Reversal of quantized Hall drifts at noninteracting and interacting topological boundaries.

The transport properties of gapless edge modes at boundaries between topologically distinct domains are of fundamental and technological importance. We experimentally studied long-distance quantized Hall drifts in a harmonically confined topological pump of ultracold fermionic atoms. We found that quantized drifts halt and reverse their direction when the atoms reach a critical slope of the confining potential, revealing the presence of a topological boundary. The drift reversal corresponded to a band transfer between a band with Chern number C = +1 and another with C = -1 through a gapless edge mode, in agreement with the bulk-edge correspondence for noninteracting particles. Nonzero repulsive Hubbard interactions led to the emergence of an additional edge in the system through a mechanism in which pairs of fermions are split.

Spin- and Momentum-Correlated Atom Pairs Mediated by Photon Exchange and Seeded by Vacuum Fluctuations.

Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this Letter, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single channel or two discernible channels. The scheme is independent of collisional interactions, fast, and tunable. We observe a collectively enhanced production of pairs and probe interspin correlations in momentum space. We characterize the emergent pair statistics and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.

Quantum Fluctuation Dynamics of Dispersive Superradiant Pulses in a Hybrid Light-Matter System.

We consider theoretically a driven-dissipative quantum many-body system consisting of an atomic ensemble in a single-mode optical cavity as described by the open Tavis-Cummings model. In this hybrid light-matter system, the interplay between coherent and dissipative processes leads to superradiant pulses with a buildup of strong correlations, even for systems comprising hundreds to thousands of particles. A central feature of the mean-field dynamics is a self-reversal of two spin degrees of freedom due to an underlying time-reversal symmetry, which is broken by quantum fluctuations. We demonstrate a quench protocol that can maintain highly non-Gaussian states over long timescales. This general mechanism offers interesting possibilities for the generation and control of complex fluctuation patterns, as suggested for the improvement of quantum sensing protocols for dissipative spin amplification.

Quantization and its breakdown in a Hubbard-Thouless pump.

Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems1. For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue-the Thouless pump2-4. However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms5-9, the study of topological matter under variations in interparticle interactions has proven challenging10. Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump's robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter10, including edge effects11 and interaction-induced topological phases12-15.

Superfluid Signatures in a Dissipative Quantum Point Contact.

We measure superfluid transport of strongly interacting fermionic lithium atoms through a quantum point contact with local, spin-dependent particle loss. We observe that the characteristic non-Ohmic superfluid transport enabled by high-order multiple Andreev reflections transitions into an excess Ohmic current as the dissipation strength exceeds the superfluid gap. We develop a model with mean-field reservoirs connected via tunneling to a dissipative site. Our calculations in the Keldysh formalism reproduce the observed nonequilibrium particle current, yet do not fully explain the observed loss rate or spin current.

Self-oscillating pump in a topological dissipative atom-cavity system.

Pumps are transport mechanisms in which direct currents result from a cyclic evolution of the potential1,2. As Thouless showed, the pumping process can have topological origins, when considering the motion of quantum particles in spatially and temporally periodic potentials3. However, the periodic evolution that drives these pumps has always been assumed to be imparted from outside, as has been the case in the experimental systems studied so far4-12. Here we report on an emergent mechanism for pumping in a quantum gas coupled to an optical resonator, where we observe a particle current without applying a periodic drive. The pumping potential experienced by the atoms is formed by the self-consistent cavity field interfering with the static laser field driving the atoms. Owing to dissipation, the cavity field evolves between its two quadratures13, each corresponding to a different centrosymmetric crystal configuration14. This self-oscillation results in a time-periodic potential analogous to that describing the transport of electrons in topological tight-binding models, such as the paradigmatic Rice-Mele pump15. In the experiment, we directly follow the evolution by measuring the phase winding of the cavity field with respect to the driving field and observing the atomic motion in situ. The observed mechanism combines the dynamics of topological and open systems, and features characteristics of continuous dissipative time crystals.

Topological Pumping in a Floquet-Bloch Band.

Constructing new topological materials is of vital interest for the development of robust quantum applications. However, engineering such materials often causes technological overhead, such as large magnetic fields, spin-orbit coupling, or dynamical superlattice potentials. Simplifying the experimental requirements has been addressed on a conceptual level-by proposing to combine simple lattice structures with Floquet engineering-but there has been no experimental implementation. Here, we demonstrate topological pumping in a Floquet-Bloch band using a plain sinusoidal lattice potential and two-tone driving with frequencies ω and 2ω. We adiabatically prepare a near-insulating Floquet band of ultracold fermions via a frequency chirp, which avoids gap closings en route from trivial to topological bands. Subsequently, we induce topological pumping by slowly cycling the amplitude and the phase of the 2ω drive. Our system is well described by an effective Shockley model, establishing a novel paradigm to engineer topological matter from simple underlying lattice geometries. This approach could enable the application of quantized pumping in metrology, following recent experimental advances on two-frequency driving in real materials.

