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.

[1]  D. R. Murray,et al.  Vortex nucleation in bose-einstein condensates due to effective magnetic fields , 2009 .

[2]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[3]  W. Ketterle,et al.  Condensation of pairs of fermionic atoms near a Feshbach resonance. , 2004, Physical review letters.

[4]  J. Dalibard,et al.  Practical scheme for a light-induced gauge field in an atomic Bose gas , 2008, 0811.3961.

[5]  Dalibard,et al.  Vortex formation in a stirred bose-einstein condensate , 1999, Physical review letters.

[6]  I Coddington,et al.  Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level. , 2003, Physical review letters.

[7]  C. E. Wieman,et al.  Vortices in a Bose Einstein condensate , 1999, QELS 2000.

[8]  R. Laughlin.  Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations , 1983 .

[9]  I. Spielman.  Raman processes and effective gauge potentials , 2009, 0905.2436.

[10]  J. Ruseckas,et al.  Light-induced effective magnetic fields for ultracold atoms in planar geometries , 2005, quant-ph/0511226.

[11]  E. J. Yarmchuk,et al.  Observation of Stationary Vortex Arrays in Rotating Superfluid Helium , 1979 .

[12]  G. Juzeliūnas,et al.  Slow light in degenerate fermi gases. , 2004, Physical review letters.

[13]  J. Dalibard,et al.  Geometric potentials in quantum optics: A semi-classical interpretation , 2008, 0807.4066.

[14]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[15]  M. Greiner,et al.  Observation of resonance condensation of fermionic atom pairs. , 2004, Physical review letters.

[16]  I. B. Spielman,et al.  A pr 2 00 9 Rapid production of 87 Rb BECs in a combined magnetic and optical potential , 2009, 0904.3314.

[17]  M. Kastner,et al.  Quasi-Particle Properties from Tunneling in the v = 5/2 Fractional Quantum Hall State , 2008, Science.

[18]  Pierre Cladé,et al.  Quantized rotation of atoms from photons with orbital angular momentum. , 2006, Physical review letters.

[19]  A. Schirotzek,et al.  Vortices and superfluidity in a strongly interacting Fermi gas , 2005, Nature.

[20]  P. Zoller,et al.  Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms , 2003, quant-ph/0304038.

[21]  D. Hofstadter.  Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields , 1976 .

[22]  C. W. Gardiner,et al.  Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques , 2008, 0809.1487.

[23]  W. Phillips,et al.  Bose-Einstein condensate in a uniform light-induced vector potential. , 2008, Physical review letters.

[24]  W. Ketterle,et al.  Observation of Vortex Lattices in Bose-Einstein Condensates , 2001, Science.

[25]  Taylor Francis Online,et al.  Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond , 2006, cond-mat/0606771.

[26]  N. Cooper.  Rapidly rotating atomic gases , 2008, 0810.4398.

[27]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[28]  C. Pethick,et al.  ZERO-TEMPERATURE PROPERTIES OF A TRAPPED BOSE-CONDENSED GAS: BEYOND THE THOMAS-FERMI APPROXIMATION , 1997 .

[29]  M. Lukin,et al.  Fractional quantum Hall states of atoms in optical lattices. , 2004, Physical Review Letters.

[30]  D. Pritchard,et al.  Imprinting vortices in a Bose-Einstein condensate using topological phases. , 2002, Physical review letters.

[31]  M. Berry.  Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[32]  D. C. Tsui,et al.  Two-Dimensional Magnetotransport in the Extreme Quantum Limit , 1982 .