Experimental realization of strong effective magnetic fields in optical superlattice potentials

We present the experimental generation of large effective magnetic fields for ultracold atoms using photon-assisted tunneling in an optical superlattice. The underlying method does not rely on the internal structure of the atoms and, therefore, constitutes a general approach to realize widely tunable artificial gauge fields without the drawbacks of near-resonant optical potentials. When hopping in the lattice, the accumulated phase shift by an atom is equivalent to the Aharonov–Bohm phase of a charged particle exposed to a staggered magnetic field of large magnitude, on the order of one flux quantum per plaquette. We study the ground state of this system and observe that the frustration induced by the magnetic field can lead to a degenerate ground state for non-interacting particles. We provide a local measurement of the phase acquired by single particles due to photon-assisted tunneling. Furthermore, the quantum cyclotron orbit of single atoms in the lattice exposed to the effective magnetic field is directly revealed.     

Fractional quantum Hall states of atoms in optical lattices

We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. In a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type, and we show how these states can be reached by melting a Mott-insulator state in a superlattice potential. Finally, we discuss techniques to observe these strongly correlated states.     

High-field fractional quantum Hall effect in optical lattices

We consider interacting bosonic atoms in an optical lattice subject to a large simulated magnetic field. We develop a model similar to a bilayer fractional quantum Hall system valid near simple rational numbers of magnetic flux quanta per lattice cell. Then we calculate its ground state, magnetic lengths, fractional fillings, and find unexpected sign changes in the Hall current. Finally we study methods for detecting these novel features via shot noise and Hall current measurements.     

Magnetism in artificial lattices

We compare magnetism in two artificial lattice structures, a quantum dot array formed in a two-dimensional electron gas and an optical lattice loaded with repulsive, contact-interacting fermionic atoms. When the tunneling between the lattice sites is strong, both lattices are non-magnetic. With reduced tunneling in the tight-binding limit, the shell-filling of the single-site quantum wells combined with Hund's rule determines the magnetism. This leads to a systematic magnetic phase diagram with non-magnetic, ferromagnetic and antiferromagnetic phases.     

Exact parent Hamiltonian for the quantum Hall states in a lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.     

Degeneracy of many-body quantum states in an optical lattice under a uniform magnetic field

We prove a theorem that shows the degeneracy of many-body states for particles in a periodic lattice and under a uniform magnetic field depends on the total particle number and the flux filling ratio. Noninteracting fermions and weakly interacting bosons are given as two examples. For the latter case, the phenomenon can also be physically understood in terms of destructive quantum interference of multiple symmetry-related tunneling paths between classical energy minima, which is reminiscent of the spin-parity effect discovered in magnetic molecular clusters. We also show that the quantum ground state of a mesoscopic number of bosons in this system is not a simple mean-field state but a fragmented state even for very weak interactions.     

弱磁场下三阱光学超晶格中自旋为1的超冷原子特性研究

双阱光学超晶格中的超冷原子是近期冷原子物理领域的研究热点. 本文推广提出了实现三阱光学超晶格的方案, 并采用精确对角化的方法分别研究了弱磁场下对称三阱 光学超晶格中铁磁性和反铁磁性的自旋为1的原子系统的基态, 发现二者的相图很不相同: 反铁磁性原子对应的相图中没有沿磁场方向总自旋磁量子数为±2的基态, 而铁磁性原子对应的相图中可能有. 在负的二次塞曼能量区域, 铁磁性原子的相图中只有完全极化态. 分析了可控参数影响基态的物理本质. 由于这些量子自旋态可以通过调节外磁场和光势垒的高度非常简便而精确地控制, 适合用来研究自旋纠缠. 关键词： 三阱光学超晶格 自旋为1的原子 弱磁场     

Generation of entanglement in finite spin systems via adiabatic quantum computation

For a finite XY chain and a finite two-dimensional Ising lattice, it is shown that the paramagnetic ground state is adiabatically transformed to the Greenberger-Horne-Zeilinger state in the ferromagnetic phase by changing slowly the external magnetic field. It is found that the fidelity between the Greenberger-Horne-Zeilinger state and an adiabatically evolved state depends on the interpolation schemes as well as the energy gap between the ground and exited states. A possibility whether quantum phase transitions can be simulated on adiabatic quantum computation is discussed.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.     

Supersolids versus phase separation in two-dimensional lattice bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.     

