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

Quantum droplets of a dysprosium BEC Igor Ferrier-Barbut Holger Kadau, Matthias Schmitt, Matthias Wenzel, Tilman Pfau 5. Physikalisches Institut,Stuttgart University SFB/TRR 21 1 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? 2 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? Beyond mean-field energy of the weakly-interacting Bose gas V = g n 2 128 E n a 3 + · · · ) √ 2 (1 + 15 √ π mean-field LHY, quantum fluctuations Phys. Rev 106 , 1135 (1957) 2 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? Beyond mean-field energy of the weakly-interacting Bose gas V = g n 2 128 E n a 3 + · · · ) √ 2 (1 + 15 √ π mean-field LHY, quantum fluctuations Phys. Rev 106 , 1135 (1957) 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). 2 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? Beyond mean-field energy of the weakly-interacting Bose gas V = g n 2 128 E n a 3 + · · · ) √ 2 (1 + 15 √ π mean-field LHY, quantum fluctuations Phys. Rev 106 , 1135 (1957) 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). Toy model: E V = e = α n 2 + β n 5 / 2 2 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? Beyond mean-field energy of the weakly-interacting Bose gas V = g n 2 128 E n a 3 + · · · ) √ 2 (1 + 15 √ π mean-field LHY, quantum fluctuations Phys. Rev 106 , 1135 (1957) 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). Gas - liquid transition! Toy model: 100 1 ∂ n κ T = 10 E V = e = α n 2 + β n 5 / 2 n 2 ∂μ 1 liquid κ T ( a.u ) 0.100 0.010 gas 0.001 10 - 4 - 10 - 5 0 5 10 α / β 2 Bad Honnef 05/2016

Can one form a liquid of dilute ultracold bosons? Beyond mean-field energy of the weakly-interacting Bose gas V = g n 2 128 E n a 3 + · · · ) √ 2 (1 + 15 √ π mean-field LHY, quantum fluctuations Phys. Rev 106 , 1135 (1957) 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). Gas - liquid transition! Toy model: 100 1 ∂ n κ T = 10 E V = e = α n 2 + β n 5 / 2 n 2 ∂μ 1 liquid κ T ( a.u ) 0.100 0.010 ◆ 2 ✓ α gas 0.001 n 0 ∝ β 10 - 4 - 10 - 5 0 5 10 α / β 2 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 3 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates V c ( r ) = 4 π ~ 2 a Contact interaction δ ( r ) m 3 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates V c ( r ) = 4 π ~ 2 a Contact interaction δ ( r ) m V dd ( r ) = µ 0 µ 2 1 − 3 cos 2 θ Dipole-dipole interaction 4 π r 3 θ ~ µ ~ r µ 3 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates V c ( r ) = 4 π ~ 2 a Contact interaction δ ( r ) m V dd ( r ) = µ 0 µ 2 1 − 3 cos 2 θ Dipole-dipole interaction 4 π r 3 θ ~ µ ~ r Characteristic length scales: µ Scattering length a a dd = m µ 0 µ 2 Dipolar length 12 π ~ 2 3 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates V c ( r ) = 4 π ~ 2 a Contact interaction δ ( r ) m V dd ( r ) = µ 0 µ 2 1 − 3 cos 2 θ Dipole-dipole interaction 4 π r 3 θ ~ µ ~ r Characteristic length scales: µ Scattering length a a dd = m µ 0 µ 2 Dipolar length 12 π ~ 2 Relative dipolar strength: ε dd = a dd a 3 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates r ) 2 r ) = g n ( ~ + n ( ~ r ) Z Mean-field e ( ~ r 0 − ~ r 0 ) r V dd ( ~ r ) n ( ~ d ~ 2 2 ~ B 2 R z 2 R r κ = R r R z 4 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates r ) 2 r ) = g n ( ~ + n ( ~ r ) Z Mean-field r 0 − ~ r 0 ) e ( ~ r V dd ( ~ r ) n ( ~ d ~ 2 2 e mf (0) = g n 2 0 2 (1 − ε dd f ( κ )) ~ B 2 R z 2 R r κ = R r R z 4 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates r ) 2 r ) = g n ( ~ + n ( ~ r ) Z Mean-field r 0 − ~ r 0 ) e ( ~ r V dd ( ~ r ) n ( ~ d ~ 2 2 e mf (0) = g n 2 0 2 (1 − ε dd f ( κ )) ~ B 2 R z 1.0 0.5 0.0 2 R r f ( κ ) - 0.5 κ = R r - 1.0 R z - 1.5 - 2.0 0.01 0.10 1 10 100 κ 4 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · e (0) = g n 2 ✓ ◆ 15 √ π (1 + 3 128 √ a 3 √ n 0 0 2 ε 2 1 − ε dd f ( κ ) + dd ) 2 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · e (0) = g n 2 ✓ ◆ 15 √ π (1 + 3 128 √ a 3 √ n 0 0 2 ε 2 1 − ε dd f ( κ ) + dd ) 2 β α 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · e (0) = g n 2 ✓ ◆ 15 √ π (1 + 3 128 √ a 3 √ n 0 0 2 ε 2 1 − ε dd f ( κ ) + dd ) 2 β α for α / β < 0 κ ⌧ 1 , ε dd > 1 Liquid-like state possible! 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · e (0) = g n 2 ✓ ◆ 15 √ π (1 + 3 128 √ a 3 √ n 0 0 2 ε 2 1 − ε dd f ( κ ) + dd ) 2 β α for α / β < 0 κ ⌧ 1 , ε dd > 1 ◆ 2 ✓ α Liquid-like state possible! n 0 ∝ β 5 Bad Honnef 05/2016

