Electron interferometry in quantum Hall edge channels Jrme Rech - - PowerPoint PPT Presentation

SLIDE 1

Electron interferometry in quantum Hall edge channels

Jérôme Rech

Centre de Physique Théorique, Marseille in collaboration with

• C. Wahl, D. Ferraro, T. Jonckheere and
• T. Martin

Iout

R

Iout

L

1 / 13

SLIDE 2

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

2 / 13

SLIDE 3

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons

2 / 13

SLIDE 4

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

2 / 13

SLIDE 5

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE

2 / 13

SLIDE 6

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

2 / 13

SLIDE 7

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

Point contact

2 / 13

SLIDE 8

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

Point contact Coherent light source

↓

2 / 13

SLIDE 9

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

Point contact Coherent light source

↓

Single electron source

2 / 13

SLIDE 10

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

Point contact Coherent light source

↓

Single electron source

Mesoscopic capacitor

[Fève et al., Science (’07)]

Surface acoustic waves

[Hermelin et al., Nature (’11)] [McNeil et al., Nature (’11)]

Quantum turnstiles

[Giblin et al., Nature Comm.(’12)]

Lorentzian pulses

[Dubois et al., Nature (’13)] 2 / 13

SLIDE 11

Electronic quantum optics in quantum Hall systems

Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors

INGREDIENT LIST

Photons

↓

Electrons Light beam

↓

Chiral edge QHE Beam-splitter

↓

Point contact Coherent light source

↓

Single electron source

Mesoscopic capacitor

[Fève et al., Science (’07)]

Surface acoustic waves

[Hermelin et al., Nature (’11)] [McNeil et al., Nature (’11)]

Quantum turnstiles

[Giblin et al., Nature Comm.(’12)]

Lorentzian pulses

[Dubois et al., Nature (’13)]

➙ opens the way to all sorts of interference experiments!

2 / 13

SLIDE 12

Hong-Ou-Mandel interference experiment

Two-photon interferences

two identical photons sent on a beam-splitter necessarily exit by the same output channel

➙ signature of bosonic statistics

3 / 13

SLIDE 13

Hong-Ou-Mandel interference experiment

Two-photon interferences

two identical photons sent on a beam-splitter necessarily exit by the same output channel

➙ signature of bosonic statistics

Interference experiment [Hong, Ou and Mandel, PRL 59, 2044 (’87)]

counts occurrences of photons present in the two output channels dip is observed when photons arrive at the same time signatures of incoming wave packets

3 / 13

SLIDE 14

Hong-Ou-Mandel interference experiment

Two-photon interferences

two identical photons sent on a beam-splitter necessarily exit by the same output channel

➙ signature of bosonic statistics

Interference experiment [Hong, Ou and Mandel, PRL 59, 2044 (’87)]

counts occurrences of photons present in the two output channels dip is observed when photons arrive at the same time signatures of incoming wave packets

Why would it be so different with electrons?

they obey fermionic statistics ➙ Fermi sea, hole excitations, ... thermal effects do matter they interact via Coulomb interaction

3 / 13

SLIDE 15

HOM with electrons: general principle and first results

Setup

2 single electron sources counter-propagating channels coupled at QPC measure output currents Iout

R

Iout

L

Single electron source

4 / 13

SLIDE 16

HOM with electrons: general principle and first results

Setup

2 single electron sources counter-propagating channels coupled at QPC measure output currents Iout

R

Iout

L

Single electron source

Zero-frequency cross-correlations of output currents Sout

RL =

• dtdt′ Iout

R (x, t)Iout L (x′, t′) − Iout R (x, t)Iout L (x′, t′)

• 4 / 13

SLIDE 17

HOM with electrons: general principle and first results

Setup

2 single electron sources counter-propagating channels coupled at QPC measure output currents Iout

R

Iout

L

Single electron source

Zero-frequency cross-correlations of output currents Sout

RL =

• dtdt′ Iout

R (x, t)Iout L (x′, t′) − Iout R (x, t)Iout L (x′, t′)

• Theory at ν = 1 [Jonckheere et al. Phys. Rev. B 86, 125425 (’12)]

−120 −100 −80 −60 −40 −20 20 40 60 80 100 120 0.2 0.4 0.6 0.8 1

δT SHOM/2SHBT

D = 0.2 D = 0.5 D = 0.8

When electrons arrive independently SRL : sum of the partition noise flat contrib. ➙ random partitioning When electrons arrive simultaneously SRL = 0 ➙ HOM/Pauli dip signatures of injected object (overlap)

4 / 13

SLIDE 18

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

✬ ✩

• 5 / 13

SLIDE 19

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

As expected ✓ Flat background contribution ✓ dip for simultaneous injection But... How come it does not reach 0?

