I. B. Spielman

Spin–orbit-coupled Bose–Einstein condensates

Spin–orbit (SO) coupling—the interaction between a quantum particle’s spin and its momentum—is ubiquitous in physical systems. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Quantum many-body systems of ultracold atoms can be precisely controlled experimentally, and would therefore seem to provide an ideal platform on which to study SO coupling. Although an atom’s intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the centre-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose–Einstein condensate by dressing two atomic spin states with a pair of lasers. Such coupling has not been realized previously for ultracold atomic gases, or indeed any bosonic system. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase-separated state (above a critical laser intensity). We develop a many-body theory that provides quantitative agreement with the observed location of the transition. The engineered SO coupling—equally applicable for bosons and fermions—sets the stage for the realization of topological insulators in fermionic neutral atom systems.

Synthetic magnetic fields for ultracold neutral atoms

Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation—a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall effect in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, which is evident from the appearance of vortices in our Bose–Einstein condensate. Our approach uses a spatially dependent optical coupling between internal states of the atoms, yielding a Berry’s phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems. With a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.

Resonantly Enhanced Tunneling in a Double Layer Quantum Hall Ferromagnet

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling

Spin–orbit coupling in quantum gases

\nu_T=1

Bose-Einstein condensate in a uniform light-induced vector potential.

the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed.

Mott-insulator transition in a two-dimensional atomic bose gas

Spin–orbit coupling links a particle’s velocity to its quantum-mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin–orbit coupling originates from the movement of electrons in a crystal’s intrinsic electric field, which is uniquely prescribed in any given material. In contrast, for ultracold atomic systems, the engineered ‘material parameters’ are tunable: a variety of synthetic spin–orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical status of spin–orbit coupling in ultracold atomic systems, discussing unique features that enable physics impossible in any other known setting.

High frequency conductivity of the high-mobility two-dimensional electron gas

We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed 87Rb atoms in the F=1 hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential whose magnitude is set by the strength and detuning of the Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to nonuniform vector potentials, giving nonzero effective magnetic fields.

Realistic time-reversal invariant topological insulators with neutral atoms.

Cold atoms confined in periodic potentials are remarkably versatile quantum systems for implementing simple models prevalent in condensed matter theory. In the current experiment, we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and we study the resulting Mott insulating state (a phase of matter in which atoms are localized on specific lattice sites). We measure momentum distributions which agree quantitatively with theory (no adjustable parameters). We also study correlations in atom shot nose and observe a pronounced dependence on the lattice depth, this dependence indicates geometric effects to first order and suggests deviations due to higher order corrections.

Visualizing edge states with an atomic Bose gas in the quantum Hall regime

We measure the real and imaginary conductivity sigma(k = 0,omega) of a high-mobility two-dimensional electron gas (2DEG) system at frequencies below and above the momentum scattering rate. The imaginary part of the 2DEG impedance is observed to be inductive, consistent with the Drude model. Using this kinetic inductance, we construct a transmission line by capacitively coupling the 2DEG to an Al Schottky barrier gate separated by 5000 A from the 2DEG. The measured wave velocity and temperature-dependent damping of this transmission line are in good agreement with a simple Drude model. Exciting these modes is equivalent to exciting a 2D plasma mode strongly modified by the interaction between the 2DEG and the gate.

Observation of Quantized Hall Drag in a Strongly Correlated Bilayer Electron System

We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multiband system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Because of their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.