Qv Qv a n t u m p h a s e t r a n s i t i o n s - - PowerPoint PPT Presentation

Qv Qv a n t u m p h a s e t r a n s i t i

• n

s i n a c h a i n

• f

f l u x

• n

i u m q u b i t s

D e p a r t m e n t s

• f

P h y s i c s a n d A p p l i e d P h y s i c s , Y a l e U n i v e r s i t y

R . T . B r i e r l e y , H e n d r i k Me i e r , A . K

• u

, S . M. G i r v i n , L . I . G l a z m a n

• I

n t r

• d

u c t i

• n

t

• s

u p e r c

• n

d u c t i n g q u b i t s

 T

r a n s m

• n

 F

l u x

• n

i u m

• C
• u

p l e d f l u x

• n

i u m c h a i n

 

• C
• n

c l u s i

• n

s

• v

e r v i e w

s u p e r c

• n

d u c t i n g q u b i t s

• Qv b

i t s m a d e f r

• m

s u p e r c

• n

d u c t i n g c i r c u i t s

• R

a p i d p r

• g

r e s s i n r e c e n t y e a r s

• T

e s t i n g f u n d a m e n t a l s

• f

q u a n t u m m e c h a n i c s a n d m e a s u r e m e n t

Devoret & Schoelkopf, Science (2013)

s u p e r c

• n

d u c t i n g c i r c u i t s

Qv Qv a n t u m L C

• s

c i l l a t

• r
• U

s e f u l t

• d

e s c r i b e i n t e r m s

• f

p h a s e

• C
• n

j u g a t e t

• C
• p

e r p a i r n u m b e r

• R

e l a t e d t

• f

l u x i n i n d u c t

• r

Girvin, Les Houches (2011)

s u p e r c

• n

d u c t i n g c i r c u i t s

Qv Qv a n t u m L C

• s

c i l l a t

• r
• L

a d d e r

• p

e r a t

• r

s

• N

e e d s

• m

e t h i n g n

• n

l i n e a r t

• m

a k e a q u b i t

• Qv a

n t u m f l u c t u a t i

• n

s i n s u p p r e s s e d b y c a p a c i t a n c e

Girvin, Les Houches (2011)

s u p e r c

• n

d u c t i n g q u b i t s

T r a n s m

• n

q u b i t U s e a J

• s

e p h s

• n

j u n c t i

• n

: S m a l l f l u c t u a t i

• n

s → w e a k l y n

• n

l i n e a r

• s

c i l l a t

• r

Koch et. al., PRA (2007)

s u p e r c

• n

d u c t i n g q u b i t s

A d d a n i n d u c t

• r

T

• h

a v e m u l t i p l e m i n i m a , n e e d B u t l a r g e i n d u c t

• r

s i n t r

• d

u c e e x t r a p a r a s i t i c → s u p p r e s s e s q u a n t u m f l u c t u a t i

• n

s

Girvin, Les Houches (2011)

s u p e r c

• n

d u c t i n g q u b i t s

F l u x

• n

i u m q u b i t

Manucharyan et al., Science (2009) Pop et al., Nature (2014) 5 μm

“ S u p e r i n d u c t

• r

” m a d e f r

• m

J J s i n s e r i e s

s u p e r c

• n

d u c t i n g q u b i t s

C a n c

• u

p l e q u b i t s t

• c

a v i t i e s

• r

s u p e r c

• n

d u c t i n g r e s

• n

a t

• r

s E fg e c t i v e J a y n e s

• C

u m m i n g s i n t e r a c t i

• n

C a n r e a c h s t r

• n

g c

• u

p l i n g → “ c i r c u i t Q E D ” S e n s i t i v e p r

• b

e

• f

q u b i t s t a t e s

350 μm 5 μm Paik et. al., PRL (2011) Blais et. al., PRA (2004) Girvin, Les Houches (2011)

q u a n t u m s i m u l a t i

• n
• L

a r g e

• s

c a l e s y s t e m s b e i n g m a d e

• O

p p

• r

t u n i t y t

• s

t u d y m a n y

• b
• d

y q u a n t u m m

• d

e l s i n a n e w e n v i r

• n

m e n t

• D

r i v e a n d d i s s i p a t i

• n

→ n e w p h y s i c s

• Wh

a t k i n d s

• f

m

• d

e l s c a n b e e a s i l y r e a l i z e d ?

