Quantum droplets of a dysprosium BEC Igor Ferrier-Barbut Holger - - PowerPoint PPT Presentation

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Quantum droplets of a dysprosium BEC

Igor Ferrier-Barbut

SFB/TRR 21

Holger Kadau, Matthias Schmitt, Matthias Wenzel, Tilman Pfau

• 5. Physikalisches Institut,Stuttgart University

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Can one form a liquid of dilute ultracold bosons?

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Beyond mean-field energy of the weakly-interacting Bose gas

E V = g n2 2 (1 + 128 15√π √ n a3 + · · · )

mean-field LHY, quantum fluctuations

• Phys. Rev 106, 1135 (1957)

Can one form a liquid of dilute ultracold bosons?

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What if these two contributions could be tuned to have opposite signs?

• G. E. Volovik, The Universe in a Helium Droplet, (Oxford University Press, 2009)
• D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015).

Beyond mean-field energy of the weakly-interacting Bose gas

E V = g n2 2 (1 + 128 15√π √ n a3 + · · · )

mean-field LHY, quantum fluctuations

• Phys. Rev 106, 1135 (1957)

Can one form a liquid of dilute ultracold bosons?

Bad Honnef 05/2016

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What if these two contributions could be tuned to have opposite signs?

• G. E. Volovik, The Universe in a Helium Droplet, (Oxford University Press, 2009)
• D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015).

Beyond mean-field energy of the weakly-interacting Bose gas

E V = g n2 2 (1 + 128 15√π √ n a3 + · · · )

Toy model:

E V = e = α n2 + β n5/2

mean-field LHY, quantum fluctuations

• Phys. Rev 106, 1135 (1957)

Can one form a liquid of dilute ultracold bosons?

Bad Honnef 05/2016

2

What if these two contributions could be tuned to have opposite signs?

• G. E. Volovik, The Universe in a Helium Droplet, (Oxford University Press, 2009)
• D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015).

Beyond mean-field energy of the weakly-interacting Bose gas

E V = g n2 2 (1 + 128 15√π √ n a3 + · · · )

Toy model:

E V = e = α n2 + β n5/2

• 10
• 5

5 10 10-4 0.001 0.010 0.100 1 10 100

α/β κT (a.u)

κT = 1 n2 ∂n ∂μ

gas liquid

Gas - liquid transition!

mean-field LHY, quantum fluctuations

• Phys. Rev 106, 1135 (1957)

Can one form a liquid of dilute ultracold bosons?

Bad Honnef 05/2016

2

What if these two contributions could be tuned to have opposite signs?

• G. E. Volovik, The Universe in a Helium Droplet, (Oxford University Press, 2009)
• D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015).

Beyond mean-field energy of the weakly-interacting Bose gas

E V = g n2 2 (1 + 128 15√π √ n a3 + · · · )

Toy model:

E V = e = α n2 + β n5/2

• 10
• 5

5 10 10-4 0.001 0.010 0.100 1 10 100

α/β κT (a.u)

κT = 1 n2 ∂n ∂μ

gas liquid

Gas - liquid transition!

mean-field LHY, quantum fluctuations

• Phys. Rev 106, 1135 (1957)

Can one form a liquid of dilute ultracold bosons?

n0 ∝ ✓α β ◆2

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Dipolar Bose-Einstein condensates

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Dipolar Bose-Einstein condensates

Vc(r) = 4π~2a m δ(r)

Contact interaction

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Dipolar Bose-Einstein condensates

Vc(r) = 4π~2a m δ(r)

Contact interaction

θ

r

~ µ

~ µ

Vdd(r) = µ0 µ2 1 − 3 cos2θ 4π r3

Dipole-dipole interaction

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Dipolar Bose-Einstein condensates

Vc(r) = 4π~2a m δ(r)

Contact interaction

θ

r

~ µ

~ µ

Vdd(r) = µ0 µ2 1 − 3 cos2θ 4π r3

Dipole-dipole interaction

Dipolar length Scattering length

a

Characteristic length scales:

add = m µ0 µ2 12π ~2

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Dipolar Bose-Einstein condensates

Vc(r) = 4π~2a m δ(r)

