Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Dipolar Interactions and Rotons in Ultracold AtomicQuantum Gases

Falk Wachtler

Workshop of the RTG 1729Luneburg

March 13., 2014

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Table of contents

1 Experiments and General PropertiesRealization of dipolar SystemsErbium

2 What is a Roton?Excitation spectrumExcitation SpectraRoton Confinement

3 Our WorkProblem of validityCalculation Scheme

4 Summary

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Dipole-Dipole Interactions

Dipolar Interactions in magnetic and electric systems

long ranged and anisotropic

U =Cdd

4π

1− 3 cos2 θ

r3

magnetic:

CBdd = µ0m

2

permanent magnetic dipoles in atoms

electric:

CEdd = 4πd2

polar molecules, Rydberg atoms, andlight-induced dipoles in atoms

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Magnetic Systems

Realized samplesBoson: 52Cr A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, and

T. Pfau, PRL 94, 160401 (2005)

Fermion: 53Cr R. Chicireanu, A. Pouderous, R. Barbe, B.

Laburthe-Tolra, E. Marechal, L. Vernac, J.-C. Keller, and O.

Gorceix, PRA 73, 053406 (2006)

Boson: 87Rb M. Vengalattore, S. R. Leslie, J. Guzman, and D. M.

Stamper-Kurn, PRL 100, 170403 (2008)

Boson: 164Dy M. Lu, N. Burdick, S. Youn, and B. Lev, PRL 107,

190401 (2011)

Boson: 168Er K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler,

R. Grimm, and F. Ferlaino, PRL 108, 210401 (2012)

Fermion: 167Er Aikawa et al., arXiv:1310.5676 (2013)

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Erbium: Collisional properties

producing BEC and degenerate Fermi gases of Erbium

complicated collisional properties → lot of Feshbachresonances

lot of Feshbach resonances within small B-range → bettercontrol of contact strength

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Cooling of Fermions

No s-wave collisions in spin-polarized Fermi gases

Without dipole-dipole interaction no direct evaporative cooling

Strong dipole-dipole interactions lead to thermalizationthrough p-wave interactions

Very small inelastic collisions due to large p-wave barrier

K. Aikawa, A.Frisch, M. Mark, S.Baier, R. Grimm,and F. Ferlaino,arXiv:1310.5676(2013)

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Realization of dipolar SystemsErbium

Stability

Dipole-dipole interaction is partially attractive → stabilitydepends on contact interaction and geometry

T.Lahaye et al., Rep. Prog. Phys. 72, 126401 (2009)

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

What is a Roton?

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Calculation of the Excitation Spectrum

weak interacting limit → most of particles stay in condensate

description by Gross-Pitaevskii Equation

ı~ψ =

[−~2∇2

2m+ V (x) + g |ψ|2 +

∫d3r ′U(r − r′)|ψ(r′, t)|2

]ψ

Bogoliubov approximation

ψ(r, t) = ψ0(r, t) + δψ(r, t)

linear transformation

δψ(r, t) = u(r)e−ı~ (µ+~ω)t + v∗(r)e

ı~ (−µ+~ω)t

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Calculation of the Excitation spectrum

[−~2∇2

2m+ V (x) + 2g |ψ0(r)|2 +

∫d3r ′U(r − r′)|ψ0(r′])|2 − µ

]u

+gψ20v + ψ0

∫d3r ′U(r − r′)

[ψ0(r′)v(r′) + ψ∗0(r′)u(r′)

]= ~ωu[

~2∇2

2m− V (x)− 2g |ψ0(r)|2 −

∫d3r ′U(r − r′)|ψ0(r′])|2 + µ

]v

−g(ψ∗0)2u − ψ∗0∫

d3r ′U(r − r′)[ψ0(r′)v(r′) + ψ∗0(r′)u(r′)

]= ~ωv

homogeneous solution

~ω = ±

√~2k22m

(~2k22m

+ 2gn0 + 2U(k)n0

)Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Excitation Spectrum for 2D homogeneous system

