simulating few- and many-body physics with rydberg...

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Simulating few- and many-body physics

with Rydberg atoms

David Petrosyan

Heraklion, 25/10/17 – p. 1/29

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FORTHIESLPlan of the Seminar

Quantum Simulations and Computations

Heraklion, 25/10/17 – p. 2/29

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Rydberg atoms and their interactions

Heraklion, 25/10/17 – p. 2/29

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Quantum gates

Heraklion, 25/10/17 – p. 2/29

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Quantum gates

Simulating lattice spin models in 1D & 2D

Heraklion, 25/10/17 – p. 2/29

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Quantum gates

Simulating lattice spin models in 1D & 2D

Summary

Heraklion, 25/10/17 – p. 2/29

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Outline of Quantum Theory

Heraklion, 25/10/17 – p. 3/29

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|Ψ〉 = c1 |e1〉+ c2 |e2〉+ c3 |e3〉+ . . . =∑N

i=1 ci |ei〉∑N

i=1 |ci|2 = 1


Composite system S = A+ B + . . .:

dimHS = dimHA × dimHB × . . .

Heraklion, 25/10/17 – p. 4/29

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|Ψ〉 = c1 |e1〉+ c2 |e2〉+ c3 |e3〉+ . . . =∑N

i=1 ci |ei〉∑N

i=1 |ci|2 = 1




Two state system: spin- 12 electron | ↑〉, | ↓〉

Ψz

yx

Bloch Sphere

Heraklion, 25/10/17 – p. 4/29

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|Ψ〉 = c1 |e1〉+ c2 |e2〉+ c3 |e3〉+ . . . =∑N

i=1 ci |ei〉∑N

i=1 |ci|2 = 1





Ψz

yx

Bloch Sphere⇒ For N two-state systems: dimHS = 2N

Heraklion, 25/10/17 – p. 4/29

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|Ψ〉 = c1 |e1〉+ c2 |e2〉+ c3 |e3〉+ . . . =∑N

i=1 ci |ei〉∑N

i=1 |ci|2 = 1





Ψz

yx

Bloch Sphere⇒ For N two-state systems: dimHS = 2N

Hilbert Space is a big place!

(Carlton M. Caves)

Heraklion, 25/10/17 – p. 4/29

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FORTHIESLTime evolution

Hamiltonian operator H: Energy 〈Ψ| H |Ψ〉 = E

Heraklion, 25/10/17 – p. 5/29

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Our favorite operator!

Heraklion, 25/10/17 – p. 5/29

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Schrödinger equation i~ ∂∂t

|Ψ〉 = H |Ψ〉 ⇒ |Ψ(t)〉 = e−i~Ht |Ψ(0)〉

Heraklion, 25/10/17 – p. 5/29

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Schrödinger equation i~ ∂∂t

|Ψ〉 = H |Ψ〉 ⇒ |Ψ(t)〉 = e−i~Ht |Ψ(0)〉

Mixed states, dissipative systems: ρ =∑

Ψ PΨ |Ψ〉〈Ψ|

Liouville – von Neumann equation i~ ∂∂tρ = [Hρ− ρH] + Lρ

Heraklion, 25/10/17 – p. 5/29

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Quantum simulations

Richard Feynman

Simulating Physics with Computers,Feynman, Int. J. Theor. Phys. 21, 467 (1982);

Lloyd, Science 273, 1073 (1996)

Heraklion, 25/10/17 – p. 6/29

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Quantum simulations

Richard Feynman


Lloyd, Science 273, 1073 (1996)

Interacting many-body quantum systemsare hard to simulate on classical computers

Many degrees of freedom (huge HS)

Quantum correlations (entanglement)

|Ψ〉S 6= |Ψ〉A ⊗ |Ψ〉B ⊗ . . .

Heraklion, 25/10/17 – p. 6/29

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Quantum simulations

Richard Feynman


Lloyd, Science 273, 1073 (1996)




|Ψ〉S 6= |Ψ〉A ⊗ |Ψ〉B ⊗ . . .