Dipolar Bose-Einstein condensates 128 na 3 Q 5 ( ε dd ) √ Beyond mean-field ∆ e = 15 √ π LHY Dipolar enhancement Lima & Pelster , PRA 84 , 041604 (2011), ibid 85 , 063609 (2012) Q 5 ( ε dd ) = 1 + 3 2 ε 2 dd + · · · e (0) = g n 2 ✓ ◆ 15 √ π (1 + 3 128 √ a 3 √ n 0 0 2 ε 2 1 − ε dd f ( κ ) + dd ) 2 β α for α / β < 0 κ ⌧ 1 , ε dd > 1 ◆ 2 ✓ α Liquid-like state possible! n 0 ∝ β See poster by R. Bisset and arXiv:1601.04501 (2016) by F . Wächtler and L. Santos 5 Bad Honnef 05/2016

Dysprosium Bose-Einstein condensates Dysprosium ( 164 Dy) µ = 9 . 93 µ B 6 Bad Honnef 05/2016

Dysprosium Bose-Einstein condensates Dysprosium ( 164 Dy) µ = 9 . 93 µ B a dd = m µ 0 µ 2 Dipolar length 12 π ~ 2 = 132 a 0 Scattering length a a bg = 92(8) a 0 Tang et al. , PRA 92 , 022703 (2015) Maier et al. , PRA 92 , 060702(R) (2015) 6 Bad Honnef 05/2016

Dysprosium Bose-Einstein condensates Dysprosium ( 164 Dy) µ = 9 . 93 µ B a dd = m µ 0 µ 2 Dipolar length 12 π ~ 2 = 132 a 0 Scattering length a a bg = 92(8) a 0 Tang et al. , PRA 92 , 022703 (2015) Maier et al. , PRA 92 , 060702(R) (2015) ε dd = a dd at ε dd = 1 . 42 a bg a 6 Bad Honnef 05/2016

Dysprosium Bose-Einstein condensates Dysprosium ( 164 Dy) µ = 9 . 93 µ B a dd = m µ 0 µ 2 Dipolar length 12 π ~ 2 = 132 a 0 Scattering length a a bg = 92(8) a 0 Tang et al. , PRA 92 , 022703 (2015) Maier et al. , PRA 92 , 060702(R) (2015) ε dd = a dd at ε dd = 1 . 42 a bg a Many Feshbach resonances 10 0 N ( a.u. ) 10 - 1 10 - 2 0 2 4 6 8 10 B ( G ) 6 Bad Honnef 05/2016

Our experiment High resolution phase-contrast imaging, 1 µm resolution at 421 nm (32.5 MHz broad), single shot 7 Bad Honnef 05/2016

Oblate dipolar BECs Trap aspect ratio λ = ω z / ω r = 2 . 9(1) κ > 1 8 Bad Honnef 05/2016

Oblate dipolar BECs Trap aspect ratio λ = ω z / ω r = 2 . 9(1) κ > 1 L. Santos et al. , PRL 90 , 250403 (2003) • Uniform case ( ): κ → ∞ Roton-Maxon dispersion relation Varies with axial trapping and short-range interactions Softening → “roton instability” 8 Bad Honnef 05/2016

Rosensweig / normal field instability of classical ferrofluids Rosensweig, R. Ferrohydrodynamics . Cambridge University Press (1985). 9 Bad Honnef 05/2016

Rosensweig / normal field instability of classical ferrofluids Incompressible, variable magnetization Competition between: Surface tension, gravity vs. dipole-dipole interaction Rosensweig, R. Ferrohydrodynamics . Cambridge University Press (1985). 9 Bad Honnef 05/2016