BOSE-EINSTEIN CONDENSATION OF MAGNONS IN SUPERFLUID 3 He-B and its - PowerPoint PPT Presentation

BOSE-EINSTEIN CONDENSATION OF MAGNONS IN SUPERFLUID 3 He-B and its applications to vortex studies V.B. Eltsov, S. Autti, Yu.M. Bunkov, P.J. Heikkinen, J.J. Hosio, M. Krusius, M. Silaev, G.E. Volovik, V.V. Zavjalov Low Temperature Laboratory Aalto University

OVERVIEW 1. Superfluid 3 He-B and traps for magnon quasiparticles. 2. Filling the ground and excited levels in the trap with magnons and spec- troscopy of the trap levels. 3. Coherent precession of the ground- and excited-level condensates. 4. Interaction of the magnon condensates with the trapping potential (self- trapping). 5. Measurements of relaxation of magnon condensates in rotating 3 He-B filled with vortex lines: A tool to observe vortex-core bound fermions.

3 SUPERFLUID He 40 Fermi system, which goes superfluid through Solid 3 Superfluids He-A Cooper pairing with S = 1 and L = 1. Pressure, bar 30 20 3 He-B 10 Normal fluid 0 0 1.0 2.0 3.0 Temperature, mK

3 SUPERFLUID He 40 Fermi system, which goes superfluid through Solid 3 Superfluids He-A Cooper pairing with S = 1 and L = 1. Pressure, bar 30 Spin-orbit interaction: 20 3 He-B Orbital momentum ⇔ spin precession 10 ∂ S H ∂ t = γ S × H + R D Normal fluid 0 0 1.0 2.0 3.0 dipole torque S Temperature, mK

3 SUPERFLUID He 40 Fermi system, which goes superfluid through Solid 3 Superfluids He-A Cooper pairing with S = 1 and L = 1. Pressure, bar 30 Spin-orbit interaction: 20 3 He-B Orbital momentum ⇔ spin precession 10 ∂ S H ∂ t = γ S × H + R D Normal fluid 0 0 1.0 2.0 3.0 dipole torque S Temperature, mK In 3 He-B in magnetic field net L and S = (χ/γ ) H appear. Connection L ⇔ S is given by the order parameter ⇒ gradient energy ⇒ equilibrium texture and waves. H Texture of ˆ l = L / L in a cylindrical sample results from competition of L � H and L ⊥ wall

3 TRAPPED MAGNON CONDENSATES IN He-B S ⊥ = S sin β M e iωt + iα Spin waves: H hk 2 / 2 m M ω ≈ ω L + ¯ S S = χH/γ , ω L = γ H , m M ∼ 10 − 4 m He β M N m = S − ˆ S z N m ∝ 1 − cos β M = 2 sin 2 β M ˆ −¯ h : Magnons with spin , 2 h ¯

3 TRAPPED MAGNON CONDENSATES IN He-B S ⊥ = S sin β M e iωt + iα Spin waves: H hk 2 / 2 m M ω ≈ ω L + ¯ S S = χH/γ , ω L = γ H , m M ∼ 10 − 4 m He β M N m = S − ˆ S z N m ∝ 1 − cos β M = 2 sin 2 β M ˆ −¯ h : Magnons with spin , 2 h ¯ Magnon condensate in 3 He-B: coherently precessing magnetization �( r ) ∝ sin β M ( r ) z e iωt + iα( r ) 2 H N 1 / 2 ∝ M ⊥ m M β l ω ≡ chemical potential H β M α ≡ phase of wave function Review: Bunkov and Volovik, arXiv:1003.4889

3 TRAPPED MAGNON CONDENSATES IN He-B S ⊥ = S sin β M e iωt + iα Spin waves: H hk 2 / 2 m M ω ≈ ω L + ¯ S S = χH/γ , ω L = γ H , m M ∼ 10 − 4 m He β M N m = S − ˆ S z N m ∝ 1 − cos β M = 2 sin 2 β M ˆ −¯ h : Magnons with spin , 2 h ¯ Magnon condensate in 3 He-B: coherently precessing magnetization �( r ) ∝ sin β M ( r ) z e iωt + iα( r ) 2 H N 1 / 2 ∝ M ⊥ m M β l ω ≡ chemical potential H β M α ≡ phase of wave function Axial trap F Z = (ω − ω L ) | � | 2 Review: Bunkov and Volovik, arXiv:1003.4889

