Fermionic Quantum Gases Research Articles

Many-Body Quantum Systems

This workshop brought together experts on the analysis of quantum many-body problems and quantum statistical mechanics, with the goal of discussing the state-of-the-art of the field, recent developments as well as challenges for the future. The main topics of discussion concerned the equilibrium and dynamical behavior of (bosonic or fermionic) quantum gases, quantum spin systems, as well as quantum field theory models like the Nelson or Fröhlich model.

Fermionic quantum gas at finite temperature within a Lorentz-violating background

In this work we consider a fermionic quantum gas within a Lorentz-violating background at finite temperature. We derive the effective action within path integral formalism considering the interaction of external electromagnetic field and Lorentz-violating background fields with quantum fermions. To introduce the temperature effects, we employ the Matsubara formalism. Comments about the corresponding phenomenology are also made.

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

Molecular state in a spin–orbital-angular-momentum coupled Fermi gas

We study the two-body bound states in a spin-orbital-angular-momentum (SOAM) coupled quantum gas of fermions. Two different configurations are considered: an attractive $s$-wave interaction exists between two spin species that are SOAM coupled; and an atom with SOAM coupled internal spins interacts state-selectively with another atom. For both cases, we identify the condition for the emergence of molecular states with finite total angular momenta.These molecular states with quantized total angular momenta correspond to the SOAM-coupling-induced vortices in the corresponding Fermi superfluid. We propose to detect the molecules through Raman spectroscopy with Laguerre-Gaussian lasers. As the molecular states can form above the superfluid temperature, they offer an experimentally more accessible route toward the study of the underlying pairing mechanism under SOAM coupling.

Low-Field Feshbach Resonances and Three-Body Losses in a Fermionic Quantum Gas of 161Dy

We report on the high-resolution Feshbach spectroscopy on a degenerate, spin-polarized Fermi gas of 161Dy atoms, measuring three-body recombination losses at a low magnetic field. For field strengths up to 1 G, we identify as much as 44 resonance features and observe the plateaus of very low losses. For four selected typical resonances, we study the dependence of the threebody recombination rate coefficient on the magnetic resonance detuning and on the temperature. We observe a strong suppression of losses with decreasing temperature already for small detunings from the resonance. The characterization of complex behavior of the three-body losses of fermionic 161Dy is important for future applications of this peculiar species in research on atomic quantum gases.

Schrieffer-Wolff transformations for experiments: Dynamically suppressing virtual doublon-hole excitations in a Fermi-Hubbard simulator

In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by virtual excitations of high-energy states: For example, virtual doublon-hole excitations in the Fermi-Hubbard model mediate antiferromagnetic spin-exchange interactions in the derived effective model, known as the $t-J-3s$ model. Formally this procedure is described by performing a unitary Schrieffer-Wolff basis transformation. In the context of quantum simulation, it can be advantageous to consider the effective model to interpret experimental results. However, virtual excitations such as doublon-hole pairs can obfuscate the measurement of physical observables. Here we show that quantum simulators allow one to access the effective model even more directly by performing measurements in a rotated basis. We propose a protocol to perform a Schrieffer-Wolff transformation on Fermi-Hubbard low-energy eigenstates (or thermal states) to dynamically prepare approximate $t-J-3s$ model states using fermionic atoms in an optical lattice. Our protocol involves performing a linear ramp of the optical lattice depth, which is slow enough to eliminate the virtual doublon-hole fluctuations but fast enough to freeze out the dynamics in the effective model. We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the $t-J-3s$ model state. We compare our numerics to experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol can be beneficial to studies of effective models by enabling the suppression of virtual excitations in a wide range of quantum simulation experiments.

Control of high-order harmonic emission in solids via the tailored intraband current

Delocalized Bloch electrons in solids are usually regarded as a kind of representative quantum Fermi gas. To unravel the real-space dynamics of Bloch electrons under a tailoring intraband current, we introduced a quasiparticle picture of a wave packet via superposing the multiple Bloch states within a given crystal-momentum region. We find that temporal characteristics and yield modulation in solid-state high-harmonic generation (HHG) depend sensitively on the crystal-momentum region of generating electron-hole pair. Its mechanism could be clarified by the gradual symmetrization of the time-dependent carrier distribution with the growing tunneling-momentum range. Manipulation of tunneling-momentum range is experimentally feasible via photon-carrier doping of appropriate preexcitation pulse. Finally, we elucidate the role of dephasing in the process of HHG. The scheme of customizing intraband current provides an alternative way to regulate the high-harmonic generation of solids.

Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudo-density matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudo-snapshots of occupation numbers on large systems can be produced. There is a sign problem even when the conventional determinantal QMC algorithm can be made sign-problem free, and every pseudo-snapshot comes with a sign and a reweighting factor. Nonetheless, this "sampling sign problem" turns out to be weak and manageable in a large, relevant parameter regime. The method allows to compute distribution functions of arbitrary quantities defined in occupation number space and, from a practical point of view, facilitates the computation of complicated conditional correlation functions. While the projective measurements in quantum gas microscope experiments achieve direct sampling of occupation number states from the density matrix, the presented numerical method requires a Markov chain as an intermediate step and thus achieves only indirect sampling, but the full distribution of pseudo-snapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements

Exact N -point-function mapping between pairs of experiments with Markovian open quantum systems

We formulate an exact spacetime mapping between the $\mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A \textbf{94}, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $\mathcal{N}$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schr\"odinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $\mathcal{N}$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

Lattice modulation spectroscopy of one-dimensional quantum gases: Universal scaling of the absorbed energy

Lattice modulation spectroscopy is a powerful tool for probing low-energy excitations of interacting many-body systems. By means of bosonization we analyze the absorbed power in a one dimensional interacting quantum gas of bosons or fermions, subjected to a periodic drive of the optical lattice. For these Tomonaga Luttinger liquids we find a universal $\omega^3$ scaling of the absorbed power, that at very low-frequency turns into an $\omega^2$ scaling when scattering processes at the boundary of the system are taken into account. We confirm this behavior numerically by simulations based on time-dependent matrix product states. Furthermore, in the presence of impurities, the theory predicts an $\omega^2$ bulk scaling. While typical response functions of Tomonaga Luttinger liquids are characterized by exponents that depend on the interaction strength, modulation spectroscopy of cold atoms leads to a universal power-law exponent of the absorbed power. Our findings can be readily demonstrated in ultracold atoms in optical lattices with current experimental technology.

Landau–Kelly representation of statistical thermodynamics of a quantum plasma and electron emission from metals

We have investigated the influence of a strong magnetic field on various aspects of a quantum Fermi plasma. Due to the strong magnetic field, the distribution function becomes anisotropic. First, we consider non-degenerate quantum, Landau and Kelly distribution function. It was found that the adiabatic equation is similar to the adiabatic equation for a Maxwell distribution function, when we include the magnetic field in the energy expression. Using the Kelly distribution for a degenerate, quantum Fermi gas, parallel and perpendicular components of the pressure were derived. It was found that perpendicular component of pressure never becomes zero and three-dimensional system always stay three-dimensional. Lastly, we investigated electron emission from metals and have shown the influence of the magnetic field. We calculated thermionic emission, the so-called Richardson effect. In addition, we investigate the influence of external electromagnetic radiation on the electron current density (Hallwachs effect) from metals.

Dipole oscillations of fermionic quantum gases along the BEC-BCS crossover in disordered potentials

We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS crossover through disordered potentials. We observe a disorder-induced damping of oscillations as well as a change of the fundamental Kohn-mode frequency. The measurement results are compared to numerical density matrix renormalization group calculations as well as to a three-dimensional simulation of non-interacting fermions. Experimentally, we find a disorder-dependent damping, which grows approximately with the second power of the disorder strength. Moreover, we observe experimentally a change of oscillation frequency which deviates from the expected behavior of a damped harmonic oscillator on a percent level. While this behavior is qualitatively expected from the theoretical models used, quantitatively the experimental observations show a significantly stronger effect than predicted by theory. Furthermore, while the frequency shift seems to scale differently with interaction strength in the BEC versus BCS regime, the damping coefficient apparently decreases with the strength of interaction, but not with the sign, which changes for BEC and BCS type Fermi gases. This is surprising, as the dominant damping mechanisms are expected to be different in the two regimes.

Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas

We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for illustration, we explicitly consider the Fermi–Dirac entropy for fermions. The maximization of entropy at fixed mass energy and particle number determines the distribution function of the system and its equation of state. It also implies the Tolman–Oppenheimer–Volkoff equations of hydrostatic equilibrium and the Tolman–Klein relations. Our paper provides all the necessary equations that are needed to construct the caloric curves of self-gravitating fermions in general relativity obtained in recent works (Roupas and Chavanis in Class Quant Grav 36:065001, 2019; Chavanis and Alberti in Phys Lett B 801:135155, 2020). We consider the nonrelativistic limit $$c\rightarrow +\infty $$ and recover the equations obtained within the framework of Newtonian gravity. We also discuss the inequivalence of statistical ensembles as well as the relation between the dynamical and thermodynamical stability of self-gravitating systems in Newtonian gravity and general relativity.

Localized Magnetic Moments with Tunable Spin Exchange in a Gas of Ultracold Fermions.

We report on the experimental realization of a state-dependent lattice for a two-orbital fermionic quantum gas with strong interorbital spin exchange. In our state-dependent lattice, the ground and metastable excited electronic states of ^{173}Yb take the roles of itinerant and localized magnetic moments, respectively. Repulsive on-site interactions in conjunction with the tunnel mobility lead to spin exchange between mobile and localized particles, modeling the coupling term in the well-known Kondo Hamiltonian. In addition, we find that this exchange process can be tuned resonantly by varying the on-site confinement. We attribute this to a resonant coupling to center-of-mass excited bound states of one interorbital scattering channel.

Spin-charge separation in atomic chains

Quantum Magnetism Strongly interacting electrons lined up along a string can experience the so-called spin-charge separation, where the electrons “split” into effective carriers of spin and charge, which then move independently. This phenomenon has been observed, somewhat indirectly, in solids. Hilker et al. show spin-charge separation in a direct way by using a one-dimensional (1D) array of cold atoms, playing the role of electrons, whose degrees of freedom of spin and charge can be monitored using a fermionic quantum gas microscope. Empty sites in the 1D lattice moved freely without disturbing the underlying antiferromagnetic order. Science , this issue p. [484][1] [1]: /lookup/doi/10.1126/science.aam8990

Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators.

Topological phases, like the Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, nonlocal string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems owing to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of nonlocal spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique, which measures nonlocal order directly, can be readily extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.

Quantum correlations at infinite temperature: The dynamical Nagaoka effect

Do quantum correlations play a role in high temperature dynamics of many-body systems? A common expectation is that thermal fluctuations lead to fast decoherence and make dynamics classical. In this paper, we provide a striking example of a single particle created in a featureless, infinite temperature spin bath which not only exhibits non-classical dynamics but also induces strong long-lived correlations between the surrounding spins. We study the non-equilibrium dynamics of a hole created in a fermionic or bosonic Mott insulator in the atomic limit, which corresponds to a degenerate spin system. In the absence of interactions, the spin correlations arise purely from quantum interference, and the correlations are both antiferromagnetic and ferromagnetic, in striking contrast to the equilibrium Nagaoka effect. These results are relevant for several condensed matter spin systems, and should be observable using state of the art bosonic or fermionic quantum gas microscopes.

Correlation length and universality in the BCS-BEC crossover for energy-dependent resonance superfluidity

We consider the BCS-BEC crossover of a quantum Fermi gas at T = 0 in the presence of an energy-dependent Fano-Feshbach resonance, driving the system from broad to narrow limits. We choose a minimal microscopic potential reproducing the two-particle resonance physics in terms of the scattering length a and the effective range R ∗ representing the resonance width, and solve the BCS mean-field equations varying a, R ∗ and the density. We show that the condensate fraction manifests a universal behavior when the correlation length, measuring the pair size, is used as the crossover parameter. Generally, a negative effective range has the effect of stretching the crossover region between the two extreme regimes, as evidenced by the behavior of the chemical potential. These results can be useful in view of the more recent perspectives of realizing narrow resonances also by optical means and amenable as a base quantum Monte Carlo simulations.

The particle structure of the quantum mechanical Bose and Fermi gas

In the framework of von Neumann’s description of measurements of discrete quantum observables we establish a one-to-one correspondence between symmetric statistical operators W of quantum mechanical systems and classical point processes κ W , thereby giving a particle picture of indistinguishable quantum particles. This holds true under irreducibility assumptions if we fix the underlying complete orthonormal system. The method of the Campbell measure is developed for such statistical operators; it is shown that the Campbell measure of a statistical operator W coincides with the Campbell measure of the corresponding point process κ W . Moreover, again under irreducibility assumptions, a symmetric statistical operator is completely determined by its Campbell measure. Themethod of the Campbell measure then is used to characterize Bose-Einstein and Fermi-Dirac statistical operators. This is an elementary introduction into the work of Fichtner and Freudenberg [10, 11] combined with the quantum mechanical investigations of [2] and the corresponding point process approach of [30]. It is based on the classical work of von Neumann [22], Segal, Cook and Chaiken [7, 8, 28] as well as Moyal [18].

Cavity-induced generation of nontrivial topological states in a two-dimensional Fermi gas

We propose how topologically non-trivial states can dynamically organize in a fermionic quantum gas which is confined to a two-dimensional optical lattice potential and coupled to the field of an optical cavity. The spontaneously emerging cavity field induces together with coherent pump laser fields a dynamical gauge field for the atoms. Upon adiabatic elimination of the cavity degree of freedom, the system is described by an effective Hofstadter model with a self-consistency condition which determines the tunneling amplitude along the cavity direction. The fermions are found to self-organize into topologically non-trivial states which carry an extended edge state for a finite system size. Due to the dissipative nature of the cavity field, the topological steady states are protected from external perturbations.