Dissipation-Engineered Family of Nearly Dark States in Many-Body Cavity-Atom Systems.

Three-level atomic systems coupled to light have the capacity to host dark states. We study a system of V-shaped three-level atoms coherently coupled to the two quadratures of a dissipative cavity. The interplay between the atomic level structure and dissipation makes the phase diagram of the open system drastically different from the closed one. In particular, it leads to the stabilization of a continuous family of dark and nearly dark excited many-body states with inverted atomic populations as the steady states. The multistability of these states can be probed via their distinct fluctuations and excitation spectra, as well as the system's Liouvillian dynamics which are highly sensitive to ramp protocols. Our model can be implemented experimentally by encoding the two higher-energy modes in orthogonal density-modulated states in a bosonic quantum gas. This implementation offers prospects for potential applications like the realization of quantum optical random walks and microscopy with subwavelength spatial resolution.

Observing Dynamical Currents in a Non-Hermitian Momentum Lattice.

We report on the experimental realization and detection of dynamical currents in a spin-textured lattice in momentum space. Collective tunneling is implemented via cavity-assisted Raman scattering of photons by a spinor Bose-Einstein condensate into an optical cavity. The photon field inducing the tunneling processes is subject to cavity dissipation, resulting in effective directional dynamics in a non-Hermitian setting. We observe that the individual tunneling events are superradiant in nature and locally resolve them in the lattice by performing real-time, frequency-resolved measurements of the leaking cavity field. The results can be extended to a regime exhibiting a cascade of currents and simultaneous coherences between multiple lattice sites, where numerical simulations provide further understanding of the dynamics. Our observations showcase dynamical tunneling in momentum-space lattices and provide prospects to realize dynamical gauge fields in driven-dissipative settings.

Dissipation-induced structural instability and chiral dynamics in a quantum gas.

Dissipative and unitary processes define the evolution of a many-body system. Their interplay gives rise to dynamical phase transitions and can lead to instabilities. In this study, we observe a nonstationary state of chiral nature in a synthetic many-body system with independently controllable unitary and dissipative couplings. Our experiment is based on a spinor Bose gas interacting with an optical resonator. Orthogonal quadratures of the resonator field coherently couple the Bose-Einstein condensate to two different atomic spatial modes, whereas the dispersive effect of the resonator losses mediates a dissipative coupling between these modes. In a regime of dominant dissipative coupling, we observe the chiral evolution and relate it to a positional instability.

Quantum Simulation Meets Nonequilibrium Dynamical Mean-Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model.

We perform an ab initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross validates the experimental and numerical approaches in a strongly correlated nonequilibrium system.

Quantized Conductance through a Spin-Selective Atomic Point Contact.

We implement a microscopic spin filter for cold fermionic atoms in a quantum point contact (QPC) and create fully spin-polarized currents while retaining conductance quantization. Key to our scheme is a near-resonant optical tweezer inducing a large effective Zeeman shift inside the QPC while its local character limits dissipation. We observe a renormalization of this shift due to interactions of only a few atoms in the QPC. Our work represents the analog of an actual spintronic device and paves the way to studying the interplay between spin splitting and interactions far from equilibrium.

Floquet Dynamics in Driven Fermi-Hubbard Systems.

We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven systems. The dynamics of double occupancies for the near- and off-resonant driving regime indicate that the effective Hamiltonian picture is valid for several orders of magnitude in modulation time. Furthermore, we show that driving a hexagonal lattice compared to a simple cubic lattice allows us to modulate the system up to 1 s, corresponding to hundreds of tunneling times, with only minor atom loss. Here, driving at a frequency close to the interaction energy does not introduce resonant features to the atom loss.

Breakdown of the Wiedemann-Franz law in a unitary Fermi gas.

We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a nonequilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we extract the transport coefficients of the QPC and deduce a Lorenz number violating the Wiedemann-Franz law by one order of magnitude, a characteristic persisting even for a wide contact. In contrast, the Seebeck coefficient takes a value close to that expected for a noninteracting Fermi gas and shows a smooth decrease as the atom density close to the QPC is increased beyond the superfluid transition. Our work represents a fermionic analog of the fountain effect observed with superfluid helium and poses challenges for microscopic modeling of the finite temperature dynamics of the unitary Fermi gas.

Coupling two order parameters in a quantum gas.

