Observation of resonance condensation of fermionic atom pairs

Long-Lived Higgs Modes in Strongly Correlated Condensates

We investigate order parameter fluctuations in the Hubbard model within a time-dependent Gutzwiller approach. While in the weak coupling limit we find that the amplitude fluctuations are short-lived due to a degeneracy with the energy of the edge of the quasiparticle continua (and in agreement with Hartree-Fock+RPA theory), these are shifted below the edge upon increasing the interaction. Our calculations therefore predict undamped amplitude (Higgs) oscillations of the order parameter in strongly coupled superconductors, cold atomic fermion condensates, and strongly interacting charge- and spin-density wave systems. We propose an experimental realization for the detection of the spin-type Higgs mode in undoped cuprates and related materials where, due to the Dzyaloshinsky-Moriya interaction, it can couple to an out-of-plane ferromagnetic excitation that is visible via the Faraday effect.

Observation of the Exotic 0_{2}^{+} Cluster State in ^{8}He

We report here the first observation of the 0_{2}^{+} state of ^{8}He, which has been predicted to feature the condensatelike α+^{2}n+^{2}n cluster structure. We show that this state is characterized by a spin parity of 0^{+}, a large isoscalar monopole transition strength, and the emission of a strongly correlated neutron pair, in line with theoretical predictions. Our finding is further supported by the state-of-the-art microscopic α+4n model calculations. The present results may lead to new insights into clustering in neutron-rich nuclear systems and the pair correlation and condensation in quantum many-body systems under strong interactions.

A quantum engine in the BEC-BCS crossover

Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes1. However, quantum theory offers genuine non-classical forms of energy, different from heat, which so far have not been exploited in cyclic engines. Here we experimentally realize a quantum many-body engine fuelled by the energy difference between fermionic and bosonic ensembles of ultracold particles that follows from the Pauli exclusion principle2. We employ a harmonically trapped superfluid gas of 6Li atoms close to a magnetic Feshbach resonance3 that allows us to effectively change the quantum statistics from Bose-Einstein to Fermi-Dirac, by tuning the gas between a Bose-Einstein condensate of bosonic molecules and a unitary Fermi gas (and back) through a magnetic field4-10. The quantum nature of such a Pauli engine is revealed by contrasting it with an engine in the classical thermal regime and with a purely interaction-driven device. We obtain a work output of several 106 vibrational quanta per cycle with an efficiency of up to 25%. Our findings establish quantum statistics as a useful thermodynamic resource for work production.

Electroassociation of Ultracold Dipolar Molecules into Tetramer Field-Linked States

The presence of electric or microwave fields can modify the long-range forces between ultracold dipolar molecules in such a way as to engineer weakly bound states of molecule pairs. These so-called field-linked states [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003).PRLTAO0031-900710.1103/PhysRevLett.90.043006; L. Lassablière and G. Quéméner, Phys. Rev. Lett. 121, 163402 (2018).PRLTAO0031-900710.1103/PhysRevLett.121.163402], in which the separation between the two bound molecules can be orders of magnitude larger than the molecules themselves, have been observed as resonances in scattering experiments [X.-Y. Chen et al., Nature (London) 614, 59 (2023).NATUAS0028-083610.1038/s41586-022-05651-8]. Here, we propose to use them as tools for the assembly of weakly bound tetramer molecules, by means of ramping an electric field, the electric-field analog of magnetoassociation in atoms. This ability would present new possibilities for constructing ultracold polyatomic molecules.

Machine Learning the Phase Diagram of a Strongly Interacting Fermi Gas

We determine the phase diagram of strongly correlated fermions in the crossover from Bose-Einstein condensates of molecules (BEC) to Cooper pairs of fermions (BCS) utilizing an artificial neural network. By applying advanced image recognition techniques to the momentum distribution of the fermions, a quantity which has been widely considered as featureless for providing information about the condensed state, we measure the critical temperature and show that it exhibits a maximum on the bosonic side of the crossover. Additionally, we backanalyze the trained neural network and demonstrate that it interprets physically relevant quantities.