Contact interaction

θ

r

~ µ

~ µ

Vdd(r) = µ0 µ2 1 − 3 cos2θ 4π r3

Dipole-dipole interaction

Dipolar length Scattering length

a

Characteristic length scales:

add = m µ0 µ2 12π ~2

Relative dipolar strength: εdd = add

a

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Dipolar Bose-Einstein condensates

Mean-field e(~

r ) = g n(~ r )2 2 + n(~ r ) 2 Z d~ r Vdd(~ r 0 − ~ r ) n(~ r 0)

~ B

κ = Rr Rz

2Rr 2Rz

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Dipolar Bose-Einstein condensates

Mean-field

emf(0) = g n2 2 (1 − εddf(κ)) e(~ r ) = g n(~ r )2 2 + n(~ r ) 2 Z d~ r Vdd(~ r 0 − ~ r ) n(~ r 0)

~ B

κ = Rr Rz

2Rr 2Rz

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Dipolar Bose-Einstein condensates

Mean-field

0.01 0.10 1 10 100

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0

κ f(κ)

emf(0) = g n2 2 (1 − εddf(κ)) e(~ r ) = g n(~ r )2 2 + n(~ r ) 2 Z d~ r Vdd(~ r 0 − ~ r ) n(~ r 0)

~ B

κ = Rr Rz

2Rr 2Rz

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

e(0) = g n2 2 ✓ 1 − εddf(κ) + 128 15√π (1 + 3 2ε2

dd)

√ a3√n0 ◆

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

e(0) = g n2 2 ✓ 1 − εddf(κ) + 128 15√π (1 + 3 2ε2

dd)

√ a3√n0 ◆ α β

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

e(0) = g n2 2 ✓ 1 − εddf(κ) + 128 15√π (1 + 3 2ε2

dd)

√ a3√n0 ◆ α/β < 0

for

κ ⌧ 1, εdd > 1

Liquid-like state possible!

α β

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

e(0) = g n2 2 ✓ 1 − εddf(κ) + 128 15√π (1 + 3 2ε2

dd)

√ a3√n0 ◆ α/β < 0

for

κ ⌧ 1, εdd > 1

Liquid-like state possible!

n0 ∝ ✓α β ◆2 α β

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Dipolar Bose-Einstein condensates

Beyond mean-field

∆e = 128 15√π √ na3 Q5(εdd)

LHY Dipolar enhancement

Lima & Pelster, PRA 84, 041604 (2011), ibid 85, 063609 (2012)

Q5(εdd) = 1 + 3 2ε2

dd + · · ·

e(0) = g n2 2 ✓ 1 − εddf(κ) + 128 15√π (1 + 3 2ε2

dd)

√ a3√n0 ◆ α/β < 0

for

κ ⌧ 1, εdd > 1

Liquid-like state possible!

n0 ∝ ✓α β ◆2 α β

See poster by R. Bisset and arXiv:1601.04501 (2016) by F . Wächtler and L. Santos

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µ = 9.93 µB

Dysprosium (164Dy)

Dysprosium Bose-Einstein condensates

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Dipolar length

add = m µ0 µ2 12π ~2 = 132 a0

Scattering length a

Tang et al., PRA 92, 022703 (2015) Maier et al., PRA 92, 060702(R) (2015)

abg = 92(8) a0

µ = 9.93 µB

Dysprosium (164Dy)

Dysprosium Bose-Einstein condensates

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Dipolar length

add = m µ0 µ2 12π ~2 = 132 a0

Scattering length a

Tang et al., PRA 92, 022703 (2015) Maier et al., PRA 92, 060702(R) (2015)

abg = 92(8) a0

εdd = add a

εdd = 1.42

abg

at

µ = 9.93 µB

Dysprosium (164Dy)

Dysprosium Bose-Einstein condensates

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Dipolar length

add = m µ0 µ2 12π ~2 = 132 a0

Scattering length a

Tang et al., PRA 92, 022703 (2015) Maier et al., PRA 92, 060702(R) (2015)

abg = 92(8) a0

εdd = add a

εdd = 1.42

abg

at

µ = 9.93 µB

Dysprosium (164Dy)

Dysprosium Bose-Einstein condensates

2 4 6 8 10

B (G)

10-2 10-1 100

N (a.u.)

Many Feshbach resonances

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Our experiment

High resolution phase-contrast imaging, 1 µm resolution at 421 nm (32.5 MHz broad), single shot

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Oblate dipolar BECs

κ > 1

Trap aspect ratio λ = ωz/ωr = 2.9(1)

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Oblate dipolar BECs

κ > 1

• L. Santos et al., PRL 90, 250403 (2003)
• Uniform case ( ):

Roton-Maxon dispersion relation Varies with axial trapping and short-range interactions Softening → “roton instability”

κ → ∞

Trap aspect ratio λ = ωz/ωr = 2.9(1)

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Rosensweig / normal field instability of classical ferrofluids

Rosensweig, R. Ferrohydrodynamics. Cambridge University Press (1985).

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Rosensweig / normal field instability of classical ferrofluids

Rosensweig, R. Ferrohydrodynamics. Cambridge University Press (1985).

Incompressible, variable magnetization Competition between: Surface tension, gravity vs. dipole-dipole interaction

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Rosensweig / normal field instability of classical ferrofluids

Dispersion relation of surface waves: Softening of a minimum at the instability

Rosensweig, R. Ferrohydrodynamics. Cambridge University Press (1985).

Incompressible, variable magnetization Competition between: Surface tension, gravity vs. dipole-dipole interaction

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Sequence

• Form BEC close to a Feshbach resonance

λ = ωz/ωr = 2.9(1)

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B

B0 a

1 εdd = add a a ∼ add 1.4

Sequence

• Form BEC close to a Feshbach resonance

λ = ωz/ωr = 2.9(1)

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B

B0 a

1 εdd = add a a ∼ add 1.4

Sequence

• Form BEC close to a Feshbach resonance
• lower a down to abg

λ = ωz/ωr = 2.9(1)

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B

B0 a

1 εdd = add a a ∼ add 1.4

Sequence

• Form BEC close to a Feshbach resonance
• lower a down to abg

λ = ωz/ωr = 2.9(1)

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Results

Uniform BEC

• H. Kadau, M. Schmitt, M.Wenzel, C. Wink, T. Maier, I. F-B, T. Pfau , Nature 530, 194 (2016)

B=BBEC

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Results

Uniform BEC

εdd = 1.4

B=B1

12 µm 12 µm

• H. Kadau, M. Schmitt, M.Wenzel, C. Wink, T. Maier, I. F-B, T. Pfau , Nature 530, 194 (2016)

B=BBEC

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In Fourier space

F [¯ n(x, y)] (kx, ky)

¯ n(x, y)

x

kx ky

• H. Kadau, M. Schmitt, M.Wenzel, C. Wink, T. Maier, I. F-B, T. Pfau , Nature 530, 194 (2016)

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In Fourier space

Angular averaging

2 4 6 8 0. 0.02 0.04 k (μm-1) S(k)

BEC droplets Extra spectral weight between 1.5 µm-1 and 5 µm-1 Quantitative marker of the transition F [¯ n(x, y)] (kx, ky)

¯ n(x, y)

x

kx ky

• H. Kadau, M. Schmitt, M.Wenzel, C. Wink, T. Maier, I. F-B, T. Pfau , Nature 530, 194 (2016)

Rosensweig instability of a dipolar BEC SYQMA 2015

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Dynamics and lifetime

Long lived, several hundred ms

0 2 4 6 810 20 200 400 600 800 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4000 8000 12000 t (ms) Relative spectral weight Number in droplets

Relative spectral weight Number

Droplet formation dynamics

• H. Kadau, M. Schmitt, M.Wenzel, C. Wink, T. Maier, I. F-B, T. Pfau , Nature 530, 194 (2016)

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Simulations

Wächtler and Santos, arXiv:1601.04501 (2016)

Elongated droplets, experimentally: κ 6 0.2 Presence of a dilute “halo”

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Simulations

Wächtler and Santos, arXiv:1601.04501 (2016)

Elongated droplets, experimentally: κ 6 0.2 Presence of a dilute “halo”

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Probing droplets in a waveguide

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Probing droplets in a waveguide

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Probing droplets in a waveguide

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Probing droplets in a waveguide

• I. F-B, H. Kadau, M. Schmitt, M.Wenzel, T. Pfau, arXiv:1601.03318 PRL (2016)

x y 0 ms 5 ms 10 ms 15 ms 20 ms

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Probing droplets in a waveguide