➙ decoherence effect

T i m e d e l a y τ [ p s ] C o r r e l a t i o n s ∆q

• Random ¡par**oning

Pauli ¡dip

5 / 13

SLIDE 20

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

As expected ✓ Flat background contribution ✓ dip for simultaneous injection But... How come it does not reach 0?

➙ decoherence effect

T i m e d e l a y τ [ p s ] C o r r e l a t i o n s ∆q

• Random ¡par**oning

Pauli ¡dip

Something special happens beyond the simple ν = 1 picture

5 / 13

SLIDE 21

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

As expected ✓ Flat background contribution ✓ dip for simultaneous injection But... How come it does not reach 0?

➙ decoherence effect

T i m e d e l a y τ [ p s ] C o r r e l a t i o n s ∆q

• Random ¡par**oning

Pauli ¡dip

Something special happens beyond the simple ν = 1 picture Interactions as a source of decoherence

ν = 1

5 / 13

SLIDE 22

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

As expected ✓ Flat background contribution ✓ dip for simultaneous injection But... How come it does not reach 0?

➙ decoherence effect

T i m e d e l a y τ [ p s ] C o r r e l a t i o n s ∆q

• Random ¡par**oning

Pauli ¡dip

Something special happens beyond the simple ν = 1 picture Interactions as a source of decoherence

✘✘ ✘ ❳❳ ❳ ν = 1 ➙ ν = 2 interactions between co-propagating channels

5 / 13

SLIDE 23

HOM with electrons: experimental results

Main experimental results [Bocquillon et al., Science 339, 1054 (’13)]

As expected ✓ Flat background contribution ✓ dip for simultaneous injection But... How come it does not reach 0?

➙ decoherence effect

T i m e d e l a y τ [ p s ] C o r r e l a t i o n s ∆q

• Random ¡par**oning

Pauli ¡dip

Something special happens beyond the simple ν = 1 picture Interactions as a source of decoherence

✘✘ ✘ ❳❳ ❳ ν = 1 ➙ ν = 2 interactions between co-propagating channels injection, propagation, tunneling

5 / 13

SLIDE 24

1 - Injection

Simplified model of injection: prepared state

injection in the past at t = −T0 : |ϕ = O† (−T0) preparation operator |0 ground-state

6 / 13

SLIDE 25

1 - Injection

Simplified model of injection: prepared state

injection in the past at t = −T0 : |ϕ = O† (−T0) preparation operator |0 ground-state preparation operator O† = O†

RO† L with

O†

R,L =

• dkϕR,L(k)ψ†

R,L(k; t = −T0)

6 / 13

SLIDE 26

1 - Injection

Simplified model of injection: prepared state

injection in the past at t = −T0 : |ϕ = O† (−T0) preparation operator |0 ground-state preparation operator O† = O†

RO† L with

O†

R,L =

• dkϕR,L(k)ψ†

R,L(k; t = −T0)

SES

• dkϕ(k)ψ†

k

True one shot injection of electron or hole Versatile: any wave-packet

6 / 13

SLIDE 27

1 - Injection

Simplified model of injection: prepared state

injection in the past at t = −T0 : |ϕ = O† (−T0) preparation operator |0 ground-state preparation operator O† = O†

RO† L with

O†

R,L =

• dkϕR,L(k)ψ†

R,L(k; t = −T0)

SES

• dkϕ(k)ψ†

k

True one shot injection of electron or hole Versatile: any wave-packet

Exponential wave-packets

ϕR,L(x) =

• 2Γ

vF e±(iǫ0+Γ)x/vF θ(∓x)

−1 1 2 3 4 5 0.2 0.4 0.6 0.8 1

x(µm) |ϕL(x)|2

−1 −0.5 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4

ǫ0 = 0.175K

ǫ(K) | ˆ ϕL(ǫ)|2

Tunable resolution γ = ǫ0/Γ [emission time τe = /(2Γ)] ǫ0 = 0.175K Γ = 0.175K

• −

→ γ = 1

6 / 13

SLIDE 28

1 - Injection

Simplified model of injection: prepared state

injection in the past at t = −T0 : |ϕ = O† (−T0) preparation operator |0 ground-state preparation operator O† = O†

RO† L with

O†

R,L =

• dkϕR,L(k)ψ†

R,L(k; t = −T0)

SES

• dkϕ(k)ψ†

k

True one shot injection of electron or hole Versatile: any wave-packet

Exponential wave-packets

ϕR,L(x) =

• 2Γ

vF e±(iǫ0+Γ)x/vF θ(∓x) Tunable resolution γ = ǫ0/Γ [emission time τe = /(2Γ)] ǫ0 = 0.175K Γ = 0.175K

• −

→ γ = 1

−1 1 2 3 4 5 0.2 0.4 0.6 0.8 1

x(µm) |ϕL(x)|2

−1 −0.5 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4

ǫ0 = 0.7K

ǫ(K) | ˆ ϕL(ǫ)|2

ǫ0 = 0.7K Γ = 0.0875K

• −

→ γ = 8

6 / 13

SLIDE 29

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r Klein factor √ 2πa cutoff exp (i φj,r(x) chiral bosonic field )

7 / 13

SLIDE 30

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r √ 2πa exp (i φj,r(x)) Hamiltonian H = H0 + Hinter r = R r = L

j = 1 j = 2 j = 1 j = 2 Propagation + intra-channel interaction H0 = π

• j=1,2
• v (0)

j

edge velocities + U interaction strength

r=R,L

• dx (∂xφj,r)2

7 / 13

SLIDE 31

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r √ 2πa exp (i φj,r(x)) Hamiltonian H = H0 + Hinter r = R r = L

j = 1 j = 2 j = 1 j = 2 Propagation + intra-channel interaction H0 = π

• j=1,2
• v (0)

j

+ U

r=R,L

• dx (∂xφj,r)2

Inter-channel interaction Hinter = 2 π u interaction strength

• r=R,L
• dx (∂xφ1,r) (∂xφ2,r)

7 / 13

SLIDE 32

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r √ 2πa exp (i φj,r(x)) Hamiltonian H = H0 + Hinter r = R r = L

j = 1 j = 2 j = 1 j = 2 Propagation + intra-channel interaction H0 = π

• j=1,2
• v (0)

j

+ U

r=R,L

• dx (∂xφj,r)2

Inter-channel interaction Hinter = 2 π u

• r=R,L
• dx (∂xφ1,r) (∂xφ2,r)

Diagonalizing H =

π

• r=R,L
• dx

j=1,2

vj (∂xφj,r)2 + 2u (∂xφ1,r) (∂xφ2,r)

• 7 / 13

SLIDE 33

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r √ 2πa exp (i φj,r(x)) Hamiltonian H = H0 + Hinter r = R r = L

j = 1 j = 2 j = 1 j = 2 Propagation + intra-channel interaction H0 = π

• j=1,2
• v (0)

j

+ U

r=R,L

• dx (∂xφj,r)2

Inter-channel interaction Hinter = 2 π u

• r=R,L
• dx (∂xφ1,r) (∂xφ2,r)

Diagonalizing H =

π

• r=R,L
• dx
• v+ (∂xφ+,r)2 + v− (∂xφ−,r)2

7 / 13

SLIDE 34

2 - Propagation

Bosonization identity: ψj,r(x) = Uj,r √ 2πa exp (i φj,r(x)) Hamiltonian H = H0 + Hinter r = R r = L

j = 1 j = 2 j = 1 j = 2 Propagation + intra-channel interaction H0 = π

• j=1,2
• v (0)

j

+ U

r=R,L

• dx (∂xφj,r)2

Inter-channel interaction Hinter = 2 π u

• r=R,L
• dx (∂xφ1,r) (∂xφ2,r)

Diagonalizing H =

π

• r=R,L
• dx
• v+ (∂xφ+,r)2 + v− (∂xφ−,r)2

Charge fractionalization: fast charged φ+, slow neutral φ−

8 10 12 14 16 18 20 −0.2 −0.1 0.1 0.2

⊕ ⊕

x qinj,L

γ = 8, L = 5µm

injection channel

8 10 12 14 16 18 20 −0.2 −0.1 0.1 0.2

⊕ ⊖

x qcopr,L

γ = 8, L = 5µm

co-propagating channel

Average charge density qs,r(x, t) = e π ∂xφs,r(x, t)ϕ Excitations characterized by the charge they carry ⊕/⊖

7 / 13

SLIDE 35

3 - Tunneling

QPC couples counter-propagating channels ➙ two possibilities

8 / 13

SLIDE 36

3 - Tunneling

QPC couples counter-propagating channels ➙ two possibilities Two setups s = 1, 2

I1 I2

+ − + + + + + −

SETUP 1

I1 I2

+ − + + + + + −

SETUP 2

8 / 13

SLIDE 37

3 - Tunneling

QPC couples counter-propagating channels ➙ two possibilities Two setups s = 1, 2

I1 I2

+ − + + + + + −

SETUP 1

I1 I2

+ − + + + + + −

SETUP 2 Tunneling Hamiltonian Htun = Γ tunnel amplitude

• ψ†

s,R(0)ψs,L(0) + ψ† s,L(0)ψs,R(0)

• 8 / 13

SLIDE 38

3 - Tunneling

QPC couples counter-propagating channels ➙ two possibilities Two setups s = 1, 2

I1 I2

+ − + + + + + −

SETUP 1

I1 I2

+ − + + + + + −

SETUP 2 Tunneling Hamiltonian Htun = Γ

• ψ†

s,R(0)ψs,L(0) + ψ† s,L(0)ψs,R(0)

• Scattering matrix:
• ψs,R

ψs,L

• utgoing

=

√

T i √ R i √ R √ T ψs,R ψs,L

incoming T is the transmission and R the reflexion probability

8 / 13

SLIDE 39

Performing the calculation: final expression

Quantity of interest: Sout

RL

• Iout

s,r (x, t)

• −

→ Sout

RL

• φin

±,r(0, t)

• 9 / 13

SLIDE 40

Performing the calculation: final expression

Quantity of interest: Sout

RL

• Iout

s,r (x, t)

• −

→ Sout

RL

• φin

±,r(0, t)

• Final expression of noise for the Hong-Ou-Mandel experiment

SHOM

RL

= −2S0Re

• dτRe

g(τ, 0)2 ×

• dyRdzR ϕR(yR)ϕ∗

R(zR)

(2πa)2NR g(0, yR − zR)

• dyLdzL ϕL(yL)ϕ∗

L(zL)

(2πa)2NL g(0, zL − yL) ×

• dt
• hs(t; yL + L, zL + L)hs(t + τ − δT; L − yR, L − zR)

hs(t + τ; yL + L, zL + L)hs(t − δT; L − yR, L − zR) − 1

• g(t, x) =
• sinh

i πa

βv+

• sinh

i πa

βv−

• sinh ia+v+t−x

βv+/π

• sinh ia+v−t−x

βv−/π

• 1

2

hs(t; x, y) =

• sinh ia−v+t+x

βv+/π

• sinh ia+v+t−y

βv+/π

• 1

2

sinh ia−v−t+x

βv−/π

• sinh ia+v−t−y

βv−/π

• s− 3

2

9 / 13

SLIDE 41

Performing the calculation: final expression

Quantity of interest: Sout

RL

• Iout

s,r (x, t)

• −

→ Sout

RL

• φin

±,r(0, t)

• Final expression of noise for the Hong-Ou-Mandel experiment

SHOM

RL

= −2S0Re

• dτRe

g(τ, 0)2 ×

• dyRdzR ϕR(yR)ϕ∗

R(zR)

(2πa)2NR g(0, yR − zR)

• dyLdzL ϕL(yL)ϕ∗

L(zL)

(2πa)2NL g(0, zL − yL) ×

• dt
• hs(t; yL + L, zL + L)hs(t + τ − δT; L − yR, L − zR)

hs(t + τ; yL + L, zL + L)hs(t − δT; L − yR, L − zR) − 1

• g(t, x) =
• sinh

i πa

βv+

• sinh

i πa

βv−

• sinh ia+v+t−x

βv+/π

• sinh ia+v−t−x

βv−/π

• 1

2

hs(t; x, y) =

• sinh ia−v+t+x

βv+/π

• sinh ia+v+t−y

βv+/π

• 1

2

sinh ia−v−t+x

βv−/π

• sinh ia+v−t−y

βv−/π

• s− 3

2

Focus on the most experimentally relevant situation

I1 I2

+ − + + + + + −

SETUP 1

time delay δT = 0

⊕ ⊕ ⊕ ⊕

v+ v+ v− v−

interference of ⊕ excitations with same velocity time delay δT = ±L

v+−v− v+v−

⊕ ⊕ ⊕ ⊕

v+ v+ v− v−

interference of ⊕ excitations with different velocity

9 / 13

SLIDE 42

Main results

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm setup 1 ǫ0 = 175mK, γ = 1

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.5 1 1.5

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm ǫ0 = 0.7K, γ = 8 setup 1

3-dip structure + flat background contribution (no interference)

10 / 13

SLIDE 43

Main results

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm setup 1 ǫ0 = 175mK, γ = 1

Central dip noise reduction ➙ destructive interference of ⊕/⊕ excitations loss of contrast due to interactions, strong dependence on resolution

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.5 1 1.5

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm ǫ0 = 0.7K, γ = 8 setup 1

3-dip structure + flat background contribution (no interference)

10 / 13

SLIDE 44

Main results

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm setup 1 ǫ0 = 175mK, γ = 1

Central dip noise reduction ➙ destructive interference of ⊕/⊕ excitations loss of contrast due to interactions, strong dependence on resolution Side dips ⊕-excitations with different velocities destructive interference velocity mismatch : asymmetry + smaller than half central dip

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.5 1 1.5

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm ǫ0 = 0.7K, γ = 8 setup 1

3-dip structure + flat background contribution (no interference)

10 / 13

SLIDE 45

Main results

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm setup 1 ǫ0 = 175mK, γ = 1

Central dip noise reduction ➙ destructive interference of ⊕/⊕ excitations loss of contrast due to interactions, strong dependence on resolution Side dips ⊕-excitations with different velocities destructive interference velocity mismatch : asymmetry + smaller than half central dip

−0.6 −0.4 −0.2 0.2 0.4 0.6 0.5 1 1.5

2|SHBT| δT(ns) |SHOM(δT)|(e2RT ) L = 2.5µm L = 5µm ǫ0 = 0.7K, γ = 8 setup 1

100 50 50 100 0.0 0.2 0.4 0.6 0.8 1.0

∆t

SHOM ∆t 2 SHBT

3-dip structure + flat background contribution (no interference)

10 / 13

SLIDE 46

Towards a more quantitative agreement

Results are functions of 4 parameters ǫ0, τe, β, τs L

• 1

v− − 1 v+

• all given by the

experiment ➙ No adjustable parameters!

11 / 13

SLIDE 47

Towards a more quantitative agreement

Results are functions of 4 parameters ǫ0, τe, β, τs all given by the experiment ➙ No adjustable parameters! Contrast η = 1 − SHOM(δT=0)

2SHBT

50 100 150 200 250 300 0.2 0.4 0.6 0.8 1

τe(ps) Contrast γ

Dramatic loss of contrast with energy resolution/emission time Experimental values: ǫ0 = 0.7 K τs = 70 ps 1/(kBβ) = 100 mK

11 / 13

SLIDE 48

Towards a more quantitative agreement

Results are functions of 4 parameters ǫ0, τe, β, τs all given by the experiment ➙ No adjustable parameters! Contrast η = 1 − SHOM(δT=0)

2SHBT

50 100 150 200 250 300 0.2 0.4 0.6 0.8 1

τe(ps) Contrast γ

Dramatic loss of contrast with energy resolution/emission time Experimental values: ǫ0 = 0.7 K τs = 70 ps 1/(kBβ) = 100 mK

Energy dependence: η vs. ǫR

ν = 1: rapid decrease consistent with packet overlap

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

ǫL = 0.7 K ǫR(K) Contrast η τe = 20ps τe = 60ps τe = 100ps

11 / 13

SLIDE 49

Towards a more quantitative agreement

Results are functions of 4 parameters ǫ0, τe, β, τs all given by the experiment ➙ No adjustable parameters! Contrast η = 1 − SHOM(δT=0)

2SHBT

50 100 150 200 250 300 0.2 0.4 0.6 0.8 1

τe(ps) Contrast γ

Dramatic loss of contrast with energy resolution/emission time Experimental values: ǫ0 = 0.7 K τs = 70 ps 1/(kBβ) = 100 mK

Energy dependence: η vs. ǫR

ν = 1: rapid decrease consistent with packet overlap ν = 2: roughly independent energy content of colliding objects?

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

ǫL = 0.7 K ǫR(K) Contrast η τe = 20ps τe = 60ps τe = 100ps

11 / 13

SLIDE 50

Towards a more quantitative agreement

Results are functions of 4 parameters ǫ0, τe, β, τs all given by the experiment ➙ No adjustable parameters! Contrast η = 1 − SHOM(δT=0)

2SHBT

50 100 150 200 250 300 0.2 0.4 0.6 0.8 1

τe(ps) Contrast γ

Dramatic loss of contrast with energy resolution/emission time Experimental values: ǫ0 = 0.7 K τs = 70 ps 1/(kBβ) = 100 mK

Energy dependence: η vs. ǫR

ν = 1: rapid decrease consistent with packet overlap ν = 2: roughly independent energy content of colliding objects?

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

ǫL = 0.7 K ǫR(K) Contrast η τe = 20ps τe = 60ps τe = 100ps

➙ interactions dramatically affect the nature of excitations

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SLIDE 51

Fractional case

Taking interactions to the next level: Fractional Quantum Hall effect IQHE FQHE

electrons e quasiparticles e∗ fermionic anyonic Fermi sea non-trivial vacuum

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SLIDE 52

Fractional case

Taking interactions to the next level: Fractional Quantum Hall effect IQHE FQHE

electrons e quasiparticles e∗ fermionic anyonic Fermi sea non-trivial vacuum

This raises tons of new and exciting open questions!

Can we emit controlled single quasiparticles in the system? Is a perturbative treatment in tunneling sufficient? Do quasiparticles show bunching? Are there signatures of non-trivial statistics in the HOM noise signal? How to extend the idea of minimal excitations?

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SLIDE 53

Fractional case

Taking interactions to the next level: Fractional Quantum Hall effect IQHE FQHE

electrons e quasiparticles e∗ fermionic anyonic Fermi sea non-trivial vacuum

This raises tons of new and exciting open questions!

Can we emit controlled single quasiparticles in the system? Is a perturbative treatment in tunneling sufficient? Do quasiparticles show bunching? Are there signatures of non-trivial statistics in the HOM noise signal? How to extend the idea of minimal excitations?

On-demand source of single quasiparticles

driven antidot as a QP source quantization of the emitted charge fluctuations? ➙ jitter noise

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SLIDE 54

Conclusions

Strong coupling between channels accounts for a sensible loss of contrast of the HOM central dip The contrast strongly depends on the energy resolution of the injected wave-packet Fast and slow modes interfere and produce, depending on the charge carried by the colliding excitations, smaller asymmetric dips or peaks Our interacting model recovers the main experimental features

➙ Detailed quantitative comparison is under way!

Interactions and charge fractionalization in an electronic HOM interferometer

• C. Wahl, J. Rech, T. Jonckheere, T. Martin, Phys. Rev. Lett. 112, 046802 (2014)

Single quasiparticle and electron emitter in the fractional quantum Hall regime

• D. Ferraro, J. Rech, T. Jonckheere, T. Martin, Phys. Rev. B 91, 205409 (2015)

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