Houck et. al., Nature Physics (2012)

c h a i n

• f

f l u x

• n

i u m q u b i t s

e x t e r n a l f l u x

c h a i n

• f

f l u x

• n

i u m q u b i t s

• H

a r d t

• f

i n d c

• n

j u g a t e m

• m

e n t a f

• r
• I

n t r

• d

u c e s l

• n

g r a n g e i n t e r a c t i

• n

s f

• r

c l a s s i c a l g r

• u

n d s t a t e

Marchand, Hood, Caillé, PRL (1987) Yokoi, Tang, Chou, PRB (1988)

S t u d i e s

• n

s i m i l a r m

• d

e l s T w

• c

l a s s i c a l p a r a m e t e r s e x t e r n a l f l u x

c l a s s i c a l g r

• u

n d s t a t e

h i g h e r

• r

d e r f r a c t i

• n

s

c l a s s i c a l g r

• u

n d s t a t e

T w

• r

e g i m e s :

c l a s s i c a l g r

• u

n d s t a t e

T w

• r

e g i m e s :

k i n k s

• e

v e r y w h e r e

• k

e p t s m a l l m a y j u m p b y , e l s e w h e r e s a t i s f i e s ( c

• n

t i n u u m l i m i t ) : S t a b l e s t a t e s f

• r

s m a l l :

k i n k s

• S
• l

u t i

• n

s t a k e t h e f

• r

m

• f

k i n k s

• S

i n g l e k i n k c

• s

t :

Kardar, PRB (1986)

k i n k s

• S
• l

u t i

• n

s t a k e t h e f

• r

m

• f

k i n k s

• S

i n g l e k i n k c

• s

t :

Kardar, PRB (1986)

g r

• u

n d s t a t e a t s

• m

e g r

• u

n d s t a t e c l

• s

e a b

• v

e

m a n y k i n k s

R e p u l s i v e k i n k

• k

i n k i n t e r a c t i

• n

O v e r l a p p i n g e x p

• n

e n t i a l t a i l s G r

• u

n d s t a t e s f

• r

l a r g e r a r e s u p e r p

• s

i t i

• n

s

• f

m a n y k i n k s

g r

• u

n d s t a t e a t s

• m

e g r

• u

n d s t a t e c l

• s

e a b

• v

e

m a n y k i n k s

k i n k a t l i n k n

• k

i n k a t l i n k I n t r

• d

u c e p s e u d

• s

p i n

l

• n

g

• r

a n g e I s i n g c h a i n

Bak, Bruinsma, PRL (1982) Aubry, J. Phys. Lett. (1983)

E fg fg e c t i v e c l a s s i c a l H a m i l t

• n

i a n l

• n

g

• r

a n g e i n t e r a c t i

• n

e fg . m a g n e t i c f i e l d F r e n k e l

• K
• n

t

• r
• v

a

• t

y p e m

• d

e l

s

• l

i t

• n

g r

• u

n d s t a t e s

• Wh

e n k i n k s a r e s p a r s e , c

• n

t i n u u m c a l c u l a t i

• n

g i v e s

• Kinks live on discrete latuice, can't have ideal separation
• e.g. for

d e v i l ' s s t a i r c a s e

s t e p w i d t h : K i n k d e n s i t y v s . m a g n e t i c f l u x

Bak & Bruinsma, PRL (1982)

e x c i t a t i

• n

s p e c t r u m

A d d i n g a n a n t e n n a

• C
• u

p l e s t

• p

h a s e a c r

• s

s s i n g l e l i n k

• A

b s

• r

p t i

• n
• f

p h

• t
• n

cavity C r e a t i

• n

/ a n n i h i l a t i

• n
• f

l

• c

a l k i n k s

e x c i t a t i

• n

s p e c t r u m

s i n g l e

• k

i n k e x c i t a t i

• n

s k i n k c r e a t i

• n

k i n k a n n i h i l a t i

• n

q u a n t u m e fg fg e c t s

Qv Qv a n t u m f l u c t u a t i

• n

s Qv Qv a n t u m l

• n

g

• r

a n g e I s i n g m

• d

e l

• v

e r l a p ( c . f . f l u x

• n

i u m )

q u a n t u m c

• r

r e c t i

• n

s t

• s

i n g l e

• k

i n k e x c i t a t i

• n

s

Qv Qv a n t u m b a n d L

• n

g

• r

a n g e q u a n t u m h

• p

p i n g T w

• p

r

• c

e s s e s : D e s t r u c t i v e l y i n t e r f e r e i f

q u a n t u m c

• r

r e c t i

• n

s t

• s

i n g l e

• k

i n k e x c i t a t i

• n

s

Qv Qv a n t u m b a n d Qv a n t u m e fg e c t s p e r t u r b a t i v e i f L

• n

g

• r

a n g e q u a n t u m h

• p

p i n g q u a n t u m c r i t i c a l

q u a n t u m p h a s e d i a g r a m

q u a n t u m p h a s e d i a g r a m

D e v i l ' s s t a i r c a s e h a s i n f i n i t e n u m b e r

• f

p i n n e d p h a s e s , p e r i

• d

...

Bak & Bruinsma, PRL 49, 249 (1982)

C l a s s i c a l p h a s e t r a n s i t i

• n

t

• s

t a t e w i t h

• n

e e x t r a / f e w e r k i n k e . g . :

q u a n t u m p h a s e d i a g r a m

A d d i n g / r e m

• v

i n g k i n k i n p i n n e d p h a s e → d e f e c t s

• cf. domain walls in AFM

R e p e l e a c h

• t

h e r t

• g

i v e n e w c l a s s i c a l g r

• u

n d s t a t e ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

A d d i n g / r e m

• v

i n g k i n k i n p i n n e d p h a s e → d e f e c t s

• cf. domain walls in AFM

R e p e l e a c h

• t

h e r t

• g

i v e n e w c l a s s i c a l g r

• u

n d s t a t e ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

A d d i n g / r e m

• v

i n g k i n k i n p i n n e d p h a s e → d e f e c t s

• cf. domain walls in AFM

R e p e l e a c h

• t

h e r t

• g

i v e n e w c l a s s i c a l g r

• u

n d s t a t e ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

A d d i n g / r e m

• v

i n g k i n k i n p i n n e d p h a s e → d e f e c t s

• cf. domain walls in AFM

R e p e l e a c h

• t

h e r t

• g

i v e n e w c l a s s i c a l g r

• u

n d s t a t e ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

A d d i n g / r e m

• v

i n g k i n k i n p i n n e d p h a s e → d e f e c t s

• cf. domain walls in AFM

R e p e l e a c h

• t

h e r t

• g

i v e n e w c l a s s i c a l g r

• u

n d s t a t e ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

d e f e c t s e a c h g a i n k i n e t i c e n e r g y P i n n e d

• r

d e r d e s t r

• y

e d i f ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

Described by Lutuinger parameter Gapless excitations K T K T I s i n g C

• I

C ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

Mobile defects → incommensurate Lutuinger liquid

q u a n t u m p h a s e d i a g r a m

A t b

• u

n d a r i e s K T t r a n s i t i

• n

t

• g

a p p e d h

• m
• g

e n e

• u

s p h a s e i f ( e fg e c t

• f

) I s i n g t r a n s i t i

• n

f

• r

K T K T I s i n g C

• I

C ...

See also: Odintsov, PRB 54, 1228 (1996); Sela et. al., PRB 84, 085434 (2014)

q u a n t u m p h a s e d i a g r a m

Power law interactions: Sela et. al., PRB 84, 085434 (2014)

• t

h e r r e g i m e

• t

h e r r e g i m e

K i n k p i c t u r e n

• t

v a l i d : s m a l l e v e r y w h e r e S e c

• n

d

• r

d e r t r a n s i t i

• n

t

• s

t a t e

I s i n g t r a n s i t i

• n

e x p a n d p

• t

e n t i a l a n d t a k e c

• n

t i n u u m l i m i t

I s i n g t r a n s i t i

• n

Qv a n t u m ( 1 + 1 )

• d

i m e n s i

• n

a l I s i n g m

• d

e l G i n z b u r g r e g i

• n

: Qv a n t u m c r i t i c a l b e h a v i

• u

r a c c e s s i b l e f

• r

I s i n g t r a n s i t i

• n

E x c i t a t i

• n

s p e c t r u m S m a l l

• s

c i l l a t i

• n

s i n

I s i n g t r a n s i t i

• n

G a p c l

• s

e s a t t r a n s i t i

• n

S m a l l

• s

c i l l a t i

• n

s i n E x c i t a t i

• n

s p e c t r u m

I s i n g t r a n s i t i

• n

U n i t c e l l d

• u

b l e d i n

• r

d e r e d p h a s e E x c i t a t i

• n

s p e c t r u m

I s i n g t r a n s i t i

• n

: g a p c l

• s

e s a t s

• m

e U n i t c e l l d

• u

b l e d i n

• r

d e r e d p h a s e E x c i t a t i

• n

s p e c t r u m

I s i n g t r a n s i t i

• n

I s i n g t r a n s i t i

• n

t

• p

h a s e

• D

e v i l ' s s t a i r c a s e n

• t

p r e s e n t a b

• v

e

• F

i r s t

• r

d e r t r a n s i t i

• n

s

• H
• w

d

• h
• m
• g

e n e

• u

s p h a s e s j

• i

n ?

i n t e r m e d i a t e r e g i m e

Marchand et. al, PRB 37, 1898 (1988) Yokoi et. al., PRB 37, 2173 (1988)

c

• n

c l u s i

• n

s

• C

h a i n

• f

f l u x

• n

i u m q u b i t s w i t h r e a l i s t i c p a r a m e t e r s

• S

e v e r a l c l a s s e s

• f

p h a s e t r a n s i t i

• n
• O

b s e r v a b l e i n e x c i t a t i

• n

s p e c t r u m

• C
• I

C

• K
• s

t e r l i t z

• T

h

• u

l e s s

• I

s i n g

• F

i r s t

• r

d e r

• Lutuinger Liquid
• Ising