Controlling matter to simultaneously support coupled properties is of fundamental and technological importance1 (for example, in multiferroics2-5 or high-temperature superconductors6-9). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology10,11 or modify properties12-16. Here, using a quantum gas to engineer an adjustable interaction at the microscopic level, we demonstrate scenarios of competition, coexistence and mutual enhancement of two orders. For the enhancement scenario, the presence of one order lowers the critical point of the other. Our system is realized by a Bose-Einstein condensate that can undergo self-organization phase transitions in two optical resonators17, resulting in two distinct crystalline density orders. We characterize the coupling between these orders by measuring the composite order parameter and the elementary excitations and explain our results with a mean-field free-energy model derived from a microscopic Hamiltonian. Our system is ideally suited to explore quantum tricritical points18 and can be extended to study the interplay of spin and density orders19 as a function of temperature20.

Metastability and avalanche dynamics in strongly correlated gases with long-range interactions.

We experimentally study the stability of a bosonic Mott insulator against the formation of a density wave induced by long-range interactions and characterize the intrinsic dynamics between these two states. The Mott insulator is created in a quantum degenerate gas of 87-Rubidium atoms, trapped in a 3D optical lattice. The gas is located inside and globally coupled to an optical cavity. This causes interactions of global range, mediated by photons dispersively scattered between a transverse lattice and the cavity. The scattering comes with an atomic density modulation, which is measured by the photon flux leaking from the cavity. We initialize the system in a Mott-insulating state and then rapidly increase the global coupling strength. We observe that the system falls into either of two distinct final states. One is characterized by a low photon flux, signaling a Mott insulator, and the other is characterized by a high photon flux, which we associate with a density wave. Ramping the global coupling slowly, we observe a hysteresis loop between the two states-a further signature of metastability. A comparison with a theoretical model confirms that the metastability originates in the competition between short- and global-range interactions. From the increasing photon flux monitored during the switching process, we find that several thousand atoms tunnel to a neighboring site on the timescale of the single-particle dynamics. We argue that a density modulation, initially forming in the compressible surface of the trapped gas, triggers an avalanche tunneling process in the Mott-insulating region.

Enhancement and sign change of magnetic correlations in a driven quantum many-body system.

Periodic driving can be used to control the properties of a many-body state coherently and to realize phases that are not accessible in static systems. For example, exposing materials to intense laser pulses makes it possible to induce metal-insulator transitions, to control magnetic order and to generate transient superconducting behaviour well above the static transition temperature. However, pinning down the mechanisms underlying these phenomena is often difficult because the response of a material to irradiation is governed by complex, many-body dynamics. For static systems, extensive calculations have been performed to explain phenomena such as high-temperature superconductivity. Theoretical analyses of driven many-body Hamiltonians are more challenging, but approaches have now been developed, motivated by recent observations. Here we report an experimental quantum simulation in a periodically modulated hexagonal lattice and show that antiferromagnetic correlations in a fermionic many-body system can be reduced, enhanced or even switched to ferromagnetic correlations (sign reversal). We demonstrate that the description of the many-body system using an effective Floquet-Hamiltonian with a renormalized tunnelling energy remains valid in the high-frequency regime by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model of the system in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetimes of the correlations in this system, periodic driving thus provides an alternative way of investigating unconventional pairing in strongly correlated systems experimentally.

Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas.

Higgs and Goldstone modes are collective excitations of the amplitude and phase of an order parameter that is related to the breaking of a continuous symmetry. We directly studied these modes in a supersolid quantum gas created by coupling a Bose-Einstein condensate to two optical cavities, whose field amplitudes form the real and imaginary parts of a U(1)-symmetric order parameter. Monitoring the cavity fields in real time allowed us to observe the dynamics of the associated Higgs and Goldstone modes and revealed their amplitude and phase nature. We used a spectroscopic method to measure their frequencies, and we gave a tunable mass to the Goldstone mode by exploring the crossover between continuous and discrete symmetry. Our experiments link spectroscopic measurements to the theoretical concept of Higgs and Goldstone modes.

Scanning Gate Microscope for Cold Atomic Gases.

We present a scanning probe microscopy technique for spatially resolving transport in cold atomic gases, in close analogy with scanning gate microscopy in semiconductor physics. The conductance of a quantum point contact connected to two atomic reservoirs is measured in the presence of a tightly focused laser beam acting as a local perturbation that can be precisely positioned in space. By scanning its position and recording the subsequent variations of conductance, we retrieve a high-resolution map of transport through a quantum point contact. We demonstrate a spatial resolution comparable to the extent of the transverse wave function of the atoms inside the channel and a position sensitivity below 10 nm. Our measurements agree well with an analytical model and ab initio numerical simulations, allowing us to identify a regime in transport where tunneling dominates over thermal effects. Our technique opens new perspectives for the high-resolution observation and manipulation of cold atomic gases.

Two-terminal transport measurements with cold atoms.

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.