Double dome structure of the Bose-Einstein condensation in diluted S = 3/2 quantum magnets

Bose-Einstein condensation (BEC) in quantum magnets, where bosonic spin excitations condense into ordered ground states, is a realization of BEC in a thermodynamic limit. Although previous magnetic BEC studies have focused on magnets with small spins of S ≤ 1, larger spin systems potentially possess richer physics because of the multiple excitations on a single site level. Here, we show the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba₂CoGe₂O₇ when the averaged interaction J is controlled by a dilution of magnetic sites. By partial substitution of Co with nonmagnetic Zn, the magnetic order dome transforms into a double dome structure, which can be explained by three kinds of magnetic BECs with distinct excitations. Furthermore, we show the importance of the randomness effects induced by the quenched disorder: we discuss the relevance of geometrical percolation and Bose/Mott glass physics near the BEC quantum critical point.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Vortex dynamics in the two-dimensional BCS-BEC crossover

The Bardeen–Cooper–Schrieffer (BCS) condensation and Bose–Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and LixZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in LixZrNCl. We observed a systematic enhancement of the Hall angle towards the BCS-BEC crossover, which was qualitatively reproduced by the phenomenological time-dependent Ginzburg-Landau (TDGL) theory. LixZrNCl exhibits a band structure free from various electronic instabilities, allowing us to achieve a comprehensive understanding of the vortex Hall effect and thereby propose a global picture of vortex dynamics within the crossover. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors.

First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the U(1) symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with 6Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime.

Resonant Control of Elastic Collisions between ^{23}Na^{40}K Molecules and ^{40}K Atoms

We have demonstrated the resonant control of the elastic scattering cross sections in the vicinity of Feshbach resonances between ^{23}Na^{40}K molecules and ^{40}K atoms by studying the thermalization between them. The elastic scattering cross sections vary by more than 2 orders of magnitude close to the resonance, and can be well described by an asymmetric Fano profile. The parameters that characterize the magnetically tunable s-wave scattering length are determined from the elastic scattering cross sections. The observation of resonantly controlled elastic scattering cross sections opens up the possibility to study strongly interacting atom-molecule mixtures and improve our understanding of the complex atom-molecule Feshbach resonances.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Superconductor superfluid density from the Bardeen–Cooper–Schrieffer/Bose crossover theory

Abstract

The superfluid density $$n_{s}(T)$$ n s ( T ) of a superconductor is calculated based on the generalized Bose–Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus two-electron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%–0% (i.e., with no condensed 2hCPs) and (ii) 0%–100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen–Cooper–Schrieffer (BCS) and Bose–Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime $$n_{s}(0)$$ n s ( 0 ) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature $$T_{c}$$ T c vs $$n_{s}(0)$$ n s ( 0 ) obtained here is just as Božović et al. (2016) found. However, in 2D with a linear relation accounting for 0%–100%, $$n_{s}(T)/n_{s}(0)$$ n s ( T ) / n s ( 0 ) compares well with some high-$$T_{c}$$ T c -cuprate SC data between the two coupling regimes.

Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas

Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.

Tunable Three-Body Interactions in Driven Two-Component Bose-Einstein Condensates

We propose and demonstrate the appearance of an effective attractive three-body interaction in coherently driven two-component Bose-Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. Importantly, its strength can be controlled with the Rabi-coupling strength and it does not come with additional losses. In the experiment, the three-body interactions are adjusted to play a predominant role in the equation of state of a cigar-shaped trapped condensate. This is confirmed through two striking observations: a downshift of the radial breathing mode frequency and the radial collapses for positive values of the dressed-state scattering length.