Topological phase interference effects in resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells in mesoscopic single-domain antiferromagnets

Resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells is investigated theoretically for a nanometer-scale single-domain antiferromagnet with biaxial crystal symmetry in the presence of an external magnetic field applied along the easy anisotropy axis, based on the two-sublattice model. Both the Wentzel-Kramers-Brillouin exponent and the preexponential factors are evaluated in the instanton contribution to the tunneling rate for finite and zero magnetic fields by applying the instanton technique in the spin-coherent-state path-integral representation, respectively. The quantum interference or spin-parity effects induced by the topological phase term in the Euclidean action are discussed in the rate of quantum tunneling of the Néel vector. In the absence of an external applied magnetic field, the effect of destructive phase interference or topological quenching on resonant quantum tunneling of the Néel vector is evident for the half-integer excess spin antiferromagnetic nanoparticle. In the weak field limit, the tunneling rates are found to oscillate with the external applied magnetic field for both integer and half-integer excess spins. We discuss the experimental condition on the applied magnetic field which may allow one to observe the topological quenching effect for nanometer-scale single-domain antiferromagnets with half-integer excess spins. Tunneling behavior in resonant quantum tunneling of the magnetization vector between nonequivalent magnetic wells is also studied for a nanometer-scale single-domain ferromagnet by applying the similar technique, but in the large noncompensation limit. Received 4 June 1999     

Two-dimensional Rydberg gases and the quantum hard-squares model

We study a two-dimensional lattice gas of atoms that are photoexcited to Rydberg states in which they interact via the van?der?Waals interaction. We explore the regime of dominant nearest-neighbor interaction where this system is intimately connected with a quantum version of Baxter's hard-squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard-squares model. This correspondence allows us to identify a phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase.     

Spectroscopic determination of the order parameter of coupled bilayers at =1

We report inelastic light scattering measurements of spin excitations on coupled electron bilayers with relatively large tunneling gaps at total filling factor ν_T=1. We show that the pseudospin polarization order parameter, where the pseudospin labels the occupation of symmetric and antisymmetric levels, can be determined from the energy of long wavelength spin excitations. Our experiments indicate that the order parameter in the quantum Hall ground state collapses at the incompressible–compressible phase transition. The latter is driven by decreasing the tunneling gap through the application of an in-plane magnetic field.     

The macroscopic quantum phase of ultracold degenerate gases in the asymmetrical two-dimensional magnetic lattice

We investigate the existence of the macroscopic quantum phase in trapped ultracold quantum degenerate gases in an asymmetrical two-dimensional magnetic lattice. We show the key to adiabatically control the tunneling in the new two-dimensional magnetic lattice by means of external magnetic bias fields. In solving the system of coupled time-dependent differential equations, described here by the Boson Josephson Junctions (BJJs), we used an order parameter that includes both time-dependent variational parameters to describe the fractional population at each lattice site and the phase difference to quantify the macroscopic quantum phase signature. A dynamical oscillation of the fractional population and the phase difference at each individual lattice site is observed when solving the BJJs system.     

Light-Induced Hofstadter＇s Butterfly Spectrum in Optical Lattices

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on A-type three-level atoms. When the dimensionless parameter a, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter＇s butterfly.     

Spin waves and quantum criticality in the frustrated XY pyrochlore antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.     

Ground state phase diagram of a spin-2 antiferromagnet on the square lattice

We use the vertex state model approach to construct optimum ground states for a large class of quantum spin-2 antiferromagnets on the square lattice. Optimum ground states are exact ground states of the model which minimize all local interaction operators. The ground state contains two continuous parameters and exhibits a second order phase transition from a disordered phase with exponentially decaying correlation functions to a Néel ordered phase. The behaviour is very similar to that of the corresponding ground state of a quantum spin-3/2 model on the hexagonal lattice, which has been investigated in an earlier paper. Received 8 April 1999     

Spin relaxation and band excitation of a dipolar Bose-Einstein condensate in 2D optical lattices

We observe interband transitions mediated by dipole-dipole interactions for an array of 1D quantum gases of chromium atoms, trapped in a 2D optical lattice. Interband transitions occur when dipolar relaxation releases an energy larger than the lattice band gap. For symmetric lattice sites, and a magnetic field parallel to the lattice axis, we compare the measured dipolar relaxation rate with a Fermi golden rule calculation. Below a magnetic field threshold, we obtain an almost complete suppression of dipolar relaxation, leading to metastable 1D gases in the highest Zeeman state.     

Vortex fusion and giant vortex states in confined superconducting condensates

In a direct scanning tunneling spectroscopy experiment we address the problem of the quantum vortex phases in strongly confined superconductors. The strong confinement regime is achieved in in situ grown ultrathin single nanocrystals of Pb by tuning their lateral size to a few coherence lengths. Upon an external magnetic field, the scanning tunneling spectroscopy revealed novel ultradense arrangements of single Abrikosov vortices characterized by an intervortex distance up to 3 times shorter than the bulk critical one. At yet stronger confinement we discovered the giant vortex phase; the spatial evolution of the excitation tunneling spectra in the cores of these unusual quantum objects was explored. We anticipate the giant vortex phase to be a common feature of other confined quantum condensates such as superfluids, Bose-Einstein condensates of cold atoms, etc.     

Quantum phases in a resonantly interacting boson-fermion mixture

We consider a resonantly interacting boson-fermion mixture of 40K and 87Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for 40K and 87Rb atoms, and 40K-87Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.