3 TRAPPED MAGNON CONDENSATES IN He-B S ⊥ = S sin β M e iωt + iα Spin waves: H hk 2 / 2 m M ω ≈ ω L + ¯ S S = χH/γ , ω L = γ H , m M ∼ 10 − 4 m He β M N m = S − ˆ S z N m ∝ 1 − cos β M = 2 sin 2 β M ˆ −¯ h : Magnons with spin , 2 h ¯ Magnon condensate in 3 He-B: coherently precessing magnetization �( r ) ∝ sin β M ( r ) z e iωt + iα( r ) 2 H N 1 / 2 ∝ M ⊥ m M β l ω ≡ chemical potential H β M α ≡ phase of wave function ˆ l texture: radial trap Axial trap F so ∝ sin 2 β l 2 | � | 2 F Z = (ω − ω L ) | � | 2 Review: Bunkov and Volovik, arXiv:1003.4889

"PERSISTENT" PRECESSION AT LOW TEMPERATURES Discovered in Lancaster in pulsed NMR experiments at T < 0 . 2 T c • Relaxation times up to ∼ 10 3 s. NMR pick-up, arb. un. PRL 69 , 3092 (1992) spin precession at 1 MHz • Precession frequency increases during relaxation. • Off-resonance excitation (even with noise) at higher frequencies. time, s tipping pulse (creating magnons)

"PERSISTENT" PRECESSION AT LOW TEMPERATURES Discovered in Lancaster in pulsed NMR experiments at T < 0 . 2 T c • Relaxation times up to ∼ 10 3 s. NMR pick-up, arb. un. PRL 69 , 3092 (1992) spin precession at 1 MHz • Precession frequency increases during relaxation. • Off-resonance excitation (even with noise) at higher frequencies. time, s tipping pulse (creating magnons) These features (and more) find explanations in the picture of the magnon BEC in the magneto-textural trap. (Bunkov and Volovik, PRL 98 , 265302 (2007))

SELF-TRAPPING OF THE MAGNON BEC H β l β M M 40 β M , degrees 30 20 10 0 F so ∝ sin 2 (β M / 2 ) sin 2 (β l / 2 ) 80 β l , degrees 60 40 P = 29 bar 20 T = 0 . 24 T c 0 0 1 2 3 r , mm

SELF-TRAPPING OF THE MAGNON BEC Texture is flexible, when β M increases H β l tends to decrease: Magnon con- β l β M M densate forms a "bubble" with ˆ l � H . 40 β M , degrees 30 20 10 0 F so ∝ sin 2 (β M / 2 ) sin 2 (β l / 2 ) 80 β l , degrees 60 40 P = 29 bar 20 T = 0 . 24 T c 0 0 1 2 3 r , mm

SELF-TRAPPING OF THE MAGNON BEC Texture is flexible, when β M increases H β l tends to decrease: Magnon con- β l β M M densate forms a "bubble" with ˆ l � H . 40 β M , degrees fit to the wave • Harmonic trap transforms to a 30 function in a box box with impenetrable walls. 20 First example of BEC in a box. 10 • Texture-mediated interaction re- 0 F so ∝ sin 2 (β M / 2 ) sin 2 (β l / 2 ) sults in d µ/ dN m < 0. 80 β l , degrees 60 • Analog of the electron bubble in 40 helium and of the MIT bag model P = 29 bar 20 of hadrons. T = 0 . 24 T c 0 0 1 2 3 r , mm PRL 108 , 145303 (2012)

FILLING TRAP WITH MAGNONS AT THE GROUND LEVEL CW NMR: downward frequency (upward field) sweep. Number of magnons N m ∝ M 2 ⊥ d µ/ dN m < 0 Chemical potential µ ∝ f − f L 5 P = 29 bar, T = 0 . 24 T c � = 0 . 8 rad/s (vortex-free) 4 3 / M max f L = 0 . 865 MHz 60 � H / H = 8 . 3 · 10 − 4 3 Excitation ( µ V) 50 M ⊥ · 10 ⇒ ⇒ 2 40 30 1 20 ⇒ ⇔ ⇔ 0 50 100 150 200 250 f − f L , Hz

