Jahn-Teller-induced Berry phase in spin-orbit-coupled Bose-Einstein condensates

We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit coupled Bose-Einstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the Exe Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection is studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of the system is addressed and we verify how it affects the dynamics.

[1]  M. Möttönen,et al.  Non-Abelian magnetic monopole in a Bose-Einstein condensate. , 2008, Physical review letters.

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

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

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

[5]  C. Clark,et al.  Spin field effect transistors with ultracold atoms. , 2008, Physical review letters.

[6]  Jonas Larson,et al.  Jahn-Teller systems from a cavity QED perspective , 2008, 0804.4416.

[7]  X. Yi,et al.  Loschmidt echo and Berry phase around degeneracies in nonlinear systems , 2008, 0803.3148.

[8]  L. Deng,et al.  Gain-assisted superluminal optical solitons at very low light intensity , 2008 .

[9]  L. Santos,et al.  Landau levels of cold atoms in non-Abelian gauge fields , 2008, 0801.2935.

[10]  J. Ruseckas,et al.  Double and negative reflection of cold atoms in non-Abelian gauge potentials. , 2008, Physical review letters.

[11]  Joel M Bowman,et al.  Beyond Born-Oppenheimer , 2008, Science.

[12]  V. Galitski,et al.  Spin-orbit coupled Bose-Einstein condensates , 2007, 0712.2256.

[13]  E. Romera,et al.  Identifying wave-packet fractional revivals by means of information entropy. , 2007, Physical review letters.

[14]  L. Santos,et al.  Cold atom dynamics in non-Abelian gauge fields , 2007, 0801.2928.

[15]  Z. D. Wang,et al.  Detecting unambiguously non-Abelian geometric phases with trapped ions , 2007, 0709.4329.

[16]  V. Galitski,et al.  Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions. , 2007, Physical review letters.

[17]  L. Duan,et al.  Simulation and detection of dirac fermions with cold atoms in an optical lattice. , 2007, Physical review letters.

[18]  Li-Hua Lu,et al.  Effects of an optically induced non-Abelian gauge field in cold atoms , 2007, cond-mat/0701481.

[19]  E. I. Duzzioni,et al.  Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates , 2006, quant-ph/0612213.

[20]  M. Lewenstein,et al.  Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond , 2006, cond-mat/0606771.

[21]  Xiong-Jun Liu,et al.  Optically induced spin-Hall effect in atoms. , 2006, Physical review letters.

[22]  L. Duan,et al.  Spin Hall effects for cold atoms in a light-induced gauge potential. , 2006, Physical review letters.

[23]  M. Baer.  Beyond Born-Oppenheimer : conical intersections and electronic nonadiabatic coupling terms , 2006 .

[24]  S. Yang,et al.  Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling , 2006, cond-mat/0602512.

[25]  S. Stenholm,et al.  Validity of adiabaticity in cavity QED , 2005, quant-ph/0512027.

[26]  T. Chakraborty,et al.  Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling , 2005, cond-mat/0509170.

[27]  P. Kim,et al.  Experimental observation of the quantum Hall effect and Berry's phase in graphene , 2005, Nature.

[28]  A. Geim,et al.  Two-dimensional gas of massless Dirac fermions in graphene , 2005, Nature.

[29]  Biao Wu,et al.  Geometric phase for adiabatic evolutions of general quantum states. , 2005, Physical review letters.

[30]  O. Mandel,et al.  Phase coherence of an atomic Mott insulator. , 2005, Physical review letters.

[31]  J. Ruseckas,et al.  Non-Abelian gauge potentials for ultracold atoms with degenerate dark states. , 2005, Physical review letters.

[32]  J. Ruseckas,et al.  Effective magnetic fields in degenerate atomic gases induced by light beams with orbital angular momenta , 2004, cond-mat/0412015.

[33]  M. Oberthaler,et al.  Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. , 2004, Physical review letters.

[34]  C. Kane,et al.  Quantum spin Hall effect in graphene. , 2004, Physical review letters.

[35]  E. Olğar,et al.  Solution of a Hamiltonian of quantum dots with Rashba spin?orbit coupling: quasi-exact solution , 2004, quant-ph/0411124.

[36]  L. Kwek,et al.  Kinematic approach to the mixed state geometric phase in nonunitary evolution. , 2004, Physical review letters.

[37]  V. Konotop,et al.  Modern Physics Letters B c ○ World Scientific Publishing Company Theory of Nonlinear Matter Waves in Optical Lattices , 2004 .

[38]  Jing Zhang,et al.  Experimental study of the BEC-BCS crossover region in lithium 6. , 2004, Physical review letters.

[39]  S. Shen,et al.  Dynamics and Berry phase of two-species Bose-Einstein condensates (9 pages) , 2004, cond-mat/0403570.