M. Jona-Lasinio, K. Lakomy, andL. Santos, Phys. Rev. A 88,025603 (2013).

linear dependence for smallmomenta

quadratic behavior for largemomenta

roton like excitationspectrum for pankace traps

if k � 1L two dimensional

excitations → particlesrepel each other →excitations are phonons

for k � 1L excitations

aquire 3D character →interparticle repulsion isreduced

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Inhomogeneous System and Fingers

R. Bisset, D. Baillie,and P. Blakie, Phys.Rev. A 88, 043606(2013).

Cylinder-symmetricsystem →z-projection ofangular momentumis ”good” quantumnumber

Emerging rotonfingers

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Roton Confinement

depth of roton minimum is interaction dependent

interaction is density dependent

-10

-5

0

5

10

x

-10

-5

0

5

10

y

0.0

0.5

1.0

nHx , yL

En,m =√ε20 + An + Bm2

M. Jona-Lasinio, K. Lakomy, and L. Santos, Phys. Rev. A 88,013619 (2013)

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

What is the difference between a Roton and a Phonon?

R. Bisset, D. Baillie, and P. Blakie, Phys. Rev.A 88, 043606 (2013).

Phonon modeextends overcondensatesize

Roton mode islocalizedaround center

Condensate-excitationinteractionattractive atshortwavelengths

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Excitation spectrumExcitation SpectraRoton Confinement

Detection of Rotons

no observation yet

analyzing the structure factor of trapped dipolar gas

stability spectroscopy

atom number fluctuations can reveal presence and locality ofrotons

problem locality → can be solved by using box potential

A. Gaunt et al., Phys. Rev. Lett. 110, 200406 (2013)Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Problem of validityCalculation Scheme

Problem of validity

Rotons are confined at high density regions

Large disturbance of density profile due to rotons

At which point is the GPE approach not valid anymore?

-10 -5 5 10x

0.2

0.4

0.6

0.8

1.0

nHxL

N0 � ND but not n0(r)� nD(r) for all r

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Problem of validityCalculation Scheme

Calculation Scheme

Solve Bogoliubov-de-Gennes Equations for full 3-dimensionalsystem

−ı~ψ =

[−~2∇2

2m+ V (x) + g |ψ0|2 +

∫d3r ′U(r − r′)|ψ0(r′)|2

]ψ0[

−~2∇2

2m+ V (x) + 2g |ψ0(r)|2 +

∫d3r ′U(r − r′)|ψ0(r′])|2 − µ

]u

+gψ20v + ψ0

∫d3r ′U(r − r′)

[ψ0(r′)v(r′) + ψ∗0(r′)u(r′)

]= ~ωu[

~2∇2

2m− V (x)− 2g |ψ0(r)|2 −

∫d3r ′U(r − r′)|ψ0(r′])|2 + µ

]v

−g(ψ∗0)2u − ψ∗0∫

d3r ′U(r − r′)[ψ0(r′)v(r′) + ψ∗0(r′)u(r′)

]= ~ωv

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Problem of validityCalculation Scheme

The Bogoliubov-de-Gennes Equations

BdG are linear set of equations

M(r)ui (r) = Eiui (r)

Number of matrix elements scales as N2 for every direction

Change to harmonic oscillator basis(φi )

Mij =

∫dxφiMφj

Calculate condensate depletion nD

nD(r) = 〈np〉(u(r)2 + v(r)2

)+ v(r)2

investigate quantum and thermal depletion, local form ofthermal cloud, effects on superfluidity etc.

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Summary

Feshbach resonances in Erbium at small magnetic fields →very good control of contact interaction

Direct evaporative cooling in Erbium due to large magneticinteractions

Roton like excitation spectrum in dipolar systems withpancake geometries

Rotons are confined to large density regions and cause largedensity disturbances

We will investigate validity and consequences of rotons

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases

Experiments and General PropertiesWhat is a Roton?

Our WorkSummary

Thanks for your attention!

Falk Wachtler Dipolar Interactions and Rotons in Atomic Quantum Gases