COHERENT PRECESSION OF THE MAGNON CONDENSATE Condensation is demonstrated by long decay times of free precession. 70 3 60 cw NMR 50 M ⊥ , arb. un. 2 Time, s 40 30 1 20 10 0 100 150 200 f − f , Hz L 0 170 180 190 200 210 f − f , Hz P = 0 . 5 bar, T = 0 . 14 T c L

COHERENT PRECESSION OF THE MAGNON CONDENSATE Condensation is demonstrated by long decay times of free precession. 70 3 60 cw NMR 50 M ⊥ , arb. un. 2 Time, s 40 30 1 20 free precession 10 0 100 150 200 f − f , Hz L 0 170 180 190 200 210 f − f , Hz P = 0 . 5 bar, T = 0 . 14 T c L

SCALING IN THE CYLINDRICAL BOX h 2 λ 2 E(R b ) = N m ¯ m Similar to electron bubble: + 2 πR b σ(R b ) → min 2 m M R 2 b β M β l surface energy ≡ kinetic energy of magnons orbital gradient m M - magnon mass β 0 energy: - root of the Bessel λ m � 2 � β 0 function 2 πR b ξ H ξ H ξ H r b ⇒ R b ∝ N 1 / 5 σ ∝ β 2 0 ∝ R 2 Scaling: m R b R b , mm 1 simulation ∝ N 1 / 5 m 0.5 14 N m 12 13 10 10 10

SCALING IN THE CYLINDRICAL BOX h 2 λ 2 E(R b ) = N m ¯ m Similar to electron bubble: + 2 πR b σ(R b ) → min 2 m M R 2 b β M β l surface energy ≡ kinetic energy of magnons orbital gradient m M - magnon mass β 0 energy: - root of the Bessel λ m � 2 � β 0 function 2 πR b ξ H ξ H ξ H r b ⇒ R b ∝ N 1 / 5 σ ∝ β 2 0 ∝ R 2 Scaling: m R b ∝ � f 10 For the magnetization: -7/4 simulation 3 / M max f − f L ∝ R − 2 b � � 1 M ⊥ · 10 M ⊥ ∝ sin β M dV , N m ∝ ( 1 − cos β M )dV ⇒ M ⊥ ∝ N 1 / 2 m R b ∝ R 7 / 2 ∝ (f − f L ) − 7 / 4 b experiment 0.1 50 100 200 f − f L , Hz

PROBING EXCITED MAGNON LEVELS Since d µ/ dN m < 0, in cw NMR sweep excited levels in the trap are encoun- tered first and macroscopic population of an excited level can be built. In the harmonic trap (small N m ): 2 π( f − f L ) = ω r ( m + 1 ) + ω z ( n + 1 / 2 ) � = 0 . 6 rad/s ω r / 2 π = 168 Hz 0.8 � H / H = 0 . 8 · 10 − 3 ω z / 2 π = 22 Hz M ⊥ · 10 3 / M max 0.6 P = 29 bar, T = 0 . 25 T c 0.4 f L = 0 . 865 MHz 0.2 0 (m,n) ⇒ (0,0) ... (0,10) (2,0) ... (2,10) (4,0) ... (4,8) (6,0) ... (6,8) 0.2 0.4 0.6 0.8 1 1.2 1.4 f − f L , kHz

PROBING EXCITED MAGNON LEVELS Since d µ/ dN m < 0, in cw NMR sweep excited levels in the trap are encoun- tered first and macroscopic population of an excited level can be built. In the harmonic trap (small N m ): 2 π( f − f L ) = ω r ( m + 1 ) + ω z ( n + 1 / 2 ) � = 0 . 6 → 0 . 8 rad/s ω r / 2 π = 168 → 253 Hz 0.8 � H / H = 0 . 8 · 10 − 3 ω z / 2 π = 22 Hz M ⊥ · 10 3 / M max 0.6 0.4 0.2 0 (m,n) ⇒ (0,0) ... (0,12) (2,0) ... (2,10) (4,0) ... (4,8) 0.2 0.4 0.6 0.8 1 1.2 1.4 f − f L , kHz