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

[41]  R. Robinett.  Quantum wave packet revivals , 2004, quant-ph/0401031.

[42]  I. Carusotto,et al.  Spin-orbit coupling and Berry phase with ultracold atoms in 2D optical lattices. , 2003, Physical review letters.

[43]  Biao Wu,et al.  Nonlinear evolution of quantum states in the adiabatic regime. , 2003, Physical review letters.

[44]  D. Leibfried,et al.  Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate , 2003, Nature.

[45]  C. Monroe,et al.  Quantum dynamics of single trapped ions , 2003 .

[46]  H. Smith,et al.  Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential , 2003, cond-mat/0301012.

[47]  Y. Ohashi,et al.  BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance. , 2002, Physical review letters.

[48]  I. Fuentes-guridi,et al.  Geometric phases of mesoscopic spin in Bose-Einstein condensates , 2001, quant-ph/0108078.

[49]  W. Xiang-bin,et al.  Nonadiabatic conditional geometric phase shift with NMR. , 2001, Physical review letters.

[50]  M. Baer,et al.  The open path phase for degenerate and non-degenerate systems and its relation to the wave-function modulus , 2004, physics/0406122.

[51]  Bose,et al.  Proposal for measurement of harmonic oscillator berry phase in ion traps , 2000, Physical review letters.

[52]  Jonathan A. Jones,et al.  Geometric quantum computation using nuclear magnetic resonance , 2000, Nature.

[53]  Biao Wu,et al.  Nonlinear Landau-Zener tunneling , 2000 .

[54]  S. Dutta,et al.  Tunneling Dynamics and Gauge Potentials in Optical Lattices , 1999 .

[55]  S. Adhikari,et al.  The conical intersection effects and adiabatic single-surface approximations on scattering processes: A time-dependent wave packet approach , 1999 .

[56]  Klaas Bergmann,et al.  LASER-DRIVEN POPULATION TRANSFER IN FOUR-LEVEL ATOMS : CONSEQUENCES OF NON-ABELIAN GEOMETRICAL ADIABATIC PHASE FACTORS , 1999 .

[57]  C. Wieman,et al.  Measurements of Relative Phase in Two-Component Bose-Einstein Condensates [Phys. Rev. Lett. 81, 1543 (1998)] , 1998 .

[58]  C. K. Law,et al.  Quantum Spins Mixing in Spinor Bose-Einstein Condensates , 1998, cond-mat/9807258.

[59]  H. Köppel,et al.  Geometric phases and quantum dynamics in spin–orbit coupled systems , 1998 .

[60]  G. Nienhuis,et al.  Geometric potentials for subrecoil dynamics , 1998 .

[61]  D. Stamper-Kurn,et al.  OPTICAL CONFINEMENT OF A BOSE-EINSTEIN CONDENSATE , 1997, cond-mat/9711273.

[62]  E. Sjöqvist,et al.  Noncyclic geometric phase, coherent states, and the time-dependent variational principle: Application to coupled electron-nuclear dynamics , 1997 .

[63]  R. Baer,et al.  A study of conical intersection effects on scattering processes: The validity of adiabatic single‐surface approximations within a quasi‐Jahn–Teller model , 1996 .

[64]  Lewenstein,et al.  Quantum Phase Diffusion of a Bose-Einstein Condensate. , 1996, Physical review letters.

[65]  D. Yarkony.  Diabolical conical intersections , 1996 .

[66]  M. Olshanii,et al.  Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice. , 1996, Physical review letters.

[67]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[68]  H. Köppel,et al.  Geometric phase effects and wave packet dynamics on intersecting potential energy surfaces , 1995 .

[69]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[70]  R. Simon,et al.  Quantum Kinematic Approach to the Geometric Phase. I. General Formalism , 1993 .

[71]  Verhaar,et al.  Threshold and resonance phenomena in ultracold ground-state collisions. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[72]  C. Mead,et al.  The geometric phase in molecular systems , 1992 .

[73]  M. Berry,et al.  The Born-Oppenheimer electric gauge force is repulsive near degeneracies , 1990 .

[74]  Samuel,et al.  General setting for Berry's phase. , 1988, Physical review letters.

[75]  E. Rashba,et al.  Oscillatory effects and the magnetic susceptibility of carriers in inversion layers , 1984 .

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

[77]  M. Feit,et al.  Solution of the Schrödinger equation by a spectral method , 1982 .

[78]  C. Mead.  The molecular Aharonov—Bohm effect in bound states , 1980 .

[79]  C. Mead,et al.  On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei , 1979 .

[80]  H. Feshbach.  Unified Theory of Nuclear Reactions , 1958 .

[81]  H. C. Longuet-Higgins,et al.  Studies of the Jahn-Teller effect .II. The dynamical problem , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[82]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .