Dipolar Interactions and Rotons in Atomic Quantum Gases. Falk Wächtler. Workshop of the RTG March 13., 2014

Transcription

1 Dipolar Interactions and Rotons in Ultracold Atomic Quantum Gases Workshop of the RTG 1729 Lüneburg March 13., 2014

2 Table of contents Realization of dipolar Systems Erbium 1 Realization of dipolar Systems Erbium 2 Excitation spectrum Excitation Spectra Roton Confinement 3 Problem of validity Calculation Scheme 4

3 Dipole-Dipole Interactions Realization of dipolar Systems Erbium Dipolar Interactions in magnetic and electric systems long ranged and anisotropic U = C dd 4π 1 3 cos 2 θ r 3 magnetic: C B dd = µ 0m 2 permanent magnetic dipoles in atoms electric: C E dd = 4πd 2 polar molecules, Rydberg atoms, and light-induced dipoles in atoms

4 Magnetic Systems Realization of dipolar Systems Erbium Realized samples Boson: 52 Cr A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, and T. Pfau, PRL 94, (2005) Fermion: 53 Cr R. Chicireanu, A. Pouderous, R. Barbé, B. Laburthe-Tolra, E. Maréchal, L. Vernac, J.-C. Keller, and O. Gorceix, PRA 73, (2006) Boson: 87 Rb M. Vengalattore, S. R. Leslie, J. Guzman, and D. M. Stamper-Kurn, PRL 100, (2008) Boson: 164 Dy M. Lu, N. Burdick, S. Youn, and B. Lev, PRL 107, (2011) Boson: 168 Er K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, PRL 108, (2012) Fermion: 167 Er Aikawa et al., arxiv: (2013)

5 Erbium: Collisional properties Realization of dipolar Systems Erbium producing BEC and degenerate Fermi gases of Erbium complicated collisional properties lot of Feshbach resonances lot of Feshbach resonances within small B-range better control of contact strength

6 Cooling of Fermions Realization of dipolar Systems Erbium No s-wave collisions in spin-polarized Fermi gases Without dipole-dipole interaction no direct evaporative cooling Strong dipole-dipole interactions lead to thermalization through 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: (2013)

7 Stability Realization of dipolar Systems Erbium Dipole-dipole interaction is partially attractive stability depends on contact interaction and geometry T.Lahaye et al., Rep. Prog. Phys. 72, (2009)

8 Excitation spectrum Excitation Spectra Roton Confinement

9 Excitation spectrum Excitation Spectra Roton 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 + d 3 r U(r r ) ψ(r, t) 2 ψ Bogoliubov approximation ψ(r, t) = ψ 0 (r, t) + δψ(r, t) linear transformation δψ(r, t) = u(r)e ı (µ+ ω)t + v (r)e ı ( µ+ ω)t

10 Excitation spectrum Excitation Spectra Roton Confinement Calculation of the Excitation spectrum [ 2 2 ] 2m + V (x) + 2g ψ 0(r) 2 + d 3 r U(r r ) ψ 0 (r ]) 2 µ u +gψ0v 2 + ψ 0 d 3 r U(r r ) [ ψ 0 (r )v(r ) + ψ0(r )u(r ) ] = ωu [ 2 2 ] 2m V (x) 2g ψ 0(r) 2 d 3 r U(r r ) ψ 0 (r ]) 2 + µ v g(ψ0) 2 u ψ0 d 3 r U(r r ) [ ψ 0 (r )v(r ) + ψ0(r )u(r ) ] = ωv homogeneous solution ω = ± 2 k 2 ( 2 k 2 ) 2m 2m + 2gn 0 + 2Û(k)n 0

11 Excitation spectrum Excitation Spectra Roton Confinement Excitation Spectrum for 2D homogeneous system M. Jona-Lasinio, K. Lakomy, and L. Santos, Phys. Rev. A 88, (2013). linear dependence for small momenta quadratic behavior for large momenta roton like excitation spectrum for pankace traps if k 1 L two dimensional excitations particles repel each other excitations are phonons for k 1 L excitations aquire 3D character interparticle repulsion is reduced

12 Excitation spectrum Excitation Spectra Roton Confinement Inhomogeneous System and Fingers R. Bisset, D. Baillie, and P. Blakie, Phys. Rev. A 88, (2013). Cylinder-symmetric system z-projection of angular momentum is good quantum number Emerging roton fingers

13 Roton Confinement Excitation spectrum Excitation Spectra Roton Confinement depth of roton minimum is interaction dependent interaction is density dependent n x, y x y E n,m = ɛ An + Bm2 M. Jona-Lasinio, K. Lakomy, and L. Santos, Phys. Rev. A 88, (2013)

14 Excitation spectrum Excitation Spectra Roton Confinement What is the difference between a Roton and a Phonon? Phonon mode extends over condensate size Roton mode is localized around center R. Bisset, D. Baillie, and P. Blakie, Phys. Rev. A 88, (2013). Condensateexcitation interaction attractive at short wavelengths

15 Detection of Rotons Excitation spectrum Excitation Spectra Roton Confinement no observation yet analyzing the structure factor of trapped dipolar gas stability spectroscopy atom number fluctuations can reveal presence and locality of rotons problem locality can be solved by using box potential A. Gaunt et al., Phys. Rev. Lett. 110, (2013)

16 Problem of validity Problem of validity Calculation Scheme 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? 1.0 n x x N 0 N D but not n 0 (r) n D (r) for all r

17 Calculation Scheme Problem of validity Calculation Scheme Solve Bogoliubov-de-Gennes Equations for full 3-dimensional system ı ψ = [ 2 2 ] 2m + V (x) + g ψ d 3 r U(r r ) ψ 0 (r ) 2 ψ 0 [ 2 2 ] 2m + V (x) + 2g ψ 0(r) 2 + d 3 r U(r r ) ψ 0 (r ]) 2 µ u +gψ0v 2 + ψ 0 d 3 r U(r r ) [ ψ 0 (r )v(r ) + ψ0(r )u(r ) ] = ωu [ 2 2 ] 2m V (x) 2g ψ 0(r) 2 d 3 r U(r r ) ψ 0 (r ]) 2 + µ v g(ψ0) 2 u ψ0 d 3 r U(r r ) [ ψ 0 (r )v(r ) + ψ0(r )u(r ) ] = ωv

18 Problem of validity Calculation Scheme The Bogoliubov-de-Gennes Equations BdG are linear set of equations M(r)u i (r) = E i u i (r) Number of matrix elements scales as N 2 for every direction Change to harmonic oscillator basis(φ i ) M ij = dxφ i Mφ j Calculate condensate depletion n D n D (r) = n p ( u(r) 2 + v(r) 2) + v(r) 2 investigate quantum and thermal depletion, local form of thermal cloud, effects on superfluidity etc.

19 Feshbach resonances in Erbium at small magnetic fields very good control of contact interaction Direct evaporative cooling in Erbium due to large magnetic interactions Roton like excitation spectrum in dipolar systems with pancake geometries Rotons are confined to large density regions and cause large density disturbances We will investigate validity and consequences of rotons

20 Thanks for your attention!