Ultracold Atoms and Quantum Simulators Marc Cheneau Igor - PowerPoint PPT Presentation

Ultracold Atoms and Quantum Simulators Marc Cheneau Igor Ferrier-Barbut Laboratoire Charles Fabry Institut d’Optique, CNRS, Université Paris-Saclay

The Saga of Ultracold Atoms at a Glance 5 5 5 5 s t r o n g l y - 8 9 0 1 t o w a r d s u l t r a - l o w w e a k l y - i n t e r a c t i n g t o w a r d s q u a n t u m 9 9 0 0 c o r r e l a t e d 1 1 2 2 t e m p e r a t u r e s q u a n t u m g a s e s s i m u l a t i o n q u a n t u m m a t t e r B o s e - E i n s t e i n o p t i c a l l a t t i c e s l a s e r c o o l i n g d y n a m i c a l c o n d e n s a t i o n a n d c o n t r o l o f ( ~ 1 0 0 μ K* ) c o n t r o l ( ~ 1 0 0 n K* ) i n t e r a c t i o n s Historical perspective From classical gases to strongly-correlated quantum systems Several periods (~10 years each) Milestone achievements and new perspectives 3

The Saga of Ultracold Atoms at a Glance 5 5 5 5 s t r o n g l y - 8 9 0 1 t o w a r d s u l t r a - l o w w e a k l y - i n t e r a c t i n g t o w a r d s q u a n t u m 9 9 0 0 c o r r e l a t e d 1 1 2 2 t e m p e r a t u r e s q u a n t u m g a s e s s i m u l a t i o n q u a n t u m m a t t e r B o s e - E i n s t e i n o p t i c a l l a t t i c e s l a s e r c o o l i n g d y n a m i c a l c o n d e n s a t i o n a n d c o n t r o l o f ( ~ 1 0 0 μ K* ) c o n t r o l ( ~ 1 0 0 n K* ) i n t e r a c t i o n s Towards ultra-low temperatures Doppler and Sisyphus cooling schemes (friction force and momentum kicks; temperature limited to the m K range; classical gas) Sub-recoil cooling ( eg VSCPT, Raman cooling, side band cooling, … ; quantum gas) Moreover, trapping (counteracts Brownian motion; magneto-optical and dipole traps) 4

The Saga of Ultracold Atoms at a Glance 5 5 5 5 s t r o n g l y - 8 9 0 1 t o w a r d s u l t r a - l o w w e a k l y - i n t e r a c t i n g t o w a r d s q u a n t u m 9 9 0 0 c o r r e l a t e d 1 1 2 2 t e m p e r a t u r e s q u a n t u m g a s e s s i m u l a t i o n q u a n t u m m a t t e r B o s e - E i n s t e i n o p t i c a l l a t t i c e s l a s e r c o o l i n g d y n a m i c a l c o n d e n s a t i o n a n d c o n t r o l o f ( ~ 1 0 0 μ K* ) c o n t r o l ( ~ 1 0 0 n K* ) i n t e r a c t i o n s Weakly-interacting quantum gases Evaporative cooling (quantum gases, weak interactions) Bose-Einstein condensation and degenerate Fermi gases ( eg coherence and supefluidity) Moreover, first simulations (Brownian motion, 5 dissipative optical lattices, …)

The Saga of Ultracold Atoms at a Glance 5 5 5 5 s t r o n g l y - 8 9 0 1 t o w a r d s u l t r a - l o w w e a k l y - i n t e r a c t i n g t o w a r d s q u a n t u m 9 9 0 0 c o r r e l a t e d 1 1 2 2 t e m p e r a t u r e s q u a n t u m g a s e s s i m u l a t i o n q u a n t u m m a t t e r B o s e - E i n s t e i n o p t i c a l l a t t i c e s l a s e r c o o l i n g d y n a m i c a l c o n d e n s a t i o n a n d c o n t r o l o f ( ~ 1 0 0 μ K* ) c o n t r o l ( ~ 1 0 0 n K* ) i n t e r a c t i o n s Strongly-correlated quantum matter Control of interactions Optical lattices (non-dissipative ; realization of tight-binding models for solids) Fano-Feshbach resonances 6 Low-dimensional systems

The Saga of Ultracold Atoms at a Glance 5 5 5 5 s t r o n g l y - 8 9 0 1 t o w a r d s u l t r a - l o w w e a k l y - i n t e r a c t i n g t o w a r d s q u a n t u m 9 9 0 0 c o r r e l a t e d 1 1 2 2 t e m p e r a t u r e s q u a n t u m g a s e s s i m u l a t i o n q u a n t u m m a t t e r B o s e - E i n s t e i n o p t i c a l l a t t i c e s l a s e r c o o l i n g d y n a m i c a l c o n d e n s a t i o n a n d c o n t r o l o f ( ~ 1 0 0 μ K* ) c o n t r o l ( ~ 1 0 0 n K* ) i n t e r a c t i o n s Towards quantum simulation Simulating the dynamics of quantum matter in true experiments Thermodynamic equilibrium Out-of-equilibrium physics 7