Crossover between strongly coupled and weakly coupled exciton superfluids

In fermionic systems, superconductivity and superfluidity occur through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, which is challenging in electronic systems. We studied graphene double layers separated by an atomically thin insulator. Under applied magnetic field, electrons and holes couple across the barrier to form bound magneto-excitons whose pairing strength can be continuously tuned by varying the effective layer separation. Using temperature-dependent Coulomb drag and counterflow current measurements, we were able to tune the magneto-exciton condensate through the entire phase diagram from weak to strong coupling. Our results establish magneto-exciton condensates in graphene as a model platform to study the crossover between two bosonic quantum condensate phases in a solid-state system.

Bose-Einstein Condensation of Efimovian Triples in the Unitary Bose Gas

In an atomic Bose-Einstein condensate quenched to the unitary regime, we predict the sequential formation of a significant fraction of condensed pairs and triples. At short distances, we demonstrate the two-body and Efimovian character of the condensed pairs and triples, respectively. As the system evolves, their size becomes comparable to the interparticle distance, such that many-body effects become significant. The structure of the condensed triples depends on the size of Efimov states compared with density scales. Unexpectedly, we find universal condensed triples in the limit where these scales are well separated. Our findings provide a new framework for understanding dynamics in the unitary regime as the Bose-Einstein condensation of few-body composites.

Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Shape Resonances in H_{2} as Photolysis Reaction Intermediates

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Electrically tunable Feshbach resonances in twisted bilayer semiconductors

[Figure: see text].

In Situ Thermometry of Fermionic Cold-Atom Quantum Wires

We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature T/T_{F} at nearly constant entropy per particle S/Nk_{B}. The ability to probe individual atomic wires in situ paves the way to quantitatively study equilibrium and transport properties of strongly interacting 1D Fermi gases.

Dynamics of a Fermi Gas Quenched to Unitarity

We present an experimental study of a two component Fermi gas following an interaction quench into the superfluid phase. Starting with a weakly attractive gas in the normal phase, interactions are ramped to unitarity at a range of rates and we measure the subsequent dynamics as the gas approaches equilibrium. Both the formation and condensation of fermion pairs are mapped via measurements of the pair momentum distribution and can take place on very different timescales, depending on the adiabaticity of the quench. The contact parameter is seen to respond very quickly to changes in the interaction strength, indicating that short-range correlations, based on the occupation of high-momentum modes, evolve far more rapidly than the correlations in low-momentum modes necessary for pair condensation.

Quantum Degenerate Fermi Gas in an Orbital Optical Lattice

Spin-polarized samples and spin mixtures of quantum degenerate fermionic atoms are prepared in selected excited Bloch bands of an optical checkerboard square lattice. For the spin-polarized case, extreme band lifetimes above 10 s are observed, reflecting the suppression of collisions by Pauli's exclusion principle. For spin mixtures, lifetimes are reduced by an order of magnitude by two-body collisions between different spin components, but still remarkably large values of about 1 s are found. By analyzing momentum spectra, we can directly observe the orbital character of the optical lattice. The observations demonstrated here form the basis for exploring the physics of Fermi gases with two paired spin components in orbital optical lattices, including the regime of unitarity.

Pairing and Pair Superfluid Density in One-Dimensional Two-Species Fermionic and Bosonic Hubbard Models

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

Critical Temperature in the BCS-BEC Crossover with Spin-Orbit Coupling

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.

Gate-controlled BCS-BEC crossover in a two-dimensional superconductor

Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS limit to the BEC limit realized by varying carrier density in a two-dimensional superconductor, electron-doped zirconium nitride chloride. The phase diagram, established by simultaneous measurements of resistivity and tunneling spectra under ionic gating, demonstrates a pseudogap phase in the low-doping regime. The ratio of the superconducting transition temperature and Fermi temperature in the low-carrier density limit is consistent with the theoretical upper bound expected in the BCS-BEC crossover regime. These results indicate that the gate-doped semiconductor provides an ideal platform for the two-dimensional BCS-BEC crossover without added complexities present in other solid-state systems.