⇒ number of c equations to solve simultaneously is dimHS

decoupling (mean field) approximations are not always correct

Heraklion, 25/10/17 – p. 6/29

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Quantum simulations

Richard Feynman


Lloyd, Science 273, 1073 (1996)




|Ψ〉S 6= |Ψ〉A ⊗ |Ψ〉B ⊗ . . .



Universal quantum simulator

Nat. Phys. 6, 382 (2010)

Discretize space & time [ST eδ(A+B) = eδAeδB +O(δ2)]

⇒ spin lattice with finite range & interval interactions

U(t) = exp(− i~Ht) ≃ ∏

j exp(− i~Hjδt1)

∏

j′ exp(− i~Hj′δt2) . . .

Heraklion, 25/10/17 – p. 6/29

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Quantum simulations

Richard Feynman


Lloyd, Science 273, 1073 (1996)




|Ψ〉S 6= |Ψ〉A ⊗ |Ψ〉B ⊗ . . .



Analog quantum simulator

Nature 415, 39 (2002)

Construct a clean system &realize appropriate interactions to mimic HS

⇒ Dynamically or adiabatically evolve |Ψ〉and read-out

Heraklion, 25/10/17 – p. 6/29

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Quantum computations

0

1

Quantum bit – qubit – is two-state quantum system

stores superposition states |ψ〉 = α |0〉+ β |1〉

Heraklion, 25/10/17 – p. 7/29

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1



N -qubit memory has 2N orthogonal states |x〉 = |00 . . . 0〉, . . . , |11 . . . 1〉|Ψ〉 = ∑

x cx |x〉 in general |Ψ〉 6= |ψ〉1 ⊗ |ψ〉2 ⊗ . . .: entanglement

Heraklion, 25/10/17 – p. 7/29

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0

1





Any computation (unitary transformation) can be realizedvia a sequence of one-, two- (and more-) qubit gates

One-qubit gates (rotations on BS): Unity I, Hadamard H, Pauli X,Y, Z, Phase S ...

Two-qubit gates: Controlled-U , Controlled-Z, CNOT= HtCZHt, SWAP,√

SWAP ...

Heraklion, 25/10/17 – p. 7/29

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1








SWAP ...

Quantum computation is inherently parallel

Prepare the input state in a superposition state of all possible “classical” inputs x:

|Ψinput〉 =∑

x cx |x〉Design an algorithm where all the computational paths interfere with each other to

yield with high probability the output state y: |Ψoutput〉 ≃ |y〉 (∑

y′ 6=y |cy′ |2 → 0)

Heraklion, 25/10/17 – p. 7/29

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0

1








SWAP ...

Quantum computation is inherently parallel

Prepare the input state in a superposition state of all possible “classical” inputs x:

|Ψinput〉 =∑

x cx |x〉Design an algorithm where all the computational paths interfere with each other to

yield with high probability the output state y: |Ψoutput〉 ≃ |y〉 (∑

y′ 6=y |cy′ |2 → 0)

Useful quantum algorithms:

Grover search of M = 2N elements in√M steps

Shor FFT for a set M = 2N in ∼ N2 steps (factorization etc.) ...Heraklion, 25/10/17 – p. 7/29

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Rydberg atoms

Niels Henrik David Bohr

Heraklion, 25/10/17 – p. 8/29

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Rydberg Atoms

High principal quantum number

n ≫ 1 (H-like)

Heraklion, 25/10/17 – p. 9/29

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Rydberg Atoms


n ≫ 1 (H-like)r

g

Energy Er = − Ryn∗2

effective PQN n∗ = n− δl (δl quantum defect)

Heraklion, 25/10/17 – p. 9/29

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Rydberg Atoms


n ≫ 1 (H-like)r

g

Energy Er = − Ryn∗2

effective PQN n∗ = n− δl (δl quantum defect)

0a2n+ −

Easily polarized

Huge dipole moments ℘ ∼ n2ea0

Gallagher, Rydberg Atoms (Cambridge 1994)Heraklion, 25/10/17 – p. 9/29

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Dipole-Dipole Interactions

D =℘(1) · ℘(2)

R3− 3

(℘(1) ·R)(℘(2) ·R)

R5∝ n4

Heraklion, 25/10/17 – p. 10/29

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D =℘(1) · ℘(2)

R3− 3

(℘(1) ·R)(℘(2) ·R)

R5∝ n4

⇒ Static DDI

Est induced Stark eigenstates

with permanent ℘ = 32nqea0

q

−q

Est

−q+1

q−1

−

+

Heraklion, 25/10/17 – p. 10/29

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D =℘(1) · ℘(2)

R3− 3

(℘(1) ·R)(℘(2) ·R)

R5∝ n4

⇒ Static DDI

Est induced Stark eigenstates

with permanent ℘ = 32nqea0

pθ

(2)p(1)

RD = ℘(1)℘(2)(1−3 cos2 θ)

R3

Heraklion, 25/10/17 – p. 10/29

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D =℘(1) · ℘(2)

R3− 3

(℘(1) ·R)(℘(2) ·R)

R5∝ n4

⇒ Resonant DDI

D12

D121

2

2a

r

b

r

1

D = 1R3

[

℘(1)+1℘

(2)−1 + ℘

(1)−1℘

(2)+1 + ℘

(1)0 ℘

(2)0 (1− 3 cos2 θ)

− 32sin2 θ(℘

(1)+1℘

(2)+1 + ℘

(1)+1℘

(2)−1 + ℘

(1)−1℘

(2)+1 + ℘

(1)−1℘

(2)−1

− 3√2sin θ cos θ(℘

(1)+1℘

(2)0 + ℘

(1)−1℘

(2)0 + ℘

(1)0 ℘

(2)+1 + ℘

(1)0 ℘

(2)−1)

]

Heraklion, 25/10/17 – p. 11/29

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D =℘(1) · ℘(2)

R3− 3

(℘(1) ·R)(℘(2) ·R)

R5∝ n4

⇒ Resonant DDI

D12

D121

2

2a

r

b

r

1

D = 1R3

[

℘(1)+1℘

(2)−1 + ℘

(1)−1℘

(2)+1 + ℘

(1)0 ℘

(2)0 (1− 3 cos2 θ)

− 32sin2 θ(℘

(1)+1℘

(2)+1 + ℘

(1)+1℘

(2)−1 + ℘

(1)−1℘

(2)+1 + ℘

(1)−1℘

(2)−1

− 3√2sin θ cos θ(℘

(1)+1℘

(2)0 + ℘

(1)−1℘

(2)0 + ℘

(1)0 ℘

(2)+1 + ℘

(1)0 ℘

(2)−1)

]

℘+1 = − e√2(x+ iy) = − e√

2r sin θeiφ = er

√

4π3Y1,1(θ, φ) r+1 = 〈n′l′,m+ 1| r |nl,m〉

℘0 = ez = er cos θ = er√

4π3Y1,0(θ, φ) r0 = 〈n′l′,m| r |nl,m〉

℘−1 = e√2(x− iy) = e√

2r sin θe−iφ = er

√

4π3Y1,−1(θ, φ) r−1 = 〈n′l′,m− 1| r |nl,m〉

Heraklion, 25/10/17 – p. 11/29

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FORTHIESLvan der Waals Interaction

12D

D12r

aatom

a1atom

r

δ δ

D21

D21

bb

2RDDI (Förster process)

D12 ≡ D(R) ∝ ℘br℘ar

R3 ∝ n4

Heraklion, 25/10/17 – p. 12/29

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12D

D12r

aatom

a1atom

r

δ δ

D21

D21

bb

2RDDI (Förster process)

D12 ≡ D(R) ∝ ℘br℘ar

R3 ∝ n4

ωrb − ωar = δω ≫ D

(δω ∝ n−3)

⇒ |r1〉 |r2〉 9 |a1,2〉 |b2,1〉: Non-Resonant DDI (Adiabatic elim. |a1,2〉 |b2,1〉)

Heraklion, 25/10/17 – p. 12/29

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r

aatom 2

a1

r

bb

atom

12∆

RDDI (Förster process)

D12 ≡ D(R) ∝ ℘br℘ar

R3 ∝ n4

ωrb − ωar = δω ≫ D

(δω ∝ n−3)

⇒ |r1〉 |r2〉 9 |a1,2〉 |b2,1〉: Non-Resonant DDI (Adiabatic elim. |a1,2〉 |b2,1〉)

⇒ Energy shift of |r1〉 |r2〉 (2nd-order in D/δω)

R

∆

VvdW = ~σ1rr∆12σ

2rr

∆12 ≡ ∆(R) = 2|D(R)|2

δω= C6

R6 ∝ n11 — vdWI strength

Saffman, Walker, Mølmer, RMP 82, 2313 (2010)

Heraklion, 25/10/17 – p. 12/29

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Two Atoms

Heraklion, 25/10/17 – p. 13/29

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Rydberg interaction blockade

2Ω

2Ω

2rg

gg

rr

+gr

∆Two-atom Hamiltonian

H/~ = Ω |r〉1〈g| +Ω |r〉2〈g| +H.c.

+∆12 |r〉1〈r| ⊗ |r〉2〈r|

Heraklion, 25/10/17 – p. 14/29

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2Ω

2Ω

2rg

gg

rr

+gr


H/~ = Ω |r〉1〈g| +Ω |r〉2〈g| +H.c.

+∆12 |r〉1〈r| ⊗ |r〉2〈r|

Resonant transition |gg〉 ↔ |gr, rg〉1~〈gr, rg|H |gg〉 = Ω

Nonresonant transition |gr, rg〉 ↔ |rr〉1~〈rr| H |rr〉 = ∆12 ≫ Ω

Heraklion, 25/10/17 – p. 14/29

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2Ω

2Ω

2rg

gg

rr

+gr


H/~ = Ω |r〉1〈g| +Ω |r〉2〈g| +H.c.

+∆12 |r〉1〈r| ⊗ |r〉2〈r|

Resonant transition |gg〉 ↔ |gr, rg〉1~〈gr, rg|H |gg〉 = Ω

Nonresonant transition |gr, rg〉 ↔ |rr〉1~〈rr| H |rr〉 = ∆12 ≫ Ω

⇒ Double excitation |rr〉 is blocked

⇒ Rabi oscillations |gg〉 ↔ 1√2( |gr〉+ |rg〉) with

√2Ω

Jaksch et al., PRL 85, 2208 (2000)Heraklion, 25/10/17 – p. 14/29

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FORTHIESLTwo-atom Rabi oscillations

a

b

R = 18 µm

R = 3.6 µm

Duration of the excitation (ns)

Excita

tio

n p

rob

ab

ility

E

xcita

tio

n p

rob

ab

ility

0 40 80 120 160 200 240 280 320

0.0

1.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Urban et al., Nature Phys. 5, 110 (2009); Gaëtan et al., Nature Phys. 5, 115 (2009)

Heraklion, 25/10/17 – p. 15/29

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FORTHIESLTwo-atom Rabi oscillations

a

b

R = 18 µm

R = 3.6 µm


Excita

tio

n p

rob

ab

ility

E

xcita

tio

n p

rob

ab

ility

0 40 80 120 160 200 240 280 320

0.0

1.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Urban et al., Nature Phys. 5, 110 (2009); Gaëtan et al., Nature Phys. 5, 115 (2009)


Excita

tio

n p

rob

ab

ility

0 40 80 120 160 200 240 280 320

0.0

1.0

0.2

0.4

0.6

0.8 R = 3.6 µm

Heraklion, 25/10/17 – p. 15/29

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Rydberg blockade gates

r

2Ω1Ω

Atom 2

2

∆12?r

Atom 1

1 3

0110

Two-atom (qubit) CZ gate

|0〉1 |0〉2 → |0〉1 |0〉2|0〉1 |1〉2 → −|0〉1 |1〉2|1〉1 |0〉2 → −|1〉1 |0〉2|1〉1 |1〉2 → −|1〉1 |1〉2

Jaksch et al., PRL 85, 2208 (2000)

Heraklion, 25/10/17 – p. 16/29

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r

2Ω1Ω

Atom 2

2

∆12?r

Atom 1

1 3

1 0 0 1

Two-atom (qubit) CNOT gate

|0〉1 |0〉2 → |0〉1 |0〉2|0〉1 |1〉2 → |0〉1 |1〉2|1〉1 |0〉2 → |1〉1 |1〉2|1〉1 |1〉2 → |1〉1 |0〉2

Heraklion, 25/10/17 – p. 16/29

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r

2Ω1Ω

Atom 2

2

∆12?r

Atom 1

1 3

1 0 0 1

Two-atom (qubit) CNOT gate

|0〉1 |0〉2 → |0〉1 |0〉2|0〉1 |1〉2 → |0〉1 |1〉2|1〉1 |0〉2 → |1〉1 |1〉2|1〉1 |1〉2 → |1〉1 |0〉2

Wilk et al., PRL 104, 010502 (2010); Isenhower et al., PRL 104, 010503 (2010)Heraklion, 25/10/17 – p. 16/29

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Spatially extended systems

Heraklion, 25/10/17 – p. 17/29

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Lattice spin models

g

r

Ω

δ

Vaa

Heraklion, 25/10/17 – p. 18/29

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Lattice spin models

g

r

Ω

δ

Vaa

spin- 12 Hamiltonian (Ising-like)

Hspin = ~∑N

j [Ωσjx − δj

2 σjz ] +

~

4

∑Ni 6=j ∆ij σ

izσ

jz

with Ω, δj = (δ − 12

∑

i 6=j ∆ij) & ∆ij ≡ ∆(xi − xj)

isotropic or anisotropic interaction

DD (∝ 1/R3) or vdW (∝ 1/R6)

Heraklion, 25/10/17 – p. 18/29

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Lattice spin models

g

r

Ω

δ

Vaa


Hspin = ~∑N

j [Ωσjx − δj

2 σjz ] +

~

4

∑Ni 6=j ∆ij σ

izσ

jz


∑

i 6=j ∆ij) & ∆ij ≡ ∆(xi − xj)


DD (∝ 1/R3) or vdW (∝ 1/R6)

Phase diagram

(mean field)

δ

Weimer et al., PRL 101, 250601 (2008)

Heraklion, 25/10/17 – p. 18/29

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Lattice spin models

g

r

Ω

δ

Vaa


Hspin = ~∑N

j [Ωσjx − δj

2 σjz ] +

~

4

∑Ni 6=j ∆ij σ

izσ

jz


∑

i 6=j ∆ij) & ∆ij ≡ ∆(xi − xj)


DD (∝ 1/R3) or vdW (∝ 1/R6)

Phase diagram

(mean field)

δ

Weimer et al., PRL 101, 250601 (2008)

Schachenmayer et al, NJP 12, 103044 (2010)Heraklion, 25/10/17 – p. 18/29

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Dynamical crystal preparation (1D)

Ω → 0

H/~ = −δ∑N

j σjrr − Ω

∑Nj (σj

rg + σjgr) +

∑Ni<j ∆ij σ

irrσ

jrr

Heraklion, 25/10/17 – p. 19/29

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Ω → 0

H/~ = −δ∑N

j σjrr − Ω

∑Nj (σj

rg + σjgr) +

∑Ni<j ∆ij σ

irrσ

jrr

Avoided crossings ±Ωnn+1 6= 0:

Ω01 =

√NΩ, Ω1

2 = 2Ω/√N, Ω2

3 = Ω, Ω34 ≃ Ω3/[C6/(l/3)

6]2 . . .

Pohl, Demler, Lukin, PRL 104, 043002 (2010)

Schachenmayer, Lesanovsky, Micheli, Daley, NJP 12, 103044 (2010)

Petrosyan, Mølmer, Fleischhauer, JPB 49, 084003 (2016)

Heraklion, 25/10/17 – p. 19/29

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Experiment

Schauß et al., Science 347 1455 (2015); Bernien et al., arXiv:1707.04344Heraklion, 25/10/17 – p. 20/29

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Simulations of adiabatic dynamics (QMC WF)

Pminn ≡

〈Rminn | ρ |Rmin

n 〉

0

0.1

0.2Ω

(2π

MH

z)

−1

0

1

δ (2

π M

Hz)

0 2 4 6 8 10 120

0.5

1

Pro

babi

litie

s

012345

Time τ

µs

Γr=Γz=0

1

Heraklion, 25/10/17 – p. 21/29

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Pminn ≡

〈Rminn | ρ |Rmin

n 〉

0

0.1

0.2Ω

(2π

MH

z)

−1

0

1

δ (2

π M

Hz)

0

0.5

1

Pro

babi

litie

s

012345

0 2 4 6 8 10 120

0.5

1

Time τ

µs

Γr=Γz=0

1

1

Γr=40 kHzΓz=0

Heraklion, 25/10/17 – p. 21/29

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Pminn ≡

〈Rminn | ρ |Rmin

n 〉

0

0.1

0.2Ω

(2π

MH

z)

−1

0

1

δ (2

π M

Hz)

0

0.5

1

Pro

babi

litie

s

012345

0

0.5

1

0 2 4 6 8 10 120

0.5

1

Time τ

µs

Γr=Γz=0

1

1

1

Γr=40 kHzΓz=0

Γz=0Γr=40 kHz

Heraklion, 25/10/17 – p. 21/29

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Pminn ≡

〈Rminn | ρ |Rmin

n 〉

0

0.1

0.2Ω

(2π

MH

z)

−1

0

1

δ (2

π M

Hz)

0

0.5

1

Pro

babi

litie

s

012345

0

0.5

1

0

0.5

1

0 2 4 6 8 10 12Time

0

0.5

1

Time τ

µs

Γr=Γz=0

1

1

1

1

Γr=40 kHzΓz=0

Γz=0Γr=40 kHz

Γr=40 kHzΓz=40 kHz

Heraklion, 25/10/17 – p. 21/29

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Simulations of adiabatic dynamics

F = Pmin3

4 8 12 16 20−1

−0.8

−0.6

0

0.2

0.4

0.6

0.8

1F

idel

ity

Γr=Γz=0 (kHz)Γr=40, Γz=0Γr=0, Γz=40Γr=Γz=40

0 4 8 12 16 20Preparation time τ (µs)

1

1.5

2

2.5

3

Mea

n ex

cita

tion

num

ber

<n>

4 8 12 16 200

0.5

1

1.5

Man

del Q

τ

τ

w

Heraklion, 25/10/17 – p. 22/29

FORTHIESL

FORTHIESL


F = Pmin3

4 8 12 16 20−1

−0.8

−0.6

0

0.2

0.4

0.6

0.8

1F

idel

ity

Γr=Γz=0 (kHz)Γr=40, Γz=0Γr=0, Γz=40Γr=Γz=40

0 4 8 12 16 20Preparation time τ (µs)

1

1.5

2

2.5

3

Mea

n ex

cita

tion

num

ber

<n>

4 8 12 16 200

0.5

1

1.5

Man

del Q

τ

τ

w

Relaxations destroy adiabatic following of the ground state

|R0〉 → |R1〉 → |Rmin2 〉 → |Rmin

3 〉Heraklion, 25/10/17 – p. 22/29

FORTHIESL

FORTHIESL


F = Pmin2 F = Pmin

4

4 8 12 16 20τ

−1−0.9−0.8

Q

1

1.5

2

<n

>

00.10.20.30.40.50.6

F

4 8 12 16 20τ

−1−0.9−0.83

3.5

4

0

0.1

0.2

0.3N=31N=13

Petrosyan, Mølmer, Fleischhauer, JPB 49, 084003 (2016)

Heraklion, 25/10/17 – p. 23/29

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Extended 2D systems

Heraklion, 25/10/17 – p. 24/29

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Rydberg Quasi-Crystals (2D)

alat = 0.532 µm, db = 3.81 µm

Schauß et al., Nature 491, 87 (2012)

Heraklion, 25/10/17 – p. 25/29

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Spatial and Angular Correlations

g(2)(r) =∑

i 6=j δr,rij 〈σirrσ

jrr〉

∑i 6=j

δr,rij 〈σirr〉〈σ

jrr〉

g(2)(∆φ) =∫

dφ2π

∑i,j δφ,φi

δφ+∆φ,φj〈σi

rrσjrr〉

∑i,j

δφ,φi〈σi

rr〉δφ+∆φ,φj〈σj

rr〉

Schauß et al., Nature 491, 87 (2012)

Heraklion, 25/10/17 – p. 26/29

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Rydberg Quasi-Crystals

0

0.05

0 1 2 3 4 5n

0

0.2

0.4

0.6

0.8

1p R

(n)

⟨nR⟩=1.17

0

0.1

0.2

0.3

0.4

CoM

ρ

φx

y

−1 −0.5 0 0.5 1φ/π

00.20.40.60.8

1

P(φ

)

0 1ρ/db

00.20.40.60.8

1

P(ρ

)

bd n=1 n=2

σrr

d=1db

Heraklion, 25/10/17 – p. 27/29

FORTHIESL

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0 1 2 3 4 5 6 7 8 9 10n

0

0.2

0.4

0.6

0.8

p R(n

)

⟨nR⟩=3.63

0

0.05

−1 −0.5 0 0.5 1φ/π

0

0.2

0.4

0.6

P(φ

)

0 1ρ/db

0

0.2

0.4

0.6

P(ρ

)

−1 −0.5 0 0.5 1φ/π

0 1ρ/db

0

0.05

0.1

0.15

d=2db

bd n=3 n=4

σrr

Heraklion, 25/10/17 – p. 27/29

FORTHIESL

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0

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15n

0

0.2

0.4

0.6

p R(n

)

⟨nR⟩=6.62

d=3db

d

−1 −0.5 0 0.5 1φ/π

0

0.2

0.4

P(φ

)0 1 2

ρ/db

0

0.2

0.4

0.6

0.8

1

P(ρ

)

−1 −0.5 0 0.5 1φ/π

0 1 2ρ/db

b n=6 n=7

σrr

Heraklion, 25/10/17 – p. 27/29

FORTHIESL

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0

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20n

0

0.2

0.4

p R(n

) ⟨nR⟩=10.4

db=4d

−1 −0.5 0 0.5 1φ/π

0.1

0.2

0.3

P(φ

)

0 1 2ρ/db

0

0.2

0.4

0.6

0.8

1

P(ρ

)

−1 −0.5 0 0.5 1φ/π

0 1 2ρ/db

bd n=10 =11n

σrr

Heraklion, 25/10/17 – p. 27/29

FORTHIESL

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0

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20n

0

0.2

0.4

p R(n

) ⟨nR⟩=10.4

db=4d

−1 −0.5 0 0.5 1φ/π

0.1

0.2

0.3

P(φ

)

0 1 2ρ/db

0

0.2

0.4

0.6

0.8

1

P(ρ

)

−1 −0.5 0 0.5 1φ/π

0 1 2ρ/db

bd n=10 =11n

σrr

Petrosyan, PRA 88, 043431 (2013)0 1 2 3 4z/db

0

0.5

1

1.5

g(2) (z

)

zmax

nearly incompressible

Liquid of Rydberg exitations

Heraklion, 25/10/17 – p. 27/29

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Summary: Rydberg states offer

Strong, long-range, switchable interactions between atoms

Heraklion, 25/10/17 – p. 28/29

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Logic gates for digital quantum computations and simulations

Heraklion, 25/10/17 – p. 28/29

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Analog simulations of few- and many-body quantum systems

Heraklion, 25/10/17 – p. 28/29

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Analog simulations of few- and many-body quantum systems

Coupling with other systems for hybrid quantum technologies

PNAS 112, 3866 (2015)

Heraklion, 25/10/17 – p. 28/29

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Thank you!

Heraklion, 25/10/17 – p. 29/29

simulating few- and many-body physics with rydberg...

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