Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.     

Phase-Modulated 2D Topological Physics in a One-Dimensional Ultracold System

We propose a one-dimensional optical lattice model to simulate and explore two-dimensional topological phases with ultracold atoms,considering the phases of the hopping strengths as an extra dimension.It is shown that the model exhibits nontrivial phases,and corresponding two chiral-edge states.Moreover,we demonstrate the connections between changes in the topological invariants and the Dirac points.Furthermore,the topological order detected by the particle pumping approach in cold atoms is also investigated.The results obtained here provide a feasible and flexible method of simulating and exploring high-dimensional topological phases in lowdimension systems via the controllable phase of the hopping strength.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

Evanescent-wave mirror for ultracold diatomic polar molecules

We describe the interaction of an ultracold diatomic polar molecule with an evanescent-wave mirror. Several features of this system are explored, such as the coupling between internal rovibrational states of the molecule and the laser field. Numerical simulations show quantum reflection and state selection under attainable physical conditions. Such molecular optics components will facilitate the manipulation and trapping of ultracold molecules, and might serve in future applications in several fields, e.g., as devices to filter and select a state for ultracold chemistry, to measure extremely low temperatures of molecules, or to manipulate states for quantum information processing.     

Interaction-Induced Chiral Quantum States of the Ultracold Polar Molecules

The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.     

Interaction-Induced Chiral Quantum States of the Ultracold Polar Molecules

The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving field. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chiral states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.     

Competition between Abelian and Zeeman magnetic field effects in a two dimensional ultracold gas of fermions

The ground state of ultracold fermions in the presence of effects of orbital and Zeeman magnetic fields is analyzed. Five different states are found: unpolarized superconducting state, partially and fully polarized normal states and phase separated regions, partially or fully polarized. The system, in the presence of orbital synthetic magnetic field effects, shows non-monotonous changes of the phase boundaries when electron concentration is varied. We observe not only reentrant phenomena, but also density dependent oscillations of different areas of the phase diagram. Moreover the chemical potential shows oscillatory behavior and discontinuities with respect to changes in the number of fermions.     

Ultracold atoms in a disordered crystal of light: towards a bose glass

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.     

Manipulating atoms and molecules with evanescent-wave mirrors

We explore how atoms and polar molecules can be manipulated using evanescent-wave mirrors (EWM). We review the simpler case of ultracold atoms incident on EWM, and show that quantum effects such as tunneling, above barrier reflection, and Casimir retardation corrections, can be probed. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the effective atom-EWM potential. We illustrate the concept with a bichromatic EWM created by using red and blue detuned lasers. Finally, we extend the treatment to ultracold diatomic polar molecules. Quantum reflection and molecular state selection are demonstrated under attainable physical conditions. By facilitating the manipulation and trapping of ultracold molecules, such molecular mirrors could have several applications, e.g., as devices to filter and select state for ultracold chemistry, or to manipulate states for quantum information processing.     

Magnetic phase transitions in one-dimensional strongly attractive three-component ultracold fermions

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.     

Integrative models for asymmetric fermi superfluids: emergence of a new exotic pairing phase

We introduce an exactly solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair excitations. It is proven that this phase is the exact ground state in the strong-coupling limit, while numerical examples in finite lattices show that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.     

Geometric phases and criticality in spin-chain systems

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that corresponds to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. It is demonstrated that the resulting phase is resilient against the main sources of errors. A physical realization with ultracold atoms in optical lattices is presented.     

Cold and ultracold Rydberg atoms in strong magnetic fields

Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases, consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms, such as giant dipole states, are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence the electronic structure of Rydberg atoms, and we describe the utility of corresponding effects for achieving tightly trapped ultracold Rydberg atoms. We review recent work on large, extended cold Rydberg gases in magnetic fields and their formation in strongly magnetized ultracold plasmas through collisional recombination. Implications of these results for current antihydrogen production experiments are pointed out, and techniques for the trapping and cooling of such atoms are investigated.     

Strongly coupled chameleons and the neutronic quantum bouncer

We consider the potential detection of chameleons using bouncing ultracold neutrons. We show that the presence of a chameleon field over a planar plate would alter the energy levels of ultracold neutrons in the terrestrial gravitational field. When chameleons are strongly coupled to nuclear matter, β?10(8), we find that the shift in energy levels would be detectable with the forthcoming GRANIT experiment, where a sensitivity of the order of 1% of a peV is expected. We also find that an extremely large coupling β?10(11) would lead to new bound states at a distance of order 2 μm, which is already ruled out by previous Grenoble experiments. The resulting bound, β?10(11), is already 3 orders of magnitude better than the upper bound, β?10(14), from precision tests of atomic spectra.     

Quantum theory of a polarization phase gate in an atomic tripod configuration

We present the quantum theory of a polarization phase gate that can be realized in a sample of ultracold rubidium atoms driven into a tripod configuration. The main advantages of this scheme are its relative simplicity and inherent symmetry. It is shown that conditional phase shifts of order π can be attained.     

Observation of Feshbach-like resonances in collisions between ultracold molecules

We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level crossing which allows us to transfer the molecules into another state. In the new state, two Feshbach-like collision resonances show up as strong inelastic loss features. We interpret these resonances as being induced by Cs4 bound states near the molecular scattering continuum. The tunability of the interactions between molecules opens up novel applications such as controlled chemical reactions and synthesis of ultracold complex molecules.     

"Stückelberg interferometry" with ultracold molecules

We report on the realization of a time-domain "Stückelberg interferometer", which is based on the internal-state structure of ultracold Feshbach molecules. Two subsequent passages through a weak avoided crossing between two different orbital angular momentum states in combination with a variable hold time lead to high-contrast population oscillations. This allows for a precise determination of the energy difference between the two molecular states. We demonstrate a high degree of control over the interferometer dynamics. The interferometric scheme provides new possibilities for precision measurements with ultracold molecules.     

Harmonically trapped quasi-two-dimensional Fermi gases with synthetic spin-orbit coupling

We study the properties of spin-orbit coupled and harmonically trapped quasi-two-dimensional Fermi gas with tunable s-wave interaction between the two spin species. We adapt an effective two-channel model which takes the excited states occupation in the strongly confined axial direction into consideration by introducing dressed molecules in the closed channel, and use a Bogoliubovde Gennes (BdG) formalism to go beyond local density approximation. We find that both the in-trap phase structure and density distribution can be significantly modified near a wide Feshbach resonance compared with the single-channel model without the dressed molecules. Our findings will be helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.     

Non-uniform Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state

We provide a general review of the properties of the non-uniform superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase. Special emphasis is made on the orbital and crystal structure effects which may result in the quantum transitions between the higher Landau level states and should be responsible for the strong modification of the anisotropy of the critical field. The FFLO-type instability may be also expected in ultracold Fermi gases. In these systems it is caused not by the Zeeman interaction but by the tuning of the population imbalance between two lowest hyperfine states of the atoms. We also briefly discuss their properties.