Fermionic Atoms Research Articles

Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics.

Motivated by the outstanding challenge of realizing low-temperature states of quantum matter in synthetic materials, we propose and study an experimentally feasible protocol for preparing topological states such as Chern insulators. By definition, such (nonsymmetry protected) topological phases cannot be attained without going through a phase transition in a closed system, largely preventing their preparation in coherent dynamics. To overcome this fundamental caveat, we propose to couple the target system to a conjugate system, so as to prepare a symmetry protected topological phase in an extended system by intermittently breaking the protecting symmetry. Finally, the decoupled conjugate system is discarded, thus projecting onto the desired topological state in the target system. By construction, this protocol may be immediately generalized to the class of invertible topological phases, characterized by the existence of an inverse topological order. We illustrate our findings with microscopic simulations on an experimentally realistic Chern insulator model of ultracold fermionic atoms in a driven spin-dependent hexagonal optical lattice.

Creutz ladder in a resonantly shaken 1D optical lattice

We report the experimental realization of a Creutz ladder for ultracold fermionic atoms in a resonantly driven 1D optical lattice. The two-leg ladder consists of the two lowest orbital states of the optical lattice and the cross inter-leg links are generated via two-photon resonant coupling between the orbitals by periodic lattice shaking. The characteristic pseudo-spin winding structure in the energy bands of the ladder system is demonstrated using momentum-resolved Ramsey-type interferometric measurements. We discuss a two-tone driving method to extend the inter-leg link control and propose a topological charge pumping scheme for the Creutz ladder system.

Application of Grassmann phase space theory to Cooper pair model

This paper concerns the application of Grassmann phase space theory (GSPT) to treat the dynamical evolution of systems of identical fermions, such as ultracold gases of fermionic atoms. Phase space theory (which originated from quantum optics) is increasing in importance since it overcomes certain issues associated with other theoretical methods, such as Greens functions, variational methods, quantum-Monte-Carlo equations, etc. In phase-space theory quantum states are represented by quasi-probability distribution functions of phase space variables associated with canonical system operators—such as annihilation, creation operators. Evolution is described via a Fokker-Planck equation for the distribution function, which is equivalent to Ito stochastic equations for (time dependent) stochastic phase space variables. Quantum correlation functions given as averages of products of phase space variables over the quasi-probability distributions then become stochastic averages of products of stochastic phase space variables. In GSPT, the phase space variables are Grassmann numbers, but as computer representation of g-numbers is difficult, Grassmann phase space methods were regarded as being computationally inaccessible. However, previous work using the un-normalised B distribution shows that computer representation of Grassmann variables is unnecessary. Stochastic averages of products for quantum correlation functions at later times are related linearly to stochastic averages at earlier times via stochastic matrices only involving c-numbers. Thus, GSPT calculations of quantum correlation functions now only involve c-number computations. This paper presents the first correct numerical calculation of a quantum correlation function for a fermionic system using stochastic methods based on Grassmann phase space theory, namely the time dependence of the coherence between two Cooper pair states in a four-mode fermion system, where the short and finite time solutions can be compared to known exact results. Good agreement between the stochastic and exact results is found, showing that GPST is a valid approach for treating fermionic systems. The treatment of time evolution involves a novel use of the eigenvalues and biorthogonal column eigenvectors of a stochastically determined c-number matrix M and its transpose. Other topics of interest in ultra-cold fermi gases for which the GSPT could be applied are highlighted, such as the strong interaction regime for the BEC/BCS crossover achieved using magnetically tuned Feshbach resonance techniques.

Light mixed alkali microclusters

A quantum cluster approach for light mixed microclusters, composed of neutral alkali atoms and considered as atomic fermion clusters, is introduced.

Critical Josephson current in BCS-BEC–crossover superfluids

We develop a microscopic model to describe the Josephson dynamics between two superfluid reservoirs of ultracold fermionic atoms which accounts for the dependence of the critical current on both the barrier height and the interaction strength along the crossover from BCS to BEC. Building on a previous study [F. Meier & W. Zwerger, Phys. Rev. A, 64 033610 (2001)] of weakly-interacting bosons, we derive analytic results for the Josephson critical current at zero temperature for homogeneous and trapped systems at arbitrary coupling. The critical current exhibits a maximum near the unitarity limit which arises from the competition between the increasing condensate fraction and a decrease of the chemical potential along the evolution from the BCS to the BEC limit. Our results agree quantitatively with numerical simulations and recent experimental data.

Dark States of Multilevel Fermionic Atoms in Doubly Filled Optical Lattices.

We propose to use fermionic atoms with degenerate ground and excited internal levels (F_{g}→F_{e}), loaded into the motional ground state of an optical lattice with two atoms per lattice site, to realize dark states with no radiative decay. The physical mechanism behind the dark states is an interplay of Pauli blocking and multilevel dipolar interactions. The dark states are independent of lattice geometry, can support an extensive number of excitations, and can be coherently prepared using a Raman scheme taking advantage of the quantum Zeno effect. These attributes make them appealing for atomic clocks, quantum memories, and quantum information on decoherence free subspaces.

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.

Reservoir engineering of Cooper-pair-assisted transport with cold atoms

We show how Cooper-pair-assisted transport, which describes the stimulated transport of electrons in the presence of Cooper-pairs, can be engineered and controlled with cold atoms, in regimes that are difficult to access for condensed matter systems. Our model is a channel connecting two cold atomic gases, and the mechanism to generate such a transport relies on the coupling of the channel to a molecular BEC, with diatomic molecules of fermionic atoms. Our results are obtained using a Floquet–Redfield master equation that accounts for an exact treatment of the interaction between atoms in the channel. We explore, in particular, the impact of the coupling to the BEC and the interaction between atoms in the junction on its transport properties, revealing non-trivial dependence of the produced particle current. We also study the effects of finite temperatures of the reservoirs and the robustness of the current against additional dissipation acting on the junction. Our work is experimentally relevant and has potential applications to dissipation engineering of transport with cold atoms, studies of thermoelectric effects, quantum heat engines, or Floquet Majorana fermions.

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

In a recent work, Murmann et al (2015 Phys. Rev. Lett. 114 080402) have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first calculate Hubbard parameters using the finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

Magnetism driven by the interplay of fluctuations and frustration in the easy-axis triangular XXZ model with transverse fields

We study the combined effects of fluctuations and frustration in frustrated antiferromagnets described by the spin-1/2 easy-axis XXZ model with transverse magnetic fields, and propose its promising quantum simulation with a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.

Interaction-driven topological phase transition in a p -orbital honeycomb optical lattice

We investigate the phase diagram of interacting $p$-orbital Fermi atoms on honeycomb optical lattice. We find that the interatomic interactions play critical roles in such $p$-orbital systems, which can drive a first-order topological transition from normal phases with trivial topology to topological phases with nonvanishing Chern numbers. Due to the interplay among atomic interactions, the sublattice potential, and the filling factors, the phase diagram of the system exhibits rich phases, which are characterized by Chern numbers and corresponding edge states. Furthermore, the evolution of the band structures and the moving of Dirac cones along with the phase transitions are also discussed.

Analogue quantum chemistry simulation.

