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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