Fermionic Atoms Research Articles

Single-particle excitations and metal-insulator transition of ultracold Fermi atoms in one-dimensional optical lattice with spin-orbit coupling

The dynamic structure factors reflecting the excitation spectra were investigated in a one-dimensional (1D) optical lattice with a spin-orbit coupling (SOC) effect. The results reveal that the single-particle excitations of both the density and spin dynamical structure factors are strongly reconstructed and split owing to the SOC effect, and a hat-like excitation band appears in the high-binding-energy region. The hat-like excitation band of the density dynamical structure factor exhibits an arc form, and has a pocket in the spin dynamical structure factor. In particular, only a gapless single-particle excitation point is left for both the density dynamical structure factor and the spin dynamical structure factor when the SOC strength reaches a critical point at half-filling. A stronger SOC strength causes the gapless excitation points to disappear, which indicates that the metal-insulator transition occurs. The metal-insulator transition only appears in half-filling and lightly doped regimes.

Signatures of discrete time-crystallinity in transport through an open Fermionic chain

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of discrete time-crystalline order are currently limited to magneto-optical experiments and it was never observed in a transport experiment performed on systems connected to external electrodes. Here we demonstrate that both discrete time-crystal and quasi-crystal survive a very general class of environments corresponding to single-particle gain and loss through system-electrode coupling over experimentally relevant timescales. Using dynamical symmetries, we analytically identify the conditions for observing time-crystalline behavior in a periodically driven open Fermi-Hubbard chain attached to electrodes. We show that the spin-polarized transport current directly manifests the existence of a time-crystalline behavior. Our findings are verifiable in present-day experiments with quantum-dot arrays and Fermionic ultra-cold atoms in optical lattices.

Numerical calculation of Green's function and momentum distribution for spin-polarized fermions by path integral molecular dynamics.

Most recently, path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of identical bosons and fermions by Hirshberg et al. In this work, we demonstrate that PIMD can be developed to calculate Green's function and extract momentum distributions for spin-polarized fermions. In particular, we show that the momentum distribution calculated by PIMD has potential applications to numerous quantum systems, e.g., ultracold fermionic atoms in optical lattices.

Two-dimensional attractive Hubbard model and the BCS-BEC crossover

Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak [Bardeen-Cooper-Schrieffer, (BCS)] and strong [Bose-Einstein condensation (BEC)] couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice from which several different quantities have been calculated and should be useful as a road map to experiments. We have obtained a detailed phase diagram for the critical superconducting temperature ${T}_{c}$ in terms of the band filling $\ensuremath{\langle}n\ensuremath{\rangle}$ and interaction strength $U$ from which we pinpoint a somewhat wide region $|U|/t\ensuremath{\approx}5\ifmmode\pm\else\textpm\fi{}1$ ($t$ is the hopping amplitude) and $\ensuremath{\langle}n\ensuremath{\rangle}\ensuremath{\approx}0.79\ifmmode\pm\else\textpm\fi{}0.09$ leading to a maximum ${T}_{c}\ensuremath{\approx}0.16t$. Two additional temperature scales, namely, pairing ${T}_{p}$ and degeneracy ${T}_{d}$ have been highlighted: The former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), whereas the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors.

Persistent Currents in Rings of Ultracold Fermionic Atoms.

We have produced persistent currents of ultracold fermionic atoms trapped in a ring, with lifetimes greater than 10sec in the strongly interacting regime. These currents remain stable well into the BCS regime at sufficiently low temperature. We drive a circulating BCS superfluid into the normal phase and back by changing the interaction strength and find that the probability for quantized superflow to reappear is remarkably insensitive to the time spent in the normal phase and the minimum interaction strength. After ruling out spontaneous current formation for our experimental conditions, we argue that the reappearance of superflow is due to weak damping of normal currents in this limit. These results establish that ultracold fermionic atoms with tunable interactions can be used to create matter-wave circuits similar to those previously created with weakly interacting bosonic atoms.

Density correlation functions and the spatial structure of the two-dimensional BEC-BCS crossover

The spatial structure of a two-dimensional homogeneous mixture of fermionic atoms in two hyperfine states is analyzed throughout the BEC-BCS crossover. Within the BCS-Leggett mean-field model we consider three functions: the pair wave function and the density-density correlation functions between atoms of the same and of different hyperfine states. For the correlation functions we derive analytical expressions which allow to unveil the rich spatial structure of the superfluid. Mainly, we are able to study the large-distance behavior of the three functions, which exhibits an exponential decay and a well-defined oscillatory behavior. We report closed-form expressions for the correlation lengths and mean pair radius. Differences and similarities emerge when comparing with the three dimensional case. Particularly, we find an expression for the large-distance correlation length, in terms of the chemical potential and the gap, valid in two and three dimensions, but whose dependence on the corresponding scattering lengths differ significantly.

Three ultracold fermions in a two-dimensional anisotropic harmonic confinement

We calculate the energy spectrum of three identical fermionic ultracold atoms in two different internal states confined in a two-dimensional anisotropic harmonic trap. Using the solutions of the corresponding two-body problems obtained in our previous work (Chen et al 2020 Phys. Rev. A 101, 053624), we derive the explicit transcendental equation for the eigen-energies, from which the energy spectrum is derived. Our results can be used for the calculation of the 3rd Virial coefficients or the studies of few-body dynamics.