Hidden Pseudogap and Excitation Spectra in a Strongly Coupled Two-Band Superfluid/Superconductor

We investigate single-particle excitation properties in the normal state of a two-band superconductor or superfluid throughout the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein-condensation (BEC) crossover, within the many-body T-matrix approximation for multichannel pairing fluctuations. We address the single-particle density of states and the spectral functions consisting of two contributions associated with a weakly interacting deep band and a strongly interacting shallow band, relevant for iron-based multiband superconductors and multicomponent fermionic superfluids. We show how the pseudogap state in the shallow band is hidden by the deep band contribution throughout the two-band BCS-BEC crossover. Our results could explain the missing pseudogap in recent scanning tunneling microscopy experiments in FeSe superconductors.

Direct laser cooling schemes for the triatomic SOH and SeOH molecules based on ab initio electronic properties

Direct laser cooling is a very promising method to obtain cold molecules for various applications. However, a molecule with satisfactory electronic and optical properties for the optical scheme is difficult to identify. By suggesting criteria for the qualified molecules, we develop a method to identify the suitable polyatomic molecules for direct laser cooling. The new criteria from the equilibrium geometrical structures and fundamental frequencies of the ground and low-lying excited states are used to replace the past ones based on Franck-Condon factors. The new method can rapidly identify the preferable one among many candidate polyatomic molecules based on ab initio calculations because the new criteria are free from the construction of potential energy surfaces. The method is testified by using triatomic molecules containing OH. All the reported and two new molecules suitable for direct laser cooling are identified by comparing 168 electronic states of 28 molecules with the new criteria. The newly found molecules have been confirmed using the Franck-Condon factors from the construction of potential energy surfaces. Finally, the optical schemes for the direct laser cooling of the SOH and SeOH molecules are established.

Intrinsic Decoherence and Recurrences in a Large Ferromagnetic F = 1 Spinor Bose–Einstein Condensate

Decoherence with recurrences appear in the dynamics of the one-body density matrix of an F=1 spinor Bose–Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, which breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations, a very accurate time evolution of large condensates is analyzed, leading to heuristic analytic expressions for the time dependence of the one-body density matrix, in the weak and strong interacting regimes, for initial coherent states. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, which show remarkable differences depending on the strength of the spin-spin interactions. The features of the stationary states in both regimes are also investigated. We discuss the nature of these limits in light of the thermodynamic limit.

Thermal bosons in 3d optical lattices via tensor networks

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose–Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.

Large phonon time-of-flight fluctuations in expanding flat condensates of cold Fermi gases

We reexamine how quantum density fluctuations in condensates of ultra-cold Fermi gases lead to fluctuations in phonon times-of-flight, an effect that increases as density is reduced. We suggest that these effects should be measurable in pancake-like (two-dimensional) condensates on their release from their confining optical traps, providing their initial (width/thickness) aspect ratio is suitably large.

Effective p-wave Fermi-Fermi Interaction Induced by Bosonic Superfluids

We study the two-dimensional Bose-Fermi mixture on square lattice at finite temperature by using the determinant quantum Monte Carlo method within the weakly interacting regime. Here we consider the attractive Bose-Hubbard model and free spinless fermions. In the absence of boson-fermion interactions, we obtain the boundary of the collapsed state of the attractive bosons. In the presence of boson-fermion interactions, an effective p-wave interaction between fermions will be induced as far as the bosons are in a superfluid state. Moreover, we find the emergence of the composite fermion pairs at low temperatures.

Fast In Situ Observation of Atomic Feshbach Resonances by Photoassociative Ionization

We propose and experimentally investigate a scheme for observing Feshbach resonances in atomic quantum gases in situ and with a high temporal resolution of several tens of nanoseconds. The method is based on the detection of molecular ions, which are optically generated from atom pairs at small interatomic distances. As a test system we use a standard rubidium gas (^{87}Rb) with well known magnetically tunable Feshbach resonances. The fast speed and the high sensitivity of our detection scheme allows us to observe a complete Feshbach resonance within one millisecond and without destroying the gas.