Computing the electronic structure of molecules with high precision is a central challenge in the field of quantum chemistry. Despite the success of approximate methods, tackling this problem exactly with conventional computers remains a formidable task. Several theoretical1,2 and experimental3-5 attempts have been made to use quantum computers to solve chemistry problems, with early proof-of-principle realizations done digitally. An appealing alternative to the digital approach is analogue quantum simulation, which does not require a scalable quantum computer and has already been successfully applied to solve condensed matter physics problems6-8. However, not all available or planned setups can be used for quantum chemistry problems, because it is not known how to engineer the required Coulomb interactions between them. Here we present an analogue approach to the simulation of quantum chemistry problems that relies on the careful combination of two technologies: ultracold atoms in optical lattices and cavity quantum electrodynamics. In the proposed simulator, fermionic atoms hopping in an optical potential play the role of electrons, additional optical potentials provide the nuclear attraction, and a single-spin excitation in a Mott insulator mediates the electronic Coulomb repulsion with the help of a cavity mode. We determine the operational conditions of the simulator and test it using a simple molecule. Our work opens up the possibility of efficiently computing the electronic structures of molecules with analogue quantum simulation.

Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling

In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge field using cold atoms. In the experiment, it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range inter-atomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, and paves the way for future characterizations of topological superfluid states in the experimentally relevant systems.

Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms.

We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.

Atoms trapped by a spin-dependent optical lattice potential: Realization of a ground-state quantum rotor

In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms undergo orbital motion around the potential minima. Such atoms are elementary quantum rotors. We develop the theory of such quantum rotors. Wave functions, energies, and degeneracies are determined for both bosonic and fermionic atoms, and magnetic dipole transitions between the states are elucidated. Quantum rotors in optical lattices with precisely one atom per unit cell can be used as high precision rotation sensors, accelerometers, and magnetometers.

Disagreement between non-relativistic and relativistic quantum dynamics of a driven electron

We show, both analytically and numerically, that the non-relativistic and relativistic quantum predictions for the dynamics of a prototypical driven electron – the periodically kicked rotor – do not always agree in the non-relativistic regime. The surprisingly different quantum predictions could be tested experimentally using ultra-cold fermionic atoms in a periodically-pulsed 1D optical lattice. Similar breakdown of agreement should occur for driven quantum systems in general. Since the relativistic theory should be empirically correct, it must be used instead of the approximate non-relativistic theory to correctly study the quantum dynamics of a driven system after the breakdown time, which could lead to important contributions in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.

Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions

Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W- and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order and second-order spin-resolved and spin-unresolved momentum correlations, aiming at matter-wave interference investigations with trapped massive particles in analogy with, and having the potential for expanding the scope of, recent three-photon quantum-optics interferometry.

Two-dimensional repulsive Fermi polarons with short- and long-range interactions

We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have the same mass and we consider the system to be composed of a uniform bath of a single species and a single atomic impurity. We use the diffusion Monte Carlo method to evaluate polaron properties such as its chemical potential and pair distribution functions, together with a discussion on the deficit of volume induced by the impurity. We also evaluate observables that allow us to determine the validity of the quasi-particle picture: the quasi-particle residue and the effective mass of the polaron. Employing two different potentials allows us to identify the universality regime, where the properties depend only on the gas parameter $n a_s^2$ fixed by the bath density and the two-dimensional scattering length.

Dynamical Thermalization of Interacting Fermionic Atoms in a Sinai Oscillator Trap

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the interactions, with a strength above a certain quantum chaos border given by the Åberg criterion, lead to the Fermi–Dirac distribution and relaxation of many-body initial states to the thermalized state in the absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt–Boltzmann dispute.

Looking for patterns in an optical lattice

Quantum Simulation One of the simplest models of interacting fermions on a two-dimensional (2D) lattice—the Hubbard model—becomes too tricky to simulate on classical computers as the density of empty lattice sites (holes) increases. Chiu et al. used a quantum microscope to take snapshots of thousands of realizations of the 2D Hubbard model in an optical lattice filled with fermionic lithium atoms at varying hole densities (see the Perspective by Schauss). The authors used pattern recognition algorithms to analyze the images, in which each lattice site was individually resolved. Comparing these patterns to the predictions of several theoretical models, they found the most consistency with the so-called geometric string model. Science , this issue p. [251][1]; see also p. [218][2] [1]: /lookup/doi/10.1126/science.aav3587 [2]: /lookup/doi/10.1126/science.aax6486