S i m u l a t i n g I n t e r e s t i n g P h e n o m e n a i n P h y s i c s I n t e r e s t i n g p h y s i c a l s y s t e m s a r e u s u a l l y c o m p l e x Ma n y b o d i e s , p o s s i b l y n o t a l l i d e n t i c a l C o m p l i c a t e d m i c r o s c o p i c i n t e r a c t i o n s S t r u c t u r e , f r u s t r a t i o n , q u a n t u m e n t a n g l e m e n t , … ⇒! C a n n o t b e s o l v e d e x a c t l y a t t h e m i c r o s c o p i c l e v e l B a s i c m o d e l s p l a y a c e n t r a l r o l e x − h ∑ H = J ∑ x ⋅ S R' z S R S R S i m p l e r a n d o f t e n r e p r o d u c e i n t e r e s t i n g p h y s i c s ⟨ R , R' ⟩ R Ma y b e e a s i e r t o s o l v e U n i v e r s a l b e h a v i o u r ⇒! S i m p l e H a m i l t o n i a n s d o n o t g u a r a n t e e s i m p l e s o l u t i o n s N u m e r i c a l s i m u l a t i o n s Ma n y - b o d y a p p r o a c h e s e x i s t ( Q MC , D MR G , D F T , D MF T , …) Me a n - fj e l d a p p r o a c h e s ( n o n l i n e a r i t i e s , …) ⇒! C a n n o t s o l v e a n y p r o b l e m , i n p a r t i c u l a r i n t h e q u a n t u m w o r l d ( e x p o n e n t i a l l y - l a r g e H i l b e r t s p a c e , e n t a n g l e m e n t , s i g n p r o b l e m f o r f e r m i o n s , …)

S i m u l a t i o n : F r o m N u m e r i c s t o Q u a n t u m S y s t e m s Wh y d o n ’ t w e l e t N a t u r e w o r k f o r u s ? D e s i g n a q u a n t u m s y s t e m e x a c t l y g o v e r n e d b y a p r e - d e fj n e d Ĥ H a m i l t o n i a n m o d e l Ĥ L e t t h e s y s t e m e v o l v e u n d e r t o w a r d s i t s g r o u n d s t a t e m o d e l ( c o o l i n g ) o r a t h e r m a l s t a t e ( c o u p l i n g t o a b a t h ) , o r s t u d y i t s t i m e - d e p e n d e n t d y n a m i c s Ĥ Me a s u r e r e l e v a n t q u a n t i t i e s s o a s t o c o n s i d e r i s s o l v e d m o d e l R.P. Feynman, Int. J. Theor. Phys. 21 , 467 (1982) ; S. Lloyd, Science 273 , 1073 (1996) R e q u i r e m e n t s a n d c h a l l e n g e s B u i l d u p : C r e a t e a q u a n t u m s y s t e m ( b o s o n s , f e r m i o n s , s p i n s , …) t h a t c a n b e m a n i p u l a t e d b y e x t e r n a l fj e l d s Q u a n t u m e n g i n e e r i n g : D e s i g n t h e d e s i r e d H a m i l t o n i a n w i t h a t l e a s t o n e c o n t r o l e g p a r a m e t e r ( b e n c h m a r k i n g ) I n i t i a l i z a t i o n : P r e p a r e t h e s y s t e m i n a w e l l - k n o w n i n i t i a l s t a t e ( p u r e o r m i x e d ) D e t e c t i o n : S u ffj c i e n t l y a c c u r a t e a n d v a r i o u s m e a s u r e m e n t s

T o w a r d s Q u a n t u m S i m u l a t i o n N e w p r o m i s i n g p l a t f o r m s Q u a n t u m o p t i c s [Aspuru-Guzik & Walther, Nat. Phys. 8 , 285 (2012)] S u p e r c o n d u c t i n g c i r c u i t s [Houck et al. , Nat. Phys. 8 , 292 (2012)] Ma g n e t i c i n s u l a t o r s [Ward et al. , J. Phys : Condens. Matter 25 , 014004 (2013)] U l t r a c o l d a t o m s a n d i o n s [Bloch et al. , Nat. Phys. 8 , 267 (2012); Blatt & Roos, Nat. Phys. 8 , 277 (2012)] … U l t r a c o l d a t o m s A m a j o r p l a y g r o u n d A l m o s t a n y p a r a m e t e r c a n b e c o n t r o l l e d e x p e r i m e n t a l l y