Optical lattices H el` ene Perrin Laboratoire de physique des - PowerPoint PPT Presentation

Optical lattices H´ el` ene Perrin Laboratoire de physique des lasers, CNRS-Universit´ e Paris 13 Sorbonne Paris Cit´ e Exploring new quantum gases Les Houches, September 14–25, 2015 H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Principle of optical lattices Standing waves along 1, 2 or 3 axes, with different frequencies. 2 standing waves: 2D lattice of tubes 3 standing waves: 3D lattice I. Bloch, Nat. Phys. (2005) H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Band structure V 0 = 0 �� [ �� ] �� Comparison with free particle �� (left) of harmonic approximation �� (right) �� - �� - �� - �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Band structure V 0 = E rec V 0 = E rec �� [ �� ] �� [ �� ] �� - �� - �� - �� [ � ] �� - �� [ � ] gray zone: potential depth V 0 zoom around q = 1: gap opening H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Band structure V 0 = 2 E rec �� [ �� ] �� - �� - �� - �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Band structure V 0 = 4 E rec V 0 = 4 E rec �� [ �� ] �� [ �� ] �� - �� - �� - �� - �� - �� [ � ] �� - �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Bloch functions Bloch functions resemble plane waves at low V 0 , and series of peaks at large V 0 . � = �� = � �� V0 = 0 �� V0 = 2 �� [ �� ] lowest band V0 = 4 V 0 = �� V0 = 8 0 . . . 32 E rec V0 = 16 �� V0 = 32 �� - �� - �� - �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Bloch functions Bloch functions resemble plane waves at low V 0 , and series of peaks at large V 0 . � = �� = � � V0 = 0 � first excited V0 = 2 �� [ �� ] band V0 = 4 � V0 = 8 V 0 = V0 = 16 0 . . . 32 E rec - � V0 = 32 - � - �� - �� - �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Momentum comb: sudden release Sudden release of the optical lattice: the momentum distribution presents a periodicity 2 � k . Expansion with time bosons in a 3D lattice Observation along two orthogonal 2 ms 6 ms 10 ms 14 ms 18 ms axes ⇒ recover the 3D distribution Interference between the wells From Markus Greiner’s PhD thesis. H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Band mapping: adiabatic release bosons in a 2D lattice Example: population in 2 bands (Greiner et al. 2001) V 0 = 4 E rec 10 10 5 5 0 0 ⇔ n = 0 only 10 several bands q/k − 1 0 1 5 0 q/k fermions in a 3D lattice describe − 3 − 2 − 1 0 1 2 3 (K¨ ohl et al. 2004) → 0 V 0 − noninteracting ~ − 3 − 2 − 1 0 1 2 3 10 5 noninteracting p/ ( ~ k ) 0 − 3 − 2 − 1 0 1 2 3 H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Wannier functions Wannier functions are located around a given lattice site. � = �� = � � = �� = � � = �� = � �� = � � �� = � � �� = � � �� ( � ) � �� ( � ) � �� ( � ) �� - � - � - � � � � � - � - � - � � � � � - � - � - � � � � � �� [ � ] �� [ � ] �� [ � ] � = �� = � � = �� = � � = �� = � �� = � � �� = � � �� = �� ( � ) � �� ( � ) � �� ( � ) �� - � - � - � � � � � - � - � - � � � � � - � - � - � � � � � �� [ � ] �� [ � ] �� [ � ] H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Mott transition Observation of the Mott insulator to superfluid transition (2002): A competition between kinetic energy and interactions Small V 0 / E rec (small U / J ) Greiner et al., Nature 2002 Large V 0 / E rec (large U / J ) H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Mott transition Mott shells in a lattice + harmonic trap (Greiner/Bloch 2011) (a) (b) SF SF 3.0 MI (n=1) MI n=3 (n=1) SF SF µ /U 2.0 MI (n=2) n=2 MI (n=1) SF 1.0 MI (n=1) n=1 x y J/U H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

Optical lattices H el` ene Perrin Laboratoire de physique des - PowerPoint PPT Presentation

Optical lattices H el` ene Perrin Laboratoire de physique des lasers, CNRS-Universit e Paris 13 Sorbonne Paris Cit e Exploring new quantum gases Les Houches, September 1425, 2015 H el` ene Perrin, LPL Les Houches 2015

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Cold atoms in 2D optical lattices under staggered rotation Cristiane MORAIS SMITH Institute for

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Optical Fiber Madhuri Jash 07/03/2015 What is Optical Fiber? An optical fiber is a flexible,

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Optical lattices H el` ene Perrin Laboratoire de physique des - PowerPoint PPT Presentation

Optical lattices H el` ene Perrin Laboratoire de physique des lasers, CNRS-Universit e Paris 13 Sorbonne Paris Cit e Exploring new quantum gases Les Houches, September 1425, 2015 H el` ene Perrin, LPL Les Houches 2015

Ultracold atoms in optical lattices: beyond the Hubbard model Sebas&amp;ano Pila&amp;

Simulations of Abelian lattice gauge theories with optical lattices Luca Tagliacozzo Alessio

Synthetic triangular antiferromagnets with ultracold fermions in optical lattices Daisuke

Numerical simulations of bosons and fermions in three dimensional optical lattices Ping Nang MA

(Abelian) Anyon-Hubbard Models in 1D (Optical) Lattices I. (Floquet) Engineering with cold

Chiral Bose and Fermi phases in orbital optical lattices W. Vincent Liu University of

Bosons in optical lattices Subroto Mukerjee Department of Physics Indian Institute of Science

Anomalous chaotic atomic transport in optical lattices Sergey Prants Pacific Oceanological

Cold atoms in 2D optical lattices under staggered rotation Cristiane MORAIS SMITH Institute for

interactions in PT-symmetric nonlinear lattices with gain and loss Andrey A. Sukhorukov

Lattices from Codes or Codes from Lattices Amin Sakzad Dept of Electrical and Computer Systems

Lecture 9: Theta functions and lattices May 12, 2020 1 / 7 Lattices in R n A lattice is an

Transcendental lattices and supersingular reduction lattices of a singular K3 surface Keio, 2007

Lattices from Octonion Algebras Octonion Algebras Lattices via Octonion Algebras Nelson G.

Optical Fiber Madhuri Jash 07/03/2015 What is Optical Fiber? An optical fiber is a flexible,

Experiment 3 Optical Rotation Optical rotation or optical activity The rotation of the plane

Unification on Subvarieties of Introduction Algebraic Unification Pseudocomplemented lattices

Computational complexity of lattice problems and cyclic lattices Lenny Fukshansky Claremont

Some topological lattices. Walter Taylor Algebras Lattices in Hawaii 2018 Honoring R. Freese, W.

USING OPTICAL FLOW CMPS261 Project Shweta Philip OPTICAL FLOW Assumptions made by optical

Order and lattices from graphs Spring School SGT 2018 Set e, June 11-15, 2018 Stefan Felsner

Paper Review Introduction Optical Generation of Microwave Signals All-Optical

Spectrum problems for structures arising from lattices and rings lattices and rings

New non-arithmetic lattices in SU (2 , 1) J. Paupert (Arizona State University), joint with M.

Ultracold atoms in optical lattices: beyond the Hubbard model Sebas&ano Pila&