regime of intermediate drive intensity. We show that these have a dramatic impact on the steady-state phase diagram, including suppressing a range of non-homogeneous instabilities and phases predicted in mean-field theory., Comment: 11 pages, 6 figures

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to typical liquids, i.e., the structure factor obeys the scaling relation $S(k)\sim \mathcal{B}k^\alpha$ with $\mathcal{B}, \alpha>0$ in the limit $k$\,$\rightarrow$\,$ 0$. Ground-state $d$-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of \textit{quantum} disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this work, we systematically address these questions by deriving the analytical small-$k$ behaviors (and associatedly, $\alpha$ and $\mathcal{B}$) of the total and spin-resolved structure factors of quasi-1D, 2D, and 3D electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-$k$ scaling exponent $\alpha$ and coefficient $\mathcal{B}$. In particular, partially polarized fermionic liquids exhibit a unique form of \textit{multihyperuniformity}, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger $\alpha$) than each individual spin component., Comment: Accepted at PRB

The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point correlation function. Utilizing simple scaling arguments, the renormalizability of the theory, and the Hellmann-Feynman theorem we identified the large-momentum tail of particle distribution and analog of Tan's energy relation for many-fermion systems with disorder in arbitrary dimension $d\ge 2$. It is shown that the energy-pressure relation manifests a kind of scale anomaly in two and three dimensions., Comment: 7 pages, 1 figure; Please, feel free to comment and provide relevant references

In two-dimensional space, we consider a system of $N$ anyons interacts via a short range attractive two-body interaction. In the stable regime, we derive the average-field Pauli functional as the mean-field limit of many-body quantum mechanics. Furthermore, we investigate the collapse phenomenon in the collapse regime where the strength of attractions tends to a critical value (defined by the cubic NLS equation) while simultaneously considering the weak field regime where the strength of the self-generated magnetic field tends to zero.

The formation of quantized vortices in a superfluid above a certain critical trap rotation frequency serves as a hallmark signature of superfluidity. Based on the beyond mean field framework, crucial for the formation of exotic supersolid and droplet states, we investigate dynamic protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC), at a significantly lower trap rotation frequency. We find that the critical rotation frequency of the trap varies with the dipole-dipole interaction strength and the polarization direction of the external magnetic field. Leveraging these characteristics of dipolar BECs, we demonstrate three dynamic protocols for vortex nucleation even when rotating below the critical rotation frequency viz.: (i) varying the $s$-wave scattering length, (ii) changing the polarizing angle, and (iii) successive modulation of both the scattering length and polarizing angle. These dynamic vortex seeding protocols could serve as important benchmarks for future experimental studies., Comment: 13 pages, 11 figures

The attractive Hubbard model has become a model readily realizable with ultracold atoms on optical lattices. However, the superconducting (superfluid) critical temperatures, $T_c$'s, are still somewhat smaller than the lowest temperatures achieved in experiments. Here we consider two possible routes, generically called layering, to increase $T_c$: a bilayer and a simple cubic lattice, both with tunable hopping, $t_z$, between attractive Hubbard planes. We have performed minus-sign--free determinant quantum Monte Carlo simulations to calculate response functions such as pairing correlation functions, uniform spin susceptibility, and double occupancy, through which we map out some physical properties. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit $T_c$'s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30\% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for $T_c$ in the attractive Hubbard model, as well as of an upper bound for $T_c$ based on the superfluid density., Comment: 12 pages, 17 figures

We theoretically study stimulated and spontaneous Hawking emission from an analog horizon for spin modes in a two-component Bose-Einstein condensate, both with and without a coherent coupling between the two components. We highlight the conceptual and practical advantages that these systems offer to the experimental observation of the phenomenon, namely the massive nature of elementary excitations and the experimental accessibility of the different quadratures of the spin excitations. In particular, we go beyond the relativistic regimes previously addressed in the literature, and identify various observables that show a signature of the Hawking process, as well as additional features associated with the massive nature of the modes, such as undulations. Semi-analytical calculations of the scattering properties of the horizon and of two-point correlation functions of the emitted radiation in an ideal stationary setup are supported by time-dependent numerical simulations based on Gross-Pitaevskii and Bogoliubov theory.

We develop a new approach for efficient and scalable simulations of measurement and control of quantum systems built upon existing phase-space methods, namely the Truncated Wigner Approximation (TWA). We benchmark against existing particle-filter methods by simulating measurement based feedback cooling in a two-mode system, whose low-dimensional nature permits a computation of an exact solution. The advantage of our method is multi-mode scalability, which we demonstrate through the first successful simulation of measurement-based feedback cooling of an incoherent quasi-1D thermal ensemble to quantum degeneracy. As the underlying principle of our approach exploits a general correspondence between measurement and coherent feedback, we anticipate it is also applicable across a broad range of other quantum control scenarios., Comment: 11 pages, 4 figures. 03/09/24 Version: Minor edits in references, fixed author list formatting

Pairing lies at the heart of superfluidity in fermionic systems. Motivated by recent experiments in mesoscopic Fermi gases, we study up to six fermionic atoms with equal masses and equal populations in two different spin states, confined in a quasi-two-dimensional harmonic trap. We couple a stochastic variational approach with the use of an explicitly correlated Gaussian basis set, which enables us to obtain highly accurate energies and structural properties. Utilising two-dimensional two-body scattering theory with a finite-range Gaussian interaction potential, we tune the effective range to model realistic quasi-two-dimensional scattering. We calculate the excitation spectrum, pair correlation function, and paired fraction as a function of increasing attractive interaction strength. For up to six fermions in the ground state, we find that opposite spin and momentum pairing is maximised well below the Fermi surface in momentum space. By contrast, corresponding experiments on twelve fermions have found that pairing is maximal at the Fermi surface and strongly suppressed beneath [M. Holten et al., Nature 606, 287-291 (2022)]. This suggests that the Fermi sea $-$ which acts to suppress pairing at low momenta through Pauli blocking $-$ emerges in the transition from six to twelve particles., Comment: 37 pages, 7 figures

The unitary Fermi gas (UFG) is a strongly correlated system of two-species (spin-1/2) fermions with a short-range attractive interaction modeled by a contact interaction and has attracted much interest across different disciplines. The UFG is considered a paradigm for strongly correlated superfluids and has been investigated extensively, with generally good agreement found between theory and experiment. However, the extent of a pseudogap regime above the critical temperature $T_c$ for superfluidity is still debated both theoretically and experimentally. Here we study thermodynamic properties of the UFG across the superfluid phase transition using finite-temperature lattice auxiliary-field quantum Monte Carlo (AFMC) methods in the canonical ensemble of fixed particle numbers. We extrapolate our lattice AFMC results to the continuous time and continuum limits, thus removing the systematic error associated with the finite filling factor of previous AFMC studies. We determine the critical temperature to be $T_c=0.16(1)\, T_{F}$. For the largest particle number studied $N=114$, the energy-staggering pairing gap is suppressed above a pairing scale temperature of $T^{*}\approx 0.2\,T_F$. The spin susceptibility displays moderate suppression above $T_c$ with a spin gap temperature of $T_s\approx 0.2 \,T_F$. We also calculate a free energy-staggering pairing gap, which shows substantially reduced statistical errors when compared with the energy-staggering gap, allowing for a clear signature of pairing correlations in the finite-size system. All results indicate that the pseudogap regime is narrow, with pseudogap signatures emerging at temperatures below $T^{*}\approx 0.2 \, T_F$. The reduced statistical errors of the free energy gap enable an extrapolation at low temperatures, allowing an estimate of the zero-temperature pairing gap $\Delta_E = 0.576(24) \, \epsilon_F$., Comment: 18 pages, 7 figures

We investigate the Doppler effect at zero temperature in superfluids with broken Galilean invariance and hosting permanent currents, with special focus on atomic gas platforms. We consider the case when Galilean invariance is broken explicitly (by an external periodic potential) or spontaneously, as it happens in a supersolid. In the first case, the presence of a stationary current affects the propagation of sound (fourth sound) via an anomalous Doppler term proportional to the density derivative of the superfluid fraction. In supersolids, where, according to Goldstone theorem, distinct sounds of hybrid superfluid and crystal nature can propagate, the Doppler effect can be very different for each sound, including the possibility of being negative for the lower phonon branch. We obtain analytical predictions within the hydrodynamic theories for superfluids and supersolids, which are compared with the numerical results of time-dependent simulations for weakly interacting atomic Bose-Einstein condensates.