• I. F-B, H. Kadau, M. Schmitt, M.Wenzel, T. Pfau, arXiv:1601.03318 PRL (2016)

x y 0 ms 5 ms 10 ms 15 ms 20 ms

5 10 15 d (µm) 5 10 15 20 tWG (ms) 1 10 100 σ (µm) BEC Droplets

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10 20 30 40 0.0 0.2 0.4 0.6 0.8 1.0 Δatof (a0) ΔEy (units of ℏω y)

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∆E ' ∆g 2 ¯ n = 2π~2 m ∆atof ¯ n

Measuring density

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10 20 30 40 0.0 0.2 0.4 0.6 0.8 1.0 Δatof (a0) ΔEy (units of ℏω y)

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10 20 30 40 0.0 0.2 0.4 0.6 0.8 1.0 Δatof (a0) ΔEy (units of ℏω y)

∆E ' ∆g 2 ¯ n = 2π~2 m ∆atof ¯ n

¯ n = 1.7(1) × 1020 m−3

Measuring density

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∆E ' ∆g 2 ¯ n = 2π~2 m ∆atof ¯ n

0.01 0.10 1 10

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 0.6 n0 (1020 m-3) 1 g ∂μ ∂n

¯ n = 1.7(1) × 1020 m−3

Measuring density

• I. F-B, H. Kadau, M. Schmitt, M.Wenzel, T. Pfau, arXiv:1601.03318 PRL (2016)

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n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

Density and lifetime scaling

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n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

Density and lifetime scaling

Hypothesis: no quantum fluctuations, but a three-body repulsion:

Xi and Saito PRA, 93, 011604 Bisset and Blakie, PRA 92, 061603

e = g3 6 n2

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n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

Density and lifetime scaling

Hypothesis: no quantum fluctuations, but a three-body repulsion:

Xi and Saito PRA, 93, 011604 Bisset and Blakie, PRA 92, 061603

e = g3 6 n2 n0 ∝ g (εddf(κ) − 1) g3

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n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

Density and lifetime scaling

Lifetime under three-body losses:

τ = 1/L3hn2i

˙ N N = L3hn2i

Hypothesis: no quantum fluctuations, but a three-body repulsion:

Xi and Saito PRA, 93, 011604 Bisset and Blakie, PRA 92, 061603

e = g3 6 n2 n0 ∝ g (εddf(κ) − 1) g3

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n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

Density and lifetime scaling

Lifetime under three-body losses:

τ = 1/L3hn2i

˙ N N = L3hn2i

τ(a1)/τ(a2) = (n(a2)/n(a1))2

The lifetime increases with a!

Hypothesis: no quantum fluctuations, but a three-body repulsion:

Xi and Saito PRA, 93, 011604 Bisset and Blakie, PRA 92, 061603

e = g3 6 n2 n0 ∝ g (εddf(κ) − 1) g3

• I. F-B, H. Kadau, M. Schmitt, M.Wenzel, T. Pfau, arXiv:1601.03318 PRL (2016)

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Density and lifetime scaling

n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

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Density and lifetime scaling

0.92 0.94 0.96 0.98 1.00 0.1 1.

af / ai τ f / τ i

Quantum fluctuations Three-body

n0 ∝ ✓α β ◆2 ∝ 1 a3 ✓εddf(κ) − 1 1 + 3

2ε2 dd

◆2

• I. F-B, H. Kadau, M. Schmitt, M.Wenzel, T. Pfau, arXiv:1601.03318 PRL (2016)

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Identification of a new liquid-like phase existing thanks to quantum fluctuations Observation of a finite-wavelength instability (related to the roton instability) Experimental verification of the density and scaling in the liquid- like phase

Summary

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Identification of a new liquid-like phase existing thanks to quantum fluctuations Observation of a finite-wavelength instability (related to the roton instability) Experimental verification of the density and scaling in the liquid- like phase

0.92 0.94 0.96 0.98 1.00 0.1 1.

af / ai τ f / τ i

Quantum fluctuations Three-body

Summary

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Thanks for your time!

• M. Wenzel
• T. Pfau
• H. Kadau
• M. Schmitt
• I. F.B.