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

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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

SLIDE 1

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

SLIDE 2

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

SLIDE 3

Band structure

V0 = 0

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Comparison with free particle (left) of harmonic approximation (right)

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 4

Band structure

V0 = Erec

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gray zone: potential depth V0 V0 = Erec

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zoom around q = 1: gap opening

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 5

Band structure

V0 = 2Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 6

Band structure

V0 = 4Erec

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V0 = 4Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 7

Band structure

V0 = 8Erec

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V0 = 8Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 8

Band structure

V0 = 16Erec

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V0 = 16Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 9

Band structure

V0 = 25Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 10

Band structure

V0 = 32Erec

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H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 11

Bloch functions

Bloch functions resemble plane waves at low V0, and series of peaks at large V0. lowest band V0 = 0 . . . 32Erec

[]

[] = =

V0=0 V0=2 V0=4 V0=8 V0=16 V0=32

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 12

Bloch functions

Bloch functions resemble plane waves at low V0, and series of peaks at large V0. first excited band V0 = 0 . . . 32Erec

[]

[] = =

V0=0 V0=2 V0=4 V0=8 V0=16 V0=32

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 13

Momentum comb: sudden release

Sudden release of the optical lattice: the momentum distribution presents a periodicity 2k.

Expansion with time

2 ms 6 ms 10 ms 14 ms 18 ms

Interference between the wells bosons in a 3D lattice Observation along two orthogonal axes ⇒ recover the 3D distribution

From Markus Greiner’s PhD thesis.

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 14

Band mapping: adiabatic release

Example: population in 2 bands V0 = 4Erec

5 10 5 10

describe ⇔

q/k −1 1 5 10 −3 −2 −1 1 2 3 q/k ~

noninteracting

V0 − → 0

−3 −2 −1 1 2 3 p/(~k) −3 −2 −1 1 2 3 5 10

noninteracting

bosons in a 2D lattice (Greiner et al. 2001) n = 0 only several bands fermions in a 3D lattice (K¨

hl et al. 2004)

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 15

Wannier functions

Wannier functions are located around a given lattice site.

[]

() = = =

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() = = =

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() = = =

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() = = =

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() = = =

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() = =

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 16

Mott transition

Observation of the Mott insulator to superfluid transition (2002): A competition between kinetic energy and interactions Small V0/Erec (small U/J) Greiner et al., Nature 2002 Large V0/Erec (large U/J)

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices

SLIDE 17

Mott transition

Mott shells in a lattice + harmonic trap (Greiner/Bloch 2011)

SF SF SF n=1 n=2 n=3 J/U µ/U 1.0 2.0 3.0 MI (n=1) MI (n=1) MI (n=1) SF SF MI (n=1) MI (n=2)

x y

(a) (b)

H´ el` ene Perrin, LPL – Les Houches 2015 Optical lattices