We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit coupled attractive Fermi-Hubbard model can potentially be realized in cold atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\Gamma$-point, as found in earlier work, and we identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a maximum of about $10-12.5\%$ of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field., Comment: 10 pages, 10 figures

In geometrically frustrated (GF) magnets, conventional long-range order is suppressed due to the presence of primitive triangular structural units, and the nature of the ensuing ground state remains elusive. One class of candidate states, extensively sought in experiments and vigorously studied theoretically, is the quantum spin liquid (QSL), a magnetically-disordered state in which all spins participate in a quantum-coherent many-body state. Randomly located impurities, present in all materials, may prevent QSL formation and instead lead to the formation of a spin-glass state. In this article, we review available data on the specific heat, magnetic susceptibility, and neutron scattering in GF materials. Such data show that a pure GF magnet possesses a characteristic ``hidden energy scale'' significantly exceeded by the other microscopic energy scales in the material. When cooled down to a temperature below the hidden energy scale, a GF material develops significant short-range order that dominates its properties and, in particular, dictates the spin-glass transition temperature for experimentally accessible impurity densities. We review the manifestations of short-range order in the commonly observed thermodynamics quantities in GF materials, possible scenarios for the hidden energy scale, and related open questions., Comment: 41 pages, 5 figures

Rydberg atom array has been established as one appealing platform for quantum simulation and quantum computation. Recent experimental development of trapping and controlling two-species atoms using optical tweezer arrays has brought more complex interactions in this game, enabling much versatile novel quantum states and phenomena to emerge and thus leading to a growing need for both theoretical and numerical investigations in this regard. In this paper we systematically calculate the ground state phase diagram of alternating two-species atom array and find some novel quantum states that cannot exist in traditional cold-atom platforms, for instance the period $4$ product state $|1100\rangle^{\otimes m}$, the period $6$ product state $|111000\rangle^{\otimes m}$ and order-disorder separation phase. We also confirm the existence of floating phase, however, in this system it has to be described by two interacting bosonic fields whereas that in the single species Rydberg atom array can be understood as free bosons. More interestingly, in the quench dynamics we discover a type of new quantum many-body scar distinct from that previous found in single species atoms which is explained by low-energy effective theory of the PXP model. Instead, the underlying physics of the newly found quantum many-body scar can be described by a perturbation theory spanning the whole energy spectrum. Detailed analysis on how to experimentally prepare these states and observe the phenomena is provided. Numerical evidence shows that the proposed scheme is robust against typical experimentally relevent imperfections and thus it is implementable. Our work opens new avenue for quantum simulating novel quantum many-body states both in and out of equilibrium arising from the interplay of competing interactions of different atom species and quantum fluctuations., Comment: 19 pages, 19 figures

Bose-Einstein condensates are suitable systems for studying fundamental aspects of quantum backreaction. Here the backreaction problem in 1D condensates is considered from the perspective of energy and momentum conservation. By assuming the validity of Bogoliubov theory, the backreaction equations are used to identify the contributions to the system energy and momentum coming from quantum fluctuations and condensate corrections. The backreaction is solved for a condensate trapped in a ring configuration and such that particle interactions are continuously switched on. It is shown that the energy in the condensate cannot be addressed without taking into account how the system entered the interacting regime, and even for homogeneous condensates the power transferred to the condensate by quantum fluctuations showcases an intricate non-monotonic pattern.

We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for number-conserving bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer models and certain Levin-Wen string-net models, and we also systematically construct solvable models with other interesting ground states, including ``quantum spin liquids,'' supersolids, ``Bose-Einstein insulators,'' Bose liquids with ``Bose surfaces'', and Bose-Einstein condensates that permit adiabatic evolution from a non-interacting limit to a Gutzwiller-projected limit.

Bogoliubov waves emerge when the system is perturbed from its ground state in a Bose-Einstein Condensate (BEC). These waves can interact nonlinearly, leading to turbulent cascades. In the present work, the turbulence of random weakly nonlinear Bogoliubov waves on the background of a uniform condensate is considered theoretically, within the Wave Turbulence approach, and numerically, via numerical simulations of the 3-dimensional (3D) Gross-Pitaevskii model and the associated wave-kinetic equations. A new Kolmogorov-like stationary spectrum is found for the short Bogoliubov waves. An exact prefactor constant was found for the previously known Zakharov-Sagdeev spectrum of long (acoustic) Bogoliubov waves. The results are used to explain the BEC equation of state experimentally obtained in [Dora et al. Nature 620,521 (2023)], and to suggest new settings for future experiments.