Algebraic theory of quantum synchronization and limit cycles under dissipation

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

Mobile ion in a Fermi sea

The remarkable single particle control of individual ions combined with the versatility of ultracold atomic gases makes hybrid ion-atom system an exciting new platform for quantum simulation of few- and many-body quantum physics. Here, we study theoretically the properties of a mobile ion immersed in a quantum degenerate gas of fermionic atoms. Using an effective low-energy atom-ion interaction together with a well established approach that includes exactly two-body correlations, we calculate the full spectral response of the ion and demonstrate the existence of several quasiparticle branches, which are charged analogues of the Fermi polaron observed in neutral atomic gases. Due to the long-range nature of the atom-ion interaction, these ionic Fermi polarons have several properties distinct from their neutral counterparts such as the simultaneous presence of several stable states and smooth transitions from repulsive to attractive polarons with increasing interaction strength. Surprisingly, the residue of the ionic polaron is shown to increase with the Fermi density for fixed interaction strength, which is in marked contrast to the neutral polaron. The properties of the ionic polaron approach that of the neutral polaron only in the low density limit where the average interparticle spacing is larger than the characteristic length of the atom-ion interaction. We finally analyse the effects of the Fermi gas on the molecular ions, which are bound atom-dimer states.

Quantum register of fermion pairs.

Quantum control of motion is central for modern atomic clocks1 and interferometers2. It enables protocols to process and distribute quantum information3,4, and allows the probing of entanglement in correlated states of matter5. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs6, molecules7 and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems8, precision metrology based on atom pairs and molecules9,10 and, by implementing further advances11-13, digital quantum computation using fermion pairs14.

Strong Correlation Effects and Localization in Metallic Systems

We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.

Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid

Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.

Pauli blocking of light scattering in degenerate fermions.

Pauli blocking of spontaneous emission is responsible for the stability of atoms. Electrons cannot decay to lower-lying internal states that are already occupied. Pauli blocking also occurs when free atoms scatter light elastically (Rayleigh scattering) and the final external momentum states are already populated. This was predicted more than 30 years ago but is challenging to realize experimentally. Here, we report on Pauli blocking of light scattering in a dense quantum-degenerate Fermi gas of ultracold lithium atoms. When the Fermi momentum is larger than the photon recoil, most final momentum states are within the Fermi surface. At low temperature, we find that light scattered even at large angles is suppressed by 37% compared with higher temperatures, where atoms scatter at the single-atom Rayleigh scattering rate.

Pauli blocking of atom-light scattering.

Transition rates between coupled states in a quantum system depend on the density of available final states. The radiative decay of an excited atomic state has been suppressed by reducing the density of electromagnetic vacuum modes near the atomic transition. Likewise, reducing the density of available momentum modes of the atomic motion when it is embedded inside a Fermi sea will suppress spontaneous emission and photon scattering rates. Here we report the experimental demonstration of suppressed light scattering in a quantum degenerate Fermi gas. We systematically measured the dependence of the suppression factor on the temperature and Fermi energy of a strontium quantum gas and achieved suppression of scattering rates by up to a factor of 2 compared with a thermal gas.

Observation of Pauli blocking in light scattering from quantum degenerate fermions.

The Pauli exclusion principle forbids indistinguishable fermions from occupying the same quantum mechanical state. The implications of this are profound; for example, it accounts for the electronic shell structure of atoms. Here, we performed measurements on the scattering of light from ultracold ensembles of atoms. For a Fermi gas in the quantum degenerate regime, we observed a marked suppression in scattering compared with a similarly prepared Bose gas. The observed decrease in fluorescence and the corresponding increase in light transmission results from Pauli blocking, where Fermi-Dirac statistics limits the number of accessible states for a scattering atom in a large Fermi sea. Our work confirms a fundamental result on the optical response of quantum gases and may contribute to cooling and thermometry schemes.

Connecting topological Anderson and Mott insulators in disordered interacting fermionic systems

The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder/interaction induced edge excitations and charge pumping in optical lattices.

Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions

The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices.

Effects of quantum mechanical identity in particle scattering: experimental observations (and lack thereof)

ABSTRACT On the occasion of the 150th anniversary of Ernest Rutherford's birth I discuss how indistinguishabilty profoundly affects the collisions of identical particles. In the case of a Coulombic interaction this leads to a dramatic modification of Rutherford's famous scattering formula as predicted by Nevill Mott. An even more extreme example is provided by a low-energy scattering experiment of identical fermions interacting via a short range potential. Here indistinguishability will make or break the observation of scattered particles. This fascinating phenomenon has been observed using a laser-based collider for ultracold fermionic potassium atoms.

Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas.

Coupling Bose-Einstein condensates to optical cavities has enabled the study of many-body states with long-range interactions. However, equivalent experiments with ultracold Fermi gases have remained largely unexplored. Here, we report an experimental realization of a superradiant quantum phase transition of a degenerate Fermi gas in a transversely pumped optical cavity. The self-ordering checkerboard density pattern of Fermi gases and superradiant transitions of the cavity field spontaneously emerge by increasing the pumping intensity above a threshold value. The effects of Fermi statistics are manifested by an inverse square root scaling of the threshold with atom number and the slow dynamics of low–atomic momentum states. Our work provides an ideal platform for studying nonequilibirium dynamics of many-body states for long-range interacting Fermi gases.

Quantum Simulating the Electron Transport in Quantum Cascade Laser Structures

AbstractUltracold fermionic atoms are proposed to be used in 1D optical lattices to quantum simulate the electronic transport in quantum cascade laser (QCL) structures. The competition between the coherent tunneling among (and within) the wells and the dissipative decay at the basis of lasing is discussed. In order to validate the proposed simulation scheme, such competition is quantitatively addressed in a simplified 1D model. The existence of optimal relationships between the model parameters is shown, maximizing the particle current, the population inversion (or their product), and the stimulated emission rate. This substantiates the concept of emulating the QCL operation mechanisms in cold‐atom optical lattice simulators, laying the groundwork for addressing open questions, such as the impact of electron–electron scattering and the origin of transport‐induced noise, in the design of new‐generation QCLs.