BCS-BEC Crossover and Pairing Fluctuations in a Two Band Superfluid/Superconductor: A T Matrix Approach

We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.

Methods for preparing quantum gases of lithium

Lithium is an important element in atomic quantum gas experiments because its interactions are highly tunable due to broad Feshbach resonances and zero-crossings and because it has two stable isotopes: ⁶Li, a fermion, and ⁷Li, a boson. Although lithium has special value for these reasons, it also presents experimental challenges. In this article, we review some of the methods that have been developed or adapted to confront these challenges, including beam and vapor sources, Zeeman slowers, sub-Doppler laser cooling, laser sources at 671 nm, and all-optical methods for trapping and cooling. Additionally, we provide spectral diagrams of both ⁶Li and ⁷Li and present plots of Feshbach resonances for both isotopes.

Light-Driven Electron-Hole Bardeen-Cooper-Schrieffer-Like State in Bulk GaAs

We investigate the photon-dressed state of excitons in bulk GaAs by optical pump-probe spectroscopy. We reveal that the high-energy branch of the dressed states continuously evolves into a singular enhancement at the absorption edge in the high-density region where the exciton picture is no longer valid. Comparing the experimental result with a simulation based on semiconductor Bloch equations, we show that the dressed state in such a high-density region is better viewed as a Bardeen-Cooper-Schrieffer-like state, which has been theoretically anticipated to exist over decades. Having seen that the dressed state can be regarded as a macroscopic coherent state driven by an external light field, we also discuss the decoherence from the dressed state to an incoherent state after the photoexcitation in view of the Coulomb enhancement in the transient absorption.

Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.

Cluster Formation in Two-Component Fermi Gases

Two-component fermions are known to behave like a gas of molecules in the limit of Bose-Einstein condensation of diatomic pairs tightly bound with zero-range interactions. We discover that the formation of cluster states occurs when the effective range of two-body interaction exceeds roughly 0.46 times the scattering length, regardless of the details of the short-range interaction. Using an explicitly correlated Gaussian basis set expansion approach, we calculate the binding energy of cluster states in trapped few-body systems and show the difference of structural properties between cluster states and gaslike states. We identify the condition for cluster formation and discuss the potential observation of cluster states in experiments.

Observation of a transition between dynamical phases in a quantum degenerate Fermi gas

A proposed paradigm for out-of-equilibrium quantum systems is that an analog of quantum phase transitions exists between parameter regimes of qualitatively distinct time-dependent behavior. Here, we present evidence of such a transition between dynamical phases in a cold-atom quantum simulator of the collective Heisenberg model. Our simulator encodes spin in the hyperfine states of ultracold fermionic potassium. Atoms are pinned in a network of single-particle modes, whose spatial extent emulates the long-range interactions of traditional quantum magnets. We find that below a critical interaction strength, magnetization of an initially polarized fermionic gas decays quickly, while above the transition point, the magnetization becomes long-lived because of an energy gap that protects against dephasing by the inhomogeneous axial field. Our quantum simulation reveals a nonequilibrium transition predicted to exist but not yet directly observed in quenched s-wave superconductors.

Sticky collisions of ultracold RbCs molecules

Understanding and controlling collisions is crucial to the burgeoning field of ultracold molecules. All experiments so far have observed fast loss of molecules from the trap. However, the dominant mechanism for collisional loss is not well understood when there are no allowed 2-body loss processes. Here we experimentally investigate collisional losses of nonreactive ultracold ⁸⁷Rb¹³³Cs molecules, and compare our findings with the sticky collision hypothesis that pairs of molecules form long-lived collision complexes. We demonstrate that loss of molecules occupying their rotational and hyperfine ground state is best described by second-order rate equations, consistent with the expectation for complex-mediated collisions, but that the rate is lower than the limit of universal loss. The loss is insensitive to magnetic field but increases for excited rotational states. We demonstrate that dipolar effects lead to significantly faster loss for an incoherent mixture of rotational states.

Ultracold polar molecules are an excellent platform for quantum science but experiments so far see fast trap losses that are poorly understood. Here the authors investigate collisional losses of nonreactive RbCs, and show they are consistent with the sticky collision hypothesis, but are slower than the universal rate.

Induced p-Wave Pairing in Bose-Fermi Mixtures

Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of p-wave pairing between spin polarized fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency and momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical temperature. Focusing on experimentally relevant systems, we perform a systematic analysis varying the boson-boson and boson-fermion interaction strength as well as their masses, and identify the most suitable system for realizing a p-wave superfluid. Our results show that such a superfluid indeed is experimentally within reach using light bosons mixed with heavy fermions.

Enhanced Shot Noise of Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot in SU(2) and SU(4) Kondo regimes

The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. Our result suggests that the Kondo effect is responsible for this strong enhancement.

Critical Vortex Shedding in a Strongly Interacting Fermionic Superfluid

We study the critical vortex shedding in a strongly interacting fermionic superfluid of ^{6}Li across the BEC-BCS crossover. By moving an optical obstacle in the sample and directly imaging the vortices after the time of flight, the critical velocity u_{vor} for vortex shedding is measured as a function of the obstacle travel distance L. The observed u_{vor} increases with decreasing L, where the rate of increase is the highest in the unitary regime. In the deep Bose-Einstein condensation regime, an empirical dissipation model well captures the dependence of u_{vor} on L, characterized by a constant value of η=-[d(1/u_{vor})/d(1/L)]. However, as the system is tuned across the resonance, a step increase of η develops about a characteristic distance L_{c} as L is increased, where L_{c} is comparable to the obstacle size. This bimodal behavior is strengthened as the system is tuned towards the BCS regime. We attribute this evolution of u_{vor} to the emergence of the underlying fermionic degree of freedom in the vortex-shedding dynamics of a Fermi condensate.

Controlling the Scattering Length of Ultracold Dipolar Molecules

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac field is increased, the long-range well becomes deeper and can support a certain number of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant B[over ˜]=B/s_{E_{3}} where s_{E_{3}} is a characteristic dipolar energy. We found that molecules with B[over ˜]>10^{8} are immune to any quenching losses when a sufficient ac field is applied, the ratio elastic to quenching processes can reach values above 10^{3}, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar to that for ultracold atoms.

High-Sensitivity rf Spectroscopy of a Strongly Interacting Fermi Gas

rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.

Nucleation of superfluid-light domains in a quenched dynamics

Strong correlation effects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-insulator to superfluid phase transition of atom-photon excitations. We demonstrate that the quenched dynamics of a finite-sized complex array of coupled resonators induces a first-order like phase transition. The latter is accompanied by domain nucleation that can be used to manipulate the photonic transport properties of the simulated superfluid phase; this in turn leads to an empirical scaling law. This universal behavior emerges from the light-matter interaction and the topology of the array. The validity of our results over a wide range of complex architectures might lead to a promising device for use in scaled quantum simulations.

Integrable Time-Dependent Quantum Hamiltonians

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Evidence from Quantum Monte Carlo Simulations of Large-Gap Superfluidity and BCS-BEC Crossover in Double Electron-Hole Layers

We report quantum Monte Carlo evidence of the existence of large gap superfluidity in electron-hole double layers over wide density ranges. The superfluid parameters evolve from normal state to BEC with decreasing density, with the BCS state restricted to a tiny range of densities due to the strong screening of Coulomb interactions, which causes the gap to rapidly become large near the onset of superfluidity. The superfluid properties exhibit similarities to ultracold fermions and iron-based superconductors, suggesting an underlying universal behavior of BCS-BEC crossovers in pairing systems.

The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.