We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant $p$-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the $p$-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the low-momentum self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of $^1S_0$ neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Moreover, adding an impurity-like neutron to symmetric nuclear matter can be regarded as a perturbation accompanied by an explicit breaking of Wigner's $ SU \left( 4 \right) $ symmetry. The relationship between the polaron energy and the Wigner term in nuclear mass formulas is discussed in the low-density limit. Our result would be useful for understanding many-body physics in astrophysical environments as well as the formation of multi-nucleon clusters in neutron-halo nuclei., Comment: 13 pages, 6 figures

We present an exact solution for effective polaron-polaron interactions between heavy impurities, mediated by a sea of non-interacting light fermions in the quantum Hall regime with highly degenerate Landau levels. For weak attraction between impurities and fermions, where only the manifold of lowest Landau levels is relevant, we obtain an analytical expression of mediated polaron-polaorn interactions. Remarkably, polaron interactions are exactly zero when fermions in lowest Landau levels outnumber heavy impurities. For strong attraction, different manifolds of higher Landau levels come into play and we derive a set of equations that can be used to numerically solve the mediated polaron interaction potential. We find that the potential vanishes when the distance R between impurities is larger than the magnetic length, but strongly diverges at short range following a Coulomb form -1/R. Our exact results of polaron-polaron interactions might be examined in cold-atom setups, where a system of Fermi polarons in the quantum Hall regime is realized with synthetic gauge field or under fast rotation. Our predictions could also be useful to understand the effective interaction between exciton-polarons in electron-doped semiconductors under strong magnetic field.

We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate analytical results for the particle energy, the particle velocity, the ground state energy of the system as well as the momentum dependent density of states. The previous classical results for the Coulombian case were reobtained as particular cases., Comment: 23 pages, 3 figures

Gaining control over chemical reactions on the quantum level is a central goal of the modern field of cold and ultracold chemistry. Here, we demonstrate a novel method to coherently steer reaction flux of a three-body recombination process across different product spin channels. For this, we employ a magnetically-tunable Feshbach resonance to admix, in a controlled way, a specific spin state to the reacting collision complex. This allows for the control of the reaction flux into the admixed spin channel, which can be used to significantly change the reaction products. Furthermore, we also investigate the influence of an Efimov resonance on the reaction dynamics. We find that while the Efimov resonance can be used to globally enhance three-body recombination, the relative flux between the reaction channels remains unchanged. Our control scheme is general and can be extended to other reaction processes. It also provides new opportunities in combination with other control schemes, such as quantum interference of reaction paths., Comment: 9 pages, 6 figures

The Thouless theory of quantum pumps establishes the conditions for quantized particle transport per cycle, and determines its value. When describing the pump from a moving reference frame, transported and existing charges transform, though not independently. This transformation is inherent to Galilean space and time, but it is underpinned by a transformation of vector bundles. Different formalisms can be used to describe this transformation, including one based on Bloch theory. Depending on the chosen formalism, the two types of charges will be realized as indices of either the same or different kinds. Finally, we apply the bulk-edge correspondence principle, so as to implement the transformation law within B\"uttiker's scattering theory of quantum pumps., Comment: 23 pages, 2 figures

The cluster Gutzwiller method is widely used to study the strongly correlated bosonic systems, owing to its ability to provide a more precise description of quantum fluctuations. However, its utility is limited by the exponential increase in computational complexity as the cluster size grows. To overcome this limitation, we propose an artificial intelligence-based method known as $\Delta$-Learning. This approach constructs a predictive model by learning the discrepancies between lower-precision (small cluster sizes) and high-precision (large cluster sizes) implementations of the cluster Gutzwiller method, requiring only a small number of training samples. Using this predictive model, we can effectively forecast the outcomes of high-precision methods with high accuracy. Applied to various Bose-Hubbard models, the $\Delta$-Learning method effectively predicts phase diagrams while significantly reducing the computational resources and time. Furthermore, we have compared the predictive accuracy of $\Delta$-Learning with other direct learning methods and found that $\Delta$-Learning exhibits superior performance in scenarios with limited training data. Therefore, when combined with the cluster Gutzwiller approximation, the $\Delta$-Learning approach offers a computationally efficient and accurate method for studying phase transitions in